## 6.2. 2017 Tether's Introduction

We now consider a smaller period of training to predict the Bitcoin prices to introduce inside the set of variables the stable coin Tether (1 USDT = 1 US$). Indeed, this cryptocurrency is valuable on derivatives exchanges such as Bitrex and Bitfinex, when the investors exchange their cryptocurrency into fiat currency.

In a seminal paper on BitMEX bitcoin derivatives (off-shore, unregulated) exchanges, Alexander et al. [117] recalls the speculative role played by Tether in the trading community as a means of exchanging 1 US$ against 1 USD Tether (USDT, supposedly backed one-to-one in BitMEX). Chief concerns among market players is the possibility of "front-running" by printing large amounts of USD into Bitcoin to provoke a price jump, and then once the market is shocked, revert back the transaction from Bitcoin to USD to effectively cash in your benefit. This illegal procedure through Tether is documented by Griffin and Shams [118]. Besides, Tether is supposed to maintain a 1-to-1 ratio to be pegged against the USD. Bitfinex is accused of unlawfully covering up the true levels of its currency reserves. The exchange, owner of Tether, was prosecuted in the USA. On 23 February 2021, the New York attorney general's office settled a nearly two-year investigation into the finances and corporate practices of the companies that operate the Bitfinex cryptocurrency exchange and the stablecoin Tether The Hong Kong-based iFinex Inc., which operates the Bitfinex exchange, and Tether Ltd. agreed to pay $18.5 million to the attorney general's office. See the Wall Street Journal (2021) at https://www.wsj.com/articles/cryptocurrency-firms-bitfinex-tether-settle-new-york-attorney-generals-probe-11614093709, accessed on 23 February 2021).

Tether has begun to be exchanged on 12 April 2017. Thus, we constitute a subsample from 12 April 2017 to 31 December 2020. Compared to full-sample results, this subperiod allows us to increase the set of cryptocurrencies, introducing the cryptocurrencies Dash and Stellar. Then, we perform the same analysis as in Section 5 using the machine learning models on 12 April 2017–30 November 2018 as a training period and until the end of December 2020 to test the models’ accuracy. As before, we introduce the input variables step by step : (1) the Bitcoin (spot and futures), (2) nine available cryptocurrencies (i.e., Litecoin, Ethereum, Ethereum Classic, Ripple, Stellar, Tether, Monero, Dash, Zcash), (3) all the traditional financial assets, (4) all the commodities, (5) all the sets.

## Sub-Sample Results

Looking at Tables 6 and 7, we find that the best machine learning forecasting model is AdaBoost, followed by Random Forest, and K-nearest neighbors. The value of the errors looking at these three machine algorithms is very far from the errors we obtain with the other modelings. Looking at the errors when we compare the results using cryptocurrencies on the one hand, or adding stocks or commodities on the other side, for spot, we have a slight enhancement of the errors (when we add stocks or commodities). Looking at the MAPE statistic, Bitcoin is better explained by 'all' (0.31), followed by stocks (0.46), commodities (0.48), and finally cryptocurrencies (0.53).

Nevertheless, when we look at the futures price, the errors are higher for stocks and lower when adding commodities. The set of results is slightly different for futures: commodities return the lowest MAPE (0.34), followed by 'all' (0.41), cryptocurrencies (0.53), and finally stocks. The analysis shows a limited interest in adding commodities and financial assets to improve Bitcoin's forecasting power beyond that already captured by other cryptocurrencies.

If we compare with the results obtained in Table 3, for instance, MAPE = 0.11 to MAPE = 0.31 (Table 7), Tether does not improve the forecasting accuracy of the Bitcoin spot price. For the futures, we compare MAPE = 0.41 (Table 8) with 0.73 (Table 4): in that case, the conclusion is reverse. The question remains open whether this specific set of results is an artifact attributable to the stable coin Tether. Although Tether has a stable coin status, it is owned by the opaque (primarily unregulated) marketplace by BitMEX. It is not easy to assess the impact of that cryptocurrency on others. As Alexander et al. [117]
put it, regulators (need to) prioritize the investigation of the legitimacy of BitMEX and its contracts based on concerns of lack of transparency and potential market manipulation.

<table><caption>**Table 6.** Sub-sample with the Introduction of Tether (USDT): forecasting of the Coinbase Bitcoin Spot Price from 12 April, 2017, to 31 December, 2020.</caption><thead><tr><th></th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><th colspan="8">CRYPTO → SPOT BTC</th></tr><tr><td>RMSE</td><td>3358.14</td><td>2582.10</td><td>296.02</td><td>2655.41</td><td>451.34</td><td>45.54</td><td>1529.02</td></tr><tr><td>MAE</td><td>2536.31</td><td>2025.75</td><td>157.97</td><td>2103.93</td><td>261.27</td><td>21.22</td><td>1130.54</td></tr><tr><td>MAPE</td><td>50.10</td><td>47.97</td><td>2.26</td><td>45.31</td><td>3.60</td><td>0.53</td><td>19.38</td></tr><tr><th colspan="8">STOCKS / BONDS / FX</th></tr><tr><td>RMSE</td><td>3358.14</td><td>2867.13</td><td>319.45</td><td>2225.41</td><td>774.69</td><td>49.49</td><td>1801.17</td></tr><tr><td>MAE</td><td>2536.31</td><td>2035.10</td><td>192.76</td><td>1633.83</td><td>481.59</td><td>20.01</td><td>1286.77</td></tr><tr><td>MAPE</td><td>50.10</td><td>42.21</td><td>2.91</td><td>26.09</td><td>6.99</td><td>0.48</td><td>21.47</td></tr><tr><th colspan="8">COMMO</th></tr><tr><td>RMSE</td><td>3358.14</td><td>2745.22</td><td>262.66</td><td>1734.43</td><td>1002.35</td><td>50.90</td><td>1339.07</td></tr><tr><td>MAE</td><td>2536.31</td><td>1928.04</td><td>148.56</td><td>1240.58</td><td>540.81</td><td>19.64</td><td>1011.37</td></tr><tr><td>MAPE</td><td>50.10</td><td>36.58</td><td>2.22</td><td>21.29</td><td>8.13</td><td>0.46</td><td>18.56</td></tr><tr><th colspan="8">ALL</th></tr><tr><td>RMSE</td><td>3358.14</td><td>1776.32</td><td>228.64</td><td>1674.18</td><td>641.75</td><td>31.83</td><td>770.54</td></tr><tr><td>MAE</td><td>2536.31</td><td>1284.93</td><td>132.58</td><td>1297.20</td><td>367.47</td><td>12.04</td><td>617.04</td></tr><tr><td>MAPE</td><td>50.10</td><td>23.04</td><td>1.85</td><td>24.04</td><td>5.41</td><td>0.31</td><td>12.36</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).

<table><caption>**Table 7.** Sub-sample with the Introduction of Tether (USDT): Forecasting of the CME Bitcoin Futures price.</caption><thead><tr><th></th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><th colspan="8">CRYPTO → FUT BTC</th></tr><tr><td>RMSE</td><td>3512.26</td><td>3008.13</td><td>472.54</td><td>3330.54</td><td>830.46</td><td>57.91</td><td>2022.13</td></tr><tr><td>MAE</td><td>2787.25</td><td>2533.75</td><td>207.79</td><td>2772.72</td><td>314.74</td><td>23.50</td><td>1567.53</td></tr><tr><td>MAPE</td><td>86.68</td><td>78.49</td><td>3.79</td><td>93.93</td><td>5.71</td><td>0.53</td><td>36.73</td></tr><tr><th colspan="8">STOCKS / BONDS / FX</th></tr><tr><td>RMSE</td><td>3512.26</td><td>3235.90</td><td>439.44</td><td>2959.64</td><td>976.71</td><td>59.26</td><td>2295.76</td></tr><tr><td>MAE</td><td>2787.25</td><td>2466.18</td><td>217.48</td><td>2041.73</td><td>527.01</td><td>26.70</td><td>1586.74</td></tr><tr><td>MAPE</td><td>86.68</td><td>74.46</td><td>4.79</td><td>55.09</td><td>10.32</td><td>0.70</td><td>34.53</td></tr><tr><th colspan="8">COMMO</th></tr><tr><td>RMSE</td><td>3512.26</td><td>2922.43</td><td>354.82</td><td>3121.00</td><td>1239.65</td><td>46.20</td><td>1613.32</td></tr><tr><td>MAE</td><td>2787.25</td><td>2018.50</td><td>169.06</td><td>2299.30</td><td>556.34</td><td>16.29</td><td>1140.27</td></tr><tr><td>MAPE</td><td>86.68</td><td>71.33</td><td>3.43</td><td>89.71</td><td>14.79</td><td>0.34</td><td>26.40</td></tr><tr><th colspan="8">ALL</th></tr><tr><td>RMSE</td><td>3512.26</td><td>2495.86</td><td>424.99</td><td>2382.42</td><td>762.66</td><td>54.96</td><td>1440.18</td></tr><tr><td>MAE</td><td>2787.25</td><td>1984.92</td><td>182.68</td><td>1785.06</td><td>349.76</td><td>21.40</td><td>960.85</td></tr><tr><td>MAPE</td><td>86.68</td><td>55.38</td><td>5.36</td><td>55.33</td><td>6.35</td><td>0.41</td><td>22.73</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).

## 6.3. 2016–18 Bitcoin’s Economic Cycle

The Bitcoin spot price was equal to 367 US$ in January 2016, skyrocketing to 19,891$ in December 2017, crashing to 3763$ in December 2018, for finally maintaining an apparent trend around 8000$ since 2019. This canonical decomposition into an economic cycle’s phases of expansion and recession leads us to gauge the sensitivity of our results during the subperiod 1 January 2016–31 December 2018.
put it, regulators (need to) prioritize the investigation of the legitimacy of BitMEX and its contracts based on concerns of lack of transparency and potential market manipulation.

<table><caption>**Table 6.** Sub-sample with the Introduction of Tether (USDT): forecasting of the Coinbase Bitcoin Spot Price from 12 April, 2017, to 31 December, 2020.</caption><thead><tr><th></th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td colspan="8"><strong>CRYPTO → SPOT BTC</strong></td></tr><tr><td>RMSE</td><td>3358.14</td><td>2582.10</td><td>296.02</td><td>2655.41</td><td>451.34</td><td>45.54</td><td>1529.02</td></tr><tr><td>MAE</td><td>2536.31</td><td>2025.75</td><td>157.97</td><td>2103.93</td><td>261.27</td><td>21.22</td><td>1130.54</td></tr><tr><td>MAPE</td><td>50.10</td><td>47.97</td><td>2.26</td><td>45.31</td><td>3.60</td><td>0.53</td><td>19.38</td></tr><tr><td colspan="8"><strong>STOCKS / BONDS / FX</strong></td></tr><tr><td>RMSE</td><td>3358.14</td><td>2867.13</td><td>319.45</td><td>2225.41</td><td>774.69</td><td>49.49</td><td>1801.17</td></tr><tr><td>MAE</td><td>2536.31</td><td>2035.10</td><td>192.76</td><td>1633.83</td><td>481.59</td><td>20.01</td><td>1286.77</td></tr><tr><td>MAPE</td><td>50.10</td><td>42.21</td><td>2.91</td><td>26.09</td><td>6.99</td><td>0.48</td><td>21.47</td></tr><tr><td colspan="8"><strong>COMMO</strong></td></tr><tr><td>RMSE</td><td>3358.14</td><td>2745.22</td><td>262.66</td><td>1734.43</td><td>1002.35</td><td>50.90</td><td>1339.07</td></tr><tr><td>MAE</td><td>2536.31</td><td>1928.04</td><td>148.56</td><td>1240.58</td><td>540.81</td><td>19.64</td><td>1011.37</td></tr><tr><td>MAPE</td><td>50.10</td><td>36.58</td><td>2.22</td><td>21.29</td><td>8.13</td><td>0.46</td><td>18.56</td></tr><tr><td colspan="8"><strong>ALL</strong></td></tr><tr><td>RMSE</td><td>3358.14</td><td>1776.32</td><td>228.64</td><td>1674.18</td><td>641.75</td><td>31.83</td><td>770.54</td></tr><tr><td>MAE</td><td>2536.31</td><td>1284.93</td><td>132.58</td><td>1297.20</td><td>367.47</td><td>12.04</td><td>617.04</td></tr><tr><td>MAPE</td><td>50.10</td><td>23.04</td><td>1.85</td><td>24.04</td><td>5.41</td><td>0.31</td><td>12.36</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).

<table><caption>**Table 7.** Sub-sample with the Introduction of Tether (USDT): Forecasting of the CME Bitcoin Futures price.</caption><thead><tr><th></th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td colspan="8"><strong>CRYPTO → FUT BTC</strong></td></tr><tr><td>RMSE</td><td>3512.26</td><td>3008.13</td><td>472.54</td><td>3330.54</td><td>830.46</td><td>57.91</td><td>2022.13</td></tr><tr><td>MAE</td><td>2787.25</td><td>2533.75</td><td>207.79</td><td>2772.72</td><td>314.74</td><td>23.50</td><td>1567.53</td></tr><tr><td>MAPE</td><td>86.68</td><td>78.49</td><td>3.79</td><td>93.93</td><td>5.71</td><td>0.53</td><td>36.73</td></tr><tr><td colspan="8"><strong>STOCKS / BONDS / FX</strong></td></tr><tr><td>RMSE</td><td>3512.26</td><td>3235.90</td><td>439.44</td><td>2959.64</td><td>976.71</td><td>59.26</td><td>2295.76</td></tr><tr><td>MAE</td><td>2787.25</td><td>2466.18</td><td>217.48</td><td>2041.73</td><td>527.01</td><td>26.70</td><td>1586.74</td></tr><tr><td>MAPE</td><td>86.68</td><td>74.46</td><td>4.79</td><td>55.09</td><td>10.32</td><td>0.70</td><td>34.53</td></tr><tr><td colspan="8"><strong>COMMO</strong></td></tr><tr><td>RMSE</td><td>3512.26</td><td>2922.43</td><td>354.82</td><td>3121.00</td><td>1239.65</td><td>46.20</td><td>1613.32</td></tr><tr><td>MAE</td><td>2787.25</td><td>2018.50</td><td>169.06</td><td>2299.30</td><td>556.34</td><td>16.29</td><td>1140.27</td></tr><tr><td>MAPE</td><td>86.68</td><td>71.33</td><td>3.43</td><td>89.71</td><td>14.79</td><td>0.34</td><td>26.40</td></tr><tr><td colspan="8"><strong>ALL</strong></td></tr><tr><td>RMSE</td><td>3512.26</td><td>2495.86</td><td>424.99</td><td>2382.42</td><td>762.66</td><td>54.96</td><td>1440.18</td></tr><tr><td>MAE</td><td>2787.25</td><td>1984.92</td><td>182.68</td><td>1785.06</td><td>349.76</td><td>21.40</td><td>960.85</td></tr><tr><td>MAPE</td><td>86.68</td><td>55.38</td><td>5.36</td><td>55.33</td><td>6.35</td><td>0.41</td><td>22.73</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).

## 6.3. 2016–18 Bitcoin’s Economic Cycle

The Bitcoin spot price was equal to 367 US$ in January 2016, skyrocketing to 19,891$ in December 2017, crashing to 3763$ in December 2018, for finally maintaining an apparent trend around 8000$ since 2019. This canonical decomposition into an economic cycle’s phases of expansion and recession leads us to gauge the sensitivity of our results during the subperiod 1 January 2016–31 December 2018.
Regarding the Tables 8 and 9, results are similar—from the algorithm's race—to the full-sample predictions done previously, as AdaBoost is still the winner of horse race among competing machine learning models in all cases (followed by Random forest and kNN algorithms). Using only the information from other cryptocurrencies returns, we obtain the lowest forecast errors, both for spot (MAPE = 0.82) and futures (MAPE = 0.98) Bitcoin. By looking at the Adaboost spot results, for instance, we cannot assimilate Bitcoin to either financial securities (MAPE = 1.42 > 0.82) or commodities (MAPE = 1.07 > 0.82) because forecast errors are increasing. We notice that the errors are nearly the same when we look at the results for the futures. In conclusion, forecast errors are higher than during the whole sample. It can be linked to the explosiveness behavior of the Bitcoin price in December 2017.

<table><caption>**Table 8.** Sub-sample forecasting results of Coinbase Bitcoin Spot price during the 2016–18 economic cycle.</caption><thead><tr><th>CRYPTO → SPOT BTC</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>3347.17</td><td>2247.75</td><td>198.81</td><td>2182.41</td><td>331.18</td><td>22.50</td><td>701.02</td></tr><tr><td>MAE</td><td>2525.98</td><td>1888.10</td><td>79.46</td><td>1586.54</td><td>136.24</td><td>9.38</td><td>474.80</td></tr><tr><td>MAPE</td><td>165.32</td><td>141.22</td><td>2.32</td><td>85.90</td><td>3.31</td><td>0.82</td><td>29.41</td></tr><tr><th>STOCKS / BONDS / FX</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>3347.17</td><td>2331.98</td><td>226.00</td><td>2161.75</td><td>556.07</td><td>31.85</td><td>1544.24</td></tr><tr><td>MAE</td><td>2525.98</td><td>1474.18</td><td>103.14</td><td>1515.32</td><td>252.90</td><td>14.69</td><td>1108.46</td></tr><tr><td>MAPE</td><td>165.32</td><td>79.01</td><td>3.53</td><td>107.53</td><td>5.83</td><td>1.42</td><td>75.59</td></tr><tr><th>COMMO</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>3347.17</td><td>2456.96</td><td>239.60</td><td>1996.15</td><td>744.25</td><td>29.21</td><td>1350.50</td></tr><tr><td>MAE</td><td>2525.98</td><td>1391.29</td><td>101.55</td><td>1417.36</td><td>304.57</td><td>12.55</td><td>1000.99</td></tr><tr><td>MAPE</td><td>165.32</td><td>77.35</td><td>3.47</td><td>122.91</td><td>8.60</td><td>1.07</td><td>77.55</td></tr><tr><th>ALL</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>3347.17</td><td>1592.95</td><td>185.40</td><td>2086.46</td><td>472.07</td><td>17.61</td><td>524.18</td></tr><tr><td>MAE</td><td>2525.98</td><td>1016.83</td><td>69.02</td><td>1567.12</td><td>207.21</td><td>7.78</td><td>360.27</td></tr><tr><td>MAPE</td><td>165.32</td><td>57.03</td><td>1.90</td><td>137.19</td><td>5.02</td><td>0.89</td><td>21.66</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).

<table><caption>**Table 9.** Sub-sample forecasting results of CME Bitcoin Futures price during the 2016–18 economic cycle.</caption><thead><tr><th>CRYPTO → FUT BTC</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>4363.09</td><td>3614.50</td><td>631.89</td><td>3802.03</td><td>1255.64</td><td>116.83</td><td>2006.04</td></tr><tr><td>MAE</td><td>3239.82</td><td>2960.70</td><td>298.57</td><td>3329.58</td><td>528.87</td><td>52.08</td><td>1408.66</td></tr><tr><td>MAPE</td><td>121.15</td><td>101.87</td><td>8.03</td><td>121.45</td><td>12.20</td><td>0.98</td><td>39.79</td></tr><tr><th>STOCKS / BONDS / FX</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>4363.09</td><td>3900.97</td><td>711.14</td><td>3518.95</td><td>1208.71</td><td>98.46</td><td>3284.64</td></tr><tr><td>MAE</td><td>3239.82</td><td>2781.09</td><td>319.38</td><td>2384.01</td><td>550.15</td><td>45.42</td><td>2252.96</td></tr><tr><td>MAPE</td><td>121.15</td><td>81.72</td><td>6.93</td><td>53.42</td><td>10.85</td><td>1.05</td><td>49.91</td></tr><tr><th>COMMO</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>4363.09</td><td>3749.76</td><td>650.19</td><td>3523.16</td><td>1763.10</td><td>89.78</td><td>2379.86</td></tr><tr><td>MAE</td><td>3239.82</td><td>2713.36</td><td>294.69</td><td>2806.55</td><td>855.68</td><td>38.94</td><td>1577.59</td></tr><tr><td>MAPE</td><td>121.15</td><td>72.63</td><td>6.43</td><td>106.25</td><td>21.38</td><td>0.98</td><td>43.29</td></tr><tr><th>ALL</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>4363.09</td><td>2864.04</td><td>564.27</td><td>2954.87</td><td>1027.13</td><td>96.35</td><td>1612.76</td></tr><tr><td>MAE</td><td>3239.82</td><td>1911.06</td><td>188.29</td><td>2309.58</td><td>439.60</td><td>44.54</td><td>1123.03</td></tr><tr><td>MAPE</td><td>121.15</td><td>46.05</td><td>3.30</td><td>77.10</td><td>8.25</td><td>1.02</td><td>31.65</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).
Regarding the Tables 8 and 9, results are similar—from the algorithm's race—to the full-sample predictions done previously, as AdaBoost is still the winner of horse race among competing machine learning models in all cases (followed by Random forest and kNN algorithms). Using only the information from other cryptocurrencies returns, we obtain the lowest forecast errors, both for spot (MAPE = 0.82) and futures (MAPE = 0.98) Bitcoin. By looking at the Adaboost spot results, for instance, we cannot assimilate Bitcoin to either financial securities (MAPE = 1.42 > 0.82) or commodities (MAPE = 1.07 > 0.82) because forecast errors are increasing. We notice that the errors are nearly the same when we look at the results for the futures. In conclusion, forecast errors are higher than during the whole sample. It can be linked to the explosiveness behavior of the Bitcoin price in December 2017.

<table><caption>**Table 8.** Sub-sample forecasting results of Coinbase Bitcoin Spot price during the 2016–18 economic cycle.</caption><thead><tr><th>CRYPTO → SPOT BTC</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>3347.17</td><td>2247.75</td><td>198.81</td><td>2182.41</td><td>331.18</td><td>22.50</td><td>701.02</td></tr><tr><td>MAE</td><td>2525.98</td><td>1888.10</td><td>79.46</td><td>1586.54</td><td>136.24</td><td>9.38</td><td>474.80</td></tr><tr><td>MAPE</td><td>165.32</td><td>141.22</td><td>2.32</td><td>85.90</td><td>3.31</td><td>0.82</td><td>29.41</td></tr><tr><th>STOCKS / BONDS / FX</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>3347.17</td><td>2331.98</td><td>226.00</td><td>2161.75</td><td>556.07</td><td>31.85</td><td>1544.24</td></tr><tr><td>MAE</td><td>2525.98</td><td>1474.18</td><td>103.14</td><td>1515.32</td><td>252.90</td><td>14.69</td><td>1108.46</td></tr><tr><td>MAPE</td><td>165.32</td><td>79.01</td><td>3.53</td><td>107.53</td><td>5.83</td><td>1.42</td><td>75.59</td></tr><tr><th>COMMO</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>3347.17</td><td>2456.96</td><td>239.60</td><td>1996.15</td><td>744.25</td><td>29.21</td><td>1350.50</td></tr><tr><td>MAE</td><td>2525.98</td><td>1391.29</td><td>101.55</td><td>1417.36</td><td>304.57</td><td>12.55</td><td>1000.99</td></tr><tr><td>MAPE</td><td>165.32</td><td>77.35</td><td>3.47</td><td>122.91</td><td>8.60</td><td>1.07</td><td>77.55</td></tr><tr><th>ALL</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>3347.17</td><td>1592.95</td><td>185.40</td><td>2086.46</td><td>472.07</td><td>17.61</td><td>524.18</td></tr><tr><td>MAE</td><td>2525.98</td><td>1016.83</td><td>69.02</td><td>1567.12</td><td>207.21</td><td>7.78</td><td>360.27</td></tr><tr><td>MAPE</td><td>165.32</td><td>57.03</td><td>1.90</td><td>137.19</td><td>5.02</td><td>0.89</td><td>21.66</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).

<table><caption>**Table 9.** Sub-sample forecasting results of CME Bitcoin Futures price during the 2016–18 economic cycle.</caption><thead><tr><th>CRYPTO → FUT BTC</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>4363.09</td><td>3614.50</td><td>631.89</td><td>3802.03</td><td>1255.64</td><td>116.83</td><td>2006.04</td></tr><tr><td>MAE</td><td>3239.82</td><td>2960.70</td><td>298.57</td><td>3329.58</td><td>528.87</td><td>52.08</td><td>1408.66</td></tr><tr><td>MAPE</td><td>121.15</td><td>101.87</td><td>8.03</td><td>121.45</td><td>12.20</td><td>0.98</td><td>39.79</td></tr><tr><th>STOCKS / BONDS / FX</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>4363.09</td><td>3900.97</td><td>711.14</td><td>3518.95</td><td>1208.71</td><td>98.46</td><td>3284.64</td></tr><tr><td>MAE</td><td>3239.82</td><td>2781.09</td><td>319.38</td><td>2384.01</td><td>550.15</td><td>45.42</td><td>2252.96</td></tr><tr><td>MAPE</td><td>121.15</td><td>81.72</td><td>6.93</td><td>53.42</td><td>10.85</td><td>1.05</td><td>49.91</td></tr><tr><th>COMMO</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>4363.09</td><td>3749.76</td><td>650.19</td><td>3523.16</td><td>1763.10</td><td>89.78</td><td>2379.86</td></tr><tr><td>MAE</td><td>3239.82</td><td>2713.36</td><td>294.69</td><td>2806.55</td><td>855.68</td><td>38.94</td><td>1577.59</td></tr><tr><td>MAPE</td><td>121.15</td><td>72.63</td><td>6.43</td><td>106.25</td><td>21.38</td><td>0.98</td><td>43.29</td></tr><tr><th>ALL</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>4363.09</td><td>2864.04</td><td>564.27</td><td>2954.87</td><td>1027.13</td><td>96.35</td><td>1612.76</td></tr><tr><td>MAE</td><td>3239.82</td><td>1911.06</td><td>188.29</td><td>2309.58</td><td>439.60</td><td>44.54</td><td>1123.03</td></tr><tr><td>MAPE</td><td>121.15</td><td>46.05</td><td>3.30</td><td>77.10</td><td>8.25</td><td>1.02</td><td>31.65</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).
## 6.4. Year 2019

We narrow down our analysis to the latest trading year in our dataset, a.k.a the year 2019, which did not bring bulls run or rallies in the price path of Bitcoin, which stayed at around 8000$. It is also far away from the next halving period, which should occur in May 2020 at current hash rates. The mining premium is halved for every 210,000 transaction blocks. About 50 bitcoins were generated every 10 min or so during the first four years, this value increased to 25 Bitcoin on 28 November 2012, and to 12.5 Bitcoin on 9 July 2016.

## Sub-Sample Results

According to Tables 10 and 11, the prediction of Bitcoin is best based on Adaboost and Random Forest. SVM performs poorly. Robustness checks validate the main forecasting results and the hypothesis of Bitcoin segmentation within cryptocurrencies. The lowest MAPE for spot forecasts is achieved for all series (=0.18). The lowest MAPE for futures forecasts is achieved for commodities (=0.18). The results are globally similar to the full-period results (2015–2020). Thus, it appears some stability during 2019 for forecasting the Bitcoin spot price, whose errors are close to the errors obtained during the whole period (2015–2020).

For the futures price, it is worth noting that the evolution of the futures market during 2019 yields increased maturity and liquidity compared to the year 2018 (which can be seen as a trial period). During the 2019 subsample, we have a better view of the futures trading activity, given its overall stability and being free of the explosiveness behavior compared to the full period estimates. During the initial 2018 year, shocks revealed the Bitcoin futures market's youth market in search of price support trends.

<table><caption>Table 10. Sub-sample forecasting results of Coinbase Bitcoin Spot price during the year 2019.</caption><thead><tr><th></th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td colspan="8"><strong>CRYPTO → SPOT BTC</strong></td></tr><tr><td>RMSE</td><td>2004.38</td><td>1839.90</td><td>269.78</td><td>1242.31</td><td>482.95</td><td>56.39</td><td>948.21</td></tr><tr><td>MAE</td><td>1621.48</td><td>1480.75</td><td>188.88</td><td>944.23</td><td>334.25</td><td>22.33</td><td>753.79</td></tr><tr><td>MAPE</td><td>19.15</td><td>19.03</td><td>2.20</td><td>11.47</td><td>3.77</td><td>0.31</td><td>8.99</td></tr><tr><td colspan="8"><strong>STOCKS / BONDS / FX</strong></td></tr><tr><td>RMSE</td><td>2004.38</td><td>1161.05</td><td>207.41</td><td>789.85</td><td>658.27</td><td>52.20</td><td>796.62</td></tr><tr><td>MAE</td><td>1621.48</td><td>960.84</td><td>146.26</td><td>658.62</td><td>494.73</td><td>23.82</td><td>641.54</td></tr><tr><td>MAPE</td><td>19.15</td><td>12.09</td><td>1.66</td><td>7.71</td><td>5.58</td><td>0.32</td><td>7.65</td></tr><tr><td colspan="8"><strong>COMMO</strong></td></tr><tr><td>RMSE</td><td>2004.38</td><td>1842.40</td><td>301.12</td><td>951.06</td><td>565.41</td><td>48.58</td><td>572.25</td></tr><tr><td>MAE</td><td>1621.48</td><td>1501.78</td><td>154.87</td><td>778.14</td><td>415.79</td><td>22.93</td><td>449.21</td></tr><tr><td>MAPE</td><td>19.15</td><td>19.21</td><td>1.72</td><td>9.65</td><td>4.80</td><td>0.30</td><td>5.51</td></tr><tr><td colspan="8"><strong>ALL</strong></td></tr><tr><td>RMSE</td><td>2004.38</td><td>1680.12</td><td>207.25</td><td>893.35</td><td>458.88</td><td>32.68</td><td>427.80</td></tr><tr><td>MAE</td><td>1621.48</td><td>1320.86</td><td>140.69</td><td>707.09</td><td>317.84</td><td>13.14</td><td>328.80</td></tr><tr><td>MAPE</td><td>19.15</td><td>17.21</td><td>1.59</td><td>8.52</td><td>3.60</td><td>0.18</td><td>3.86</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).
## 6.4. Year 2019

We narrow down our analysis to the latest trading year in our dataset, a.k.a the year 2019, which did not bring bulls run or rallies in the price path of Bitcoin, which stayed at around 8000$. It is also far away from the next halving period, which should occur in May 2020 at current hash rates. The mining premium is halved for every 210,000 transaction blocks. About 50 bitcoins were generated every 10 min or so during the first four years, this value increased to 25 Bitcoin on 28 November 2012, and to 12.5 Bitcoin on 9 July 2016.

## Sub-Sample Results

According to Tables 10 and 11, the prediction of Bitcoin is best based on Adaboost and Random Forest. SVM performs poorly. Robustness checks validate the main forecasting results and the hypothesis of Bitcoin segmentation within cryptocurrencies. The lowest MAPE for spot forecasts is achieved for all series (=0.18). The lowest MAPE for futures forecasts is achieved for commodities (=0.18). The results are globally similar to the full-period results (2015–2020). Thus, it appears some stability during 2019 for forecasting the Bitcoin spot price, whose errors are close to the errors obtained during the whole period (2015–2020).

For the futures price, it is worth noting that the evolution of the futures market during 2019 yields increased maturity and liquidity compared to the year 2018 (which can be seen as a trial period). During the 2019 subsample, we have a better view of the futures trading activity, given its overall stability and being free of the explosiveness behavior compared to the full period estimates. During the initial 2018 year, shocks revealed the Bitcoin futures market's youth market in search of price support trends.

<table><caption>Table 10. Sub-sample forecasting results of Coinbase Bitcoin Spot price during the year 2019.</caption><thead><tr><th></th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td colspan="8"><strong>CRYPTO → SPOT BTC</strong></td></tr><tr><td>RMSE</td><td>2004.38</td><td>1839.90</td><td>269.78</td><td>1242.31</td><td>482.95</td><td>56.39</td><td>948.21</td></tr><tr><td>MAE</td><td>1621.48</td><td>1480.75</td><td>188.88</td><td>944.23</td><td>334.25</td><td>22.33</td><td>753.79</td></tr><tr><td>MAPE</td><td>19.15</td><td>19.03</td><td>2.20</td><td>11.47</td><td>3.77</td><td>0.31</td><td>8.99</td></tr><tr><td colspan="8"><strong>STOCKS / BONDS / FX</strong></td></tr><tr><td>RMSE</td><td>2004.38</td><td>1161.05</td><td>207.41</td><td>789.85</td><td>658.27</td><td>52.20</td><td>796.62</td></tr><tr><td>MAE</td><td>1621.48</td><td>960.84</td><td>146.26</td><td>658.62</td><td>494.73</td><td>23.82</td><td>641.54</td></tr><tr><td>MAPE</td><td>19.15</td><td>12.09</td><td>1.66</td><td>7.71</td><td>5.58</td><td>0.32</td><td>7.65</td></tr><tr><td colspan="8"><strong>COMMO</strong></td></tr><tr><td>RMSE</td><td>2004.38</td><td>1842.40</td><td>301.12</td><td>951.06</td><td>565.41</td><td>48.58</td><td>572.25</td></tr><tr><td>MAE</td><td>1621.48</td><td>1501.78</td><td>154.87</td><td>778.14</td><td>415.79</td><td>22.93</td><td>449.21</td></tr><tr><td>MAPE</td><td>19.15</td><td>19.21</td><td>1.72</td><td>9.65</td><td>4.80</td><td>0.30</td><td>5.51</td></tr><tr><td colspan="8"><strong>ALL</strong></td></tr><tr><td>RMSE</td><td>2004.38</td><td>1680.12</td><td>207.25</td><td>893.35</td><td>458.88</td><td>32.68</td><td>427.80</td></tr><tr><td>MAE</td><td>1621.48</td><td>1320.86</td><td>140.69</td><td>707.09</td><td>317.84</td><td>13.14</td><td>328.80</td></tr><tr><td>MAPE</td><td>19.15</td><td>17.21</td><td>1.59</td><td>8.52</td><td>3.60</td><td>0.18</td><td>3.86</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).
<table><caption>Table 11. Sub-sample forecasting results of CME Bitcoin Futures price during the year 2019.</caption><thead><tr><th></th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><th colspan="8" style="text-align: left; background-color: #d9871f;">CRYPTO → FUT BTC</th></tr><tr><th scope="row">RMSE</th><td>2526.17</td><td>2274.59</td><td>336.84</td><td>2274.13</td><td>774.28</td><td>51.70</td><td>859.54</td></tr><tr><th scope="row">MAE</th><td>2161.69</td><td>1844.83</td><td>216.16</td><td>1843.04</td><td>400.58</td><td>19.00</td><td>665.93</td></tr><tr><th scope="row">MAPE</th><td>28.19</td><td>27.87</td><td>2.85</td><td>27.79</td><td>4.76</td><td>0.28</td><td>8.54</td></tr><tr><th colspan="8" style="text-align: left; background-color: #d9871f;">STOCKS / BONDS / FX</th></tr><tr><th scope="row">RMSE</th><td>2526.17</td><td>2261.82</td><td>262.58</td><td>1486.93</td><td>870.11</td><td>39.54</td><td>1141.02</td></tr><tr><th scope="row">MAE</th><td>2161.69</td><td>1812.25</td><td>156.25</td><td>1133.90</td><td>627.91</td><td>12.06</td><td>889.87</td></tr><tr><th scope="row">MAPE</th><td>28.19</td><td>27.70</td><td>1.93</td><td>14.25</td><td>7.89</td><td>0.20</td><td>10.98</td></tr><tr><th colspan="8" style="text-align: left; background-color: #d9871f;">COMMO</th></tr><tr><th scope="row">RMSE</th><td>2526.17</td><td>2246.32</td><td>240.88</td><td>1699.47</td><td>784.03</td><td>34.63</td><td>837.17</td></tr><tr><th scope="row">MAE</th><td>2161.69</td><td>1847.42</td><td>142.97</td><td>1360.78</td><td>426.04</td><td>11.74</td><td>663.65</td></tr><tr><th scope="row">MAPE</th><td>28.19</td><td>28.10</td><td>1.63</td><td>19.23</td><td>5.25</td><td>0.18</td><td>8.62</td></tr><tr><th colspan="8" style="text-align: left; background-color: #d9871f;">ALL</th></tr><tr><th scope="row">RMSE</th><td>2526.17</td><td>2112.05</td><td>232.87</td><td>1844.38</td><td>507.67</td><td>38.29</td><td>598.87</td></tr><tr><th scope="row">MAE</th><td>2161.69</td><td>1753.21</td><td>150.59</td><td>1428.00</td><td>338.29</td><td>16.17</td><td>463.48</td></tr><tr><th scope="row">MAPE</th><td>28.19</td><td>26.91</td><td>1.82</td><td>20.40</td><td>4.16</td><td>0.23</td><td>6.07</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).

## 6.5. 2020: The Next “Bull Run”?

Market observers have suggested that the year 2020 would be bound to new “all-time highs”, partly due to the halving of Bitcoin mining rewards, partly because of investors’ behavior (FOMO, or fear-of-missing-out). Bill Gates advised against such investment, by stating merely that “Bitcoin will randomly go up or down, so you should probably watch out”. (See MSN Money (2021) at https://www.msn.com/en-us/money/companies/bill-gates-vs-elon-musk-over-bitcoin/ar-BB1e1p7v, accessed on 2 February 2021). Many shrewd investors in the vein of Bill Gates have similarly noticed the “Tulip Mania” around Bitcoin in 2020, which led in the 1600s to the first recorded story of a financial bubble. Or maybe the blockchain revolution is inevitable, much like the internet revolution for its contemporary back in 1994 (when modem connection to the world wide web was in its infancy)? Only History will tell.

In parallel, Bitcoin has been advanced as a refuge for money during the Covid-19 sanitary crisis, challenging the role of Gold for several years to come. With the arrival of new institutional investors (who pledged, for instance, 5% of their portfolio allocation to Bitcoin futures (Kraken [119] documents BTC investments coming from several institutional investors, such as JP Morgan, Massachusetts Mutual Life Insurance, One River Asset Management, Guggenheim Global, Jefferies Investment Bank in the US, or BBVA in Switzerland)), a new economic cycle seems to have begun breaking all previous lines of resistance (that of $30,000 significantly) for BTC traders with increased market liquidity ($126 billion worth of trading in Bitcoin in December 2020, with a record-high of $16 billion traded on December 30 alone). The interest in Bitcoin as a financial store of value is further confirmed by the recent interest of hedge funds, such as Black Rock, who has begun entering the Bitcoin space (without revealing precisely the percentage of exposure to Bitcoin in its portfolio). (See CNBC (2021) at https://www.cnbc.com/2021/02/17/blackrock-started-to-dabble-in-bitcoin-says-rick-rieder.html, accessed on 17 February 2021).

The main findings from Tables 12 and 13 can be summarized as follows. In 2020, the quality of forecasts was overall the same as in 2019, with the Adaboost model standing out as the best machine learning model. The kNN, random forest, or Stochastic Gradient Descent algorithms rank closely as second best models depending on the statistic used. Nonetheless, we remark a higher dispersion across the statistics used for prediction, especially for the spot. This may be linked to the parabolic rise near the end of 2020.
<table><caption>**Table 11.** Sub-sample forecasting results of CME Bitcoin Futures price during the year 2019.</caption><thead><tr><th></th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td colspan="8"><strong>CRYPTO → FUT BTC</strong></td></tr><tr><td>RMSE</td><td>2526.17</td><td>2274.59</td><td>336.84</td><td>2274.13</td><td>774.28</td><td>51.70</td><td>859.54</td></tr><tr><td>MAE</td><td>2161.69</td><td>1844.83</td><td>216.16</td><td>1843.04</td><td>400.58</td><td>19.00</td><td>665.93</td></tr><tr><td>MAPE</td><td>28.19</td><td>27.87</td><td>2.85</td><td>27.79</td><td>4.76</td><td>0.28</td><td>8.54</td></tr><tr><td colspan="8"><strong>STOCKS / BONDS / FX</strong></td></tr><tr><td>RMSE</td><td>2526.17</td><td>2261.82</td><td>262.58</td><td>1486.93</td><td>870.11</td><td>39.54</td><td>1141.02</td></tr><tr><td>MAE</td><td>2161.69</td><td>1812.25</td><td>156.25</td><td>1133.90</td><td>627.91</td><td>12.06</td><td>889.87</td></tr><tr><td>MAPE</td><td>28.19</td><td>27.70</td><td>1.93</td><td>14.25</td><td>7.89</td><td>0.20</td><td>10.98</td></tr><tr><td colspan="8"><strong>COMMO</strong></td></tr><tr><td>RMSE</td><td>2526.17</td><td>2246.32</td><td>240.88</td><td>1699.47</td><td>784.03</td><td>34.63</td><td>837.17</td></tr><tr><td>MAE</td><td>2161.69</td><td>1847.42</td><td>142.97</td><td>1360.78</td><td>426.04</td><td>11.74</td><td>663.65</td></tr><tr><td>MAPE</td><td>28.19</td><td>28.10</td><td>1.63</td><td>19.23</td><td>5.25</td><td>0.18</td><td>8.62</td></tr><tr><td colspan="8"><strong>ALL</strong></td></tr><tr><td>RMSE</td><td>2526.17</td><td>2112.05</td><td>232.87</td><td>1844.38</td><td>507.67</td><td>38.29</td><td>598.87</td></tr><tr><td>MAE</td><td>2161.69</td><td>1753.21</td><td>150.59</td><td>1428.00</td><td>338.29</td><td>16.17</td><td>463.48</td></tr><tr><td>MAPE</td><td>28.19</td><td>26.91</td><td>1.82</td><td>20.40</td><td>4.16</td><td>0.23</td><td>6.07</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).

## 6.5. 2020: The Next “Bull Run”?

Market observers have suggested that the year 2020 would be bound to new “all-time highs”, partly due to the halving of Bitcoin mining rewards, partly because of investors’ behavior (FOMO, or fear-of-missing-out). Bill Gates advised against such investment, by stating merely that “Bitcoin will randomly go up or down, so you should probably watch out”. (See MSN Money (2021) at https://www.msn.com/en-us/money/companies/bill-gates-vs-elon-musk-over-bitcoin/ar-BB1e1p7v, accessed on 2 February 2021). Many shrewd investors in the vein of Bill Gates have similarly noticed the “Tulip Mania” around Bitcoin in 2020, which led in the 1600s to the first recorded story of a financial bubble. Or maybe the blockchain revolution is inevitable, much like the internet revolution for its contemporary back in 1994 (when modem connection to the world wide web was in its infancy)? Only History will tell.

In parallel, Bitcoin has been advanced as a refuge for money during the Covid-19 sanitary crisis, challenging the role of Gold for several years to come. With the arrival of new institutional investors (who pledged, for instance, 5% of their portfolio allocation to Bitcoin futures (Kraken [119] documents BTC investments coming from several institutional investors, such as JP Morgan, Massachusetts Mutual Life Insurance, One River Asset Management, Guggenheim Global, Jefferies Investment Bank in the US, or BBVA in Switzerland)), a new economic cycle seems to have begun breaking all previous lines of resistance (that of $30,000 significantly) for BTC traders with increased market liquidity ($126 billion worth of trading in Bitcoin in December 2020, with a record-high of $16 billion traded on December 30 alone). The interest in Bitcoin as a financial store of value is further confirmed by the recent interest of hedge funds, such as Black Rock, who has begun entering the Bitcoin space (without revealing precisely the percentage of exposure to Bitcoin in its portfolio). (See CNBC (2021) at https://www.cnbc.com/2021/02/17/blackrock-hastarted-to-dabble-in-bitcoin-says-rick-rieder.html, accessed on 17 February 2021).

The main findings from Tables 12 and 13 can be summarized as follows. In 2020, the quality of forecasts was overall the same as in 2019, with the Adaboost model standing out as the best machine learning model. The kNN, random forest, or Stochastic Gradient Descent algorithms rank closely as second best models depending on the statistic used. Nonetheless, we remark a higher dispersion across the statistics used for prediction, especially for the spot. This may be linked to the parabolic rise near the end of 2020.
<table><caption>**Table 12.** Sub-sample forecasting results of Coinbase Bitcoin Spot price during the year 2020.</caption><thead><tr><th>CRYPTO → SPOT BTC</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>1414.49</td><td>3307.80</td><td>197.38</td><td>2900.38</td><td>349.39</td><td>33.70</td><td>338.91</td></tr><tr><td>MAE</td><td>1070.73</td><td>2459.54</td><td>103.34</td><td>2052.99</td><td>234.06</td><td>17.80</td><td>241.83</td></tr><tr><td>MAPE</td><td>11.22</td><td>24.93</td><td>0.84</td><td>17.58</td><td>2.25</td><td>0.20</td><td>2.39</td></tr></tbody><thead><tr><th>STOCKS / BONDS / FX</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>1414.49</td><td>2512.15</td><td>311.51</td><td>2529.41</td><td>740.23</td><td>78.17</td><td>1471.50</td></tr><tr><td>MAE</td><td>1070.73</td><td>1975.08</td><td>180.96</td><td>1894.31</td><td>459.15</td><td>38.99</td><td>1163.68</td></tr><tr><td>MAPE</td><td>11.22</td><td>18.58</td><td>1.71</td><td>16.96</td><td>4.23</td><td>0.41</td><td>11.20</td></tr></tbody><thead><tr><th>COMMO</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>1414.49</td><td>2883.19</td><td>357.88</td><td>2420.39</td><td>676.30</td><td>96.19</td><td>1304.25</td></tr><tr><td>MAE</td><td>1070.73</td><td>2249.76</td><td>184.10</td><td>1728.99</td><td>417.52</td><td>46.36</td><td>996.39</td></tr><tr><td>MAPE</td><td>11.22</td><td>22.40</td><td>1.76</td><td>14.71</td><td>4.09</td><td>0.47</td><td>9.49</td></tr></tbody><thead><tr><th>ALL</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>1414.49</td><td>1644.56</td><td>196.82</td><td>2632.90</td><td>358.02</td><td>44.44</td><td>262.89</td></tr><tr><td>MAE</td><td>1070.73</td><td>1382.10</td><td>101.25</td><td>1860.75</td><td>249.53</td><td>22.85</td><td>187.06</td></tr><tr><td>MAPE</td><td>11.22</td><td>13.66</td><td>0.85</td><td>15.90</td><td>2.41</td><td>0.25</td><td>1.80</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).

<table><caption>**Table 13.** Sub-sample forecasting results of CME Bitcoin Futures price during the year 2020.</caption><thead><tr><th>CRYPTO → FUT BTC</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>1410.81</td><td>3312.17</td><td>215.78</td><td>3393.32</td><td>707.28</td><td>58.42</td><td>534.98</td></tr><tr><td>MAE</td><td>1067.87</td><td>2445.28</td><td>134.71</td><td>2490.83</td><td>306.53</td><td>26.25</td><td>385.49</td></tr><tr><td>MAPE</td><td>11.01</td><td>24.57</td><td>1.28</td><td>24.85</td><td>2.89</td><td>0.27</td><td>3.77</td></tr></tbody><thead><tr><th>STOCKS / BONDS / FX</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>1410.81</td><td>1962.39</td><td>324.59</td><td>2734.47</td><td>771.51</td><td>46.64</td><td>2074.45</td></tr><tr><td>MAE</td><td>1067.87</td><td>1486.87</td><td>167.88</td><td>1937.63</td><td>465.15</td><td>17.82</td><td>1598.52</td></tr><tr><td>MAPE</td><td>11.01</td><td>14.34</td><td>1.46</td><td>17.68</td><td>4.25</td><td>0.18</td><td>15.33</td></tr></tbody><thead><tr><th>COMMO</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>1410.81</td><td>2888.13</td><td>455.97</td><td>2350.38</td><td>709.81</td><td>60.48</td><td>1396.80</td></tr><tr><td>MAE</td><td>1067.87</td><td>2251.41</td><td>223.21</td><td>1670.00</td><td>429.37</td><td>22.26</td><td>1105.12</td></tr><tr><td>MAPE</td><td>11.01</td><td>22.37</td><td>2.14</td><td>15.51</td><td>4.04</td><td>0.22</td><td>10.72</td></tr></tbody><thead><tr><th>ALL</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>1410.81</td><td>1520.44</td><td>401.66</td><td>1910.55</td><td>352.58</td><td>53.12</td><td>659.22</td></tr><tr><td>MAE</td><td>1067.87</td><td>1217.22</td><td>148.97</td><td>1268.20</td><td>248.24</td><td>20.27</td><td>515.52</td></tr><tr><td>MAPE</td><td>11.01</td><td>11.96</td><td>1.44</td><td>12.25</td><td>2.32</td><td>0.20</td><td>5.43</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).

Despite the soaring prices near the end of the year 2020, ultimately breaching the barrier of $30k at the beginning of 2021, it is reassuring to observe that the machine learning models implemented keep delivering approximately the same forecasting accuracy metric as when the prices were in the low $3k or $8k average. We are confident that, for instance, the Adaboost or Random forest algorithms could be implemented as a decision-making tool in a banking environment, either for spot or futures forecasts, given their stability.

## 6.6. Trading Strategies

Most of the crypto traders continue to use chartist methods to decide to sell or buy (Shynkevich [120]). They also use the notion of profit and loss. With our exercise, we can provide interesting information to these investors who are interested in short positions.
<table><caption>**Table 12.** Sub-sample forecasting results of Coinbase Bitcoin Spot price during the year 2020.</caption><thead><tr><th>CRYPTO → SPOT BTC</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>1414.49</td><td>3307.80</td><td>197.38</td><td>2900.38</td><td>349.39</td><td>33.70</td><td>338.91</td></tr><tr><td>MAE</td><td>1070.73</td><td>2459.54</td><td>103.34</td><td>2052.99</td><td>234.06</td><td>17.80</td><td>241.83</td></tr><tr><td>MAPE</td><td>11.22</td><td>24.93</td><td>0.84</td><td>17.58</td><td>2.25</td><td>0.20</td><td>2.39</td></tr><tr><th>STOCKS / BONDS / FX</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>1414.49</td><td>2512.15</td><td>311.51</td><td>2529.41</td><td>740.23</td><td>78.17</td><td>1471.50</td></tr><tr><td>MAE</td><td>1070.73</td><td>1975.08</td><td>180.96</td><td>1894.31</td><td>459.15</td><td>38.99</td><td>1163.68</td></tr><tr><td>MAPE</td><td>11.22</td><td>18.58</td><td>1.71</td><td>16.96</td><td>4.23</td><td>0.41</td><td>11.20</td></tr><tr><th>COMMO</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>1414.49</td><td>2883.19</td><td>357.88</td><td>2420.39</td><td>676.30</td><td>96.19</td><td>1304.25</td></tr><tr><td>MAE</td><td>1070.73</td><td>2249.76</td><td>184.10</td><td>1728.99</td><td>417.52</td><td>46.36</td><td>996.39</td></tr><tr><td>MAPE</td><td>11.22</td><td>22.40</td><td>1.76</td><td>14.71</td><td>4.09</td><td>0.47</td><td>9.49</td></tr><tr><th>ALL</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>1414.49</td><td>1644.56</td><td>196.82</td><td>2632.90</td><td>358.02</td><td>44.44</td><td>262.89</td></tr><tr><td>MAE</td><td>1070.73</td><td>1382.10</td><td>101.25</td><td>1860.75</td><td>249.53</td><td>22.85</td><td>187.06</td></tr><tr><td>MAPE</td><td>11.22</td><td>13.66</td><td>0.85</td><td>15.90</td><td>2.41</td><td>0.25</td><td>1.80</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).

<table><caption>**Table 13.** Sub-sample forecasting results of CME Bitcoin Futures price during the year 2020.</caption><thead><tr><th>CRYPTO → FUT BTC</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>RMSE</td><td>1410.81</td><td>3312.17</td><td>215.78</td><td>3393.32</td><td>707.28</td><td>58.42</td><td>534.98</td></tr><tr><td>MAE</td><td>1067.87</td><td>2445.28</td><td>134.71</td><td>2490.83</td><td>306.53</td><td>26.25</td><td>385.49</td></tr><tr><td>MAPE</td><td>11.01</td><td>24.57</td><td>1.28</td><td>24.85</td><td>2.89</td><td>0.27</td><td>3.77</td></tr><tr><th>STOCKS / BONDS / FX</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>1410.81</td><td>1962.39</td><td>324.59</td><td>2734.47</td><td>771.51</td><td>46.64</td><td>2074.45</td></tr><tr><td>MAE</td><td>1067.87</td><td>1486.87</td><td>167.88</td><td>1937.63</td><td>465.15</td><td>17.82</td><td>1598.52</td></tr><tr><td>MAPE</td><td>11.01</td><td>14.34</td><td>1.46</td><td>17.68</td><td>4.25</td><td>0.18</td><td>15.33</td></tr><tr><th>COMMO</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>1410.81</td><td>2888.13</td><td>455.97</td><td>2350.38</td><td>709.81</td><td>60.48</td><td>1396.80</td></tr><tr><td>MAE</td><td>1067.87</td><td>2251.41</td><td>223.21</td><td>1670.00</td><td>429.37</td><td>22.26</td><td>1105.12</td></tr><tr><td>MAPE</td><td>11.01</td><td>22.37</td><td>2.14</td><td>15.51</td><td>4.04</td><td>0.22</td><td>10.72</td></tr><tr><th>ALL</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr><tr><td>RMSE</td><td>1410.81</td><td>1520.44</td><td>401.66</td><td>1910.55</td><td>352.58</td><td>53.12</td><td>659.22</td></tr><tr><td>MAE</td><td>1067.87</td><td>1217.22</td><td>148.97</td><td>1268.20</td><td>248.24</td><td>20.27</td><td>515.52</td></tr><tr><td>MAPE</td><td>11.01</td><td>11.96</td><td>1.44</td><td>12.25</td><td>2.32</td><td>0.20</td><td>5.43</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression. In terms of forecast statistics, we resort to the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE), and the Mean Absolute Percent Error (MAPE).

Despite the soaring prices near the end of the year 2020, ultimately breaching the barrier of $30k at the beginning of 2021, it is reassuring to observe that the machine learning models implemented keep delivering approximately the same forecasting accuracy metric as when the prices were in the low $3k or $8k average. We are confident that, for instance, the Adaboost or Random forest algorithms could be implemented as a decision-making tool in a banking environment, either for spot or futures forecasts, given their stability.

## 6.6. Trading Strategies

Most of the crypto traders continue to use chartist methods to decide to sell or buy (Shynkevich [120]). They also use the notion of profit and loss. With our exercise, we can provide interesting information to these investors who are interested in short positions.
Indeed, with the trends we observe in our predictions, we can provide new alternative trading strategies.

### 6.6.1. Hit Rates

To achieve this objective, we follow the methodology by [64]. We assess the accuracy of the Bitcoin price predictions based on the following formula:

$$ \text{Hit rate} = \frac{h}{n}, \qquad (16) $$

with *h* the number of out-of-sample correct forecasts of the Bitcoin underlying price (e.g., spot or futures), and *n* the number of tests (a.k.a, sessions of tests of different sizes depending on full- or sub-samples).

The key idea behind computing hit rates is to assess whether the ML algorithms can help the trader in his daily routine (by giving him consistent up/down price directions), or whether the trader is better off counting on his luck, a.k.a, flipping a coin every morning with 50% of success whatsoever (independent trials).

Regarding Table 14, we report a superior forecasting accuracy superior to 50% chance of flipping a coin. Ada Boost performs best above 70% in all cases in the full sample. Performance is consistent across the various subsamples. Variations exist, as the lowest hit rate is recorded at 61.89% for Bitcoin spot during the year 2019, whereas the highest hit rate is equal to 93.90% for Bitcoin spot during the 2016–18 economic cycle for all series. Random forest ranks second, oscillating around 60% for the full sample. The hit rate of Random forest is even higher for futures Bitcoin, where it can beat in one case the Ada Boost model (for cryptocurrencies only; random = 73.17% whereas boosting = 70.43%). For the subsamples, the Random forest model’s predictive power remains around the hit rate of 60%. Its performance is slightly better when the underlying asset is the futures (see especially the case of the Bitcoin 2016–18 economic cycle sub-sample, where the Random forest ranks first in three cases). kNN and ridge regression hit consistently above than 50% threshold. AR(1), ANN, and SVM perform poorly (below 50% chance of flipping a coin). In 2020, the best hit rates ranged around 62%, down from 65% during the year 2019 (maybe attributable to the intramonth volatility push during December 2020?). Besides, we identify two instances (for spot forecasts) during which the random forest algorithm beats the Adaboost one.

In the literature, other authors have also studied the interest of using machine learning to predict asset prices. In Atsalakis et al. [64], the PATSOS (neuro-fuzzy algorithm) hit rate to predict Bitcoin is equal to 63.22%. In our approach, we perform slightly better for Bitcoin spot and futures, on specific periods. In 2019, our performance was in the range of literature by Atsalakis et al. [64]. In Fischer and Krauss [121], the average accuracy of the random forest algorithm to predict the S&P 500 oscillates between 52% and 57%. Based on Random Forest and Gradient Descent, Saad et al. [122] evaluate that a state-of-the-art machine learning model can achieve more than 90% forecast accuracy of the Bitcoin price (based on MAE and RMSE statistics).

Regarding the prediction of cryptocurrency returns, [123] document that machine learning classification algorithms reach about 55-65% predictive accuracy on average at the daily or minute level frequencies. However, our results depart from the latter authors. They attributed the best and consistent results in terms of predictive accuracy to the support vector machines compared to the logistic regression, artificial neural networks, and random forest classification algorithms.
Indeed, with the trends we observe in our predictions, we can provide new alternative trading strategies.

### 6.6.1. Hit Rates

To achieve this objective, we follow the methodology by [64]. We assess the accuracy of the Bitcoin price predictions based on the following formula:

$$ \text{Hit rate} = \frac{h}{n}, \qquad (16) $$

with *h* the number of out-of-sample correct forecasts of the Bitcoin underlying price (e.g., spot or futures), and *n* the number of tests (a.k.a, sessions of tests of different sizes depending on full- or sub-samples).

The key idea behind computing hit rates is to assess whether the ML algorithms can help the trader in his daily routine (by giving him consistent up/down price directions), or whether the trader is better off counting on his luck, a.k.a, flipping a coin every morning with 50% of success whatsoever (independent trials).

Regarding Table 14, we report a superior forecasting accuracy superior to 50% chance of flipping a coin. Ada Boost performs best above 70% in all cases in the full sample. Performance is consistent across the various subsamples. Variations exist, as the lowest hit rate is recorded at 61.89% for Bitcoin spot during the year 2019, whereas the highest hit rate is equal to 93.90% for Bitcoin spot during the 2016–18 economic cycle for all series. Random forest ranks second, oscillating around 60% for the full sample. The hit rate of Random forest is even higher for futures Bitcoin, where it can beat in one case the Ada Boost model (for cryptocurrencies only; random = 73.17% whereas boosting = 70.43%). For the subsamples, the Random forest model’s predictive power remains around the hit rate of 60%. Its performance is slightly better when the underlying asset is the futures (see especially the case of the Bitcoin 2016–18 economic cycle sub-sample, where the Random forest ranks first in three cases). kNN and ridge regression hit consistently above than 50% threshold. AR(1), ANN, and SVM perform poorly (below 50% chance of flipping a coin). In 2020, the best hit rates ranged around 62%, down from 65% during the year 2019 (maybe attributable to the intramonth volatility push during December 2020?). Besides, we identify two instances (for spot forecasts) during which the random forest algorithm beats the Adaboost one.

In the literature, other authors have also studied the interest of using machine learning to predict asset prices. In Atsalakis et al. [64], the PATSOS (neuro-fuzzy algorithm) hit rate to predict Bitcoin is equal to 63.22%. In our approach, we perform slightly better for Bitcoin spot and futures, on specific periods. In 2019, our performance was in the range of literature by Atsalakis et al. [64]. In Fischer and Krauss [121], the average accuracy of the random forest algorithm to predict the S&P 500 oscillates between 52% and 57%. Based on Random Forest and Gradient Descent, Saad et al. [122] evaluate that a state-of-the-art machine learning model can achieve more than 90% forecast accuracy of the Bitcoin price (based on MAE and RMSE statistics).

Regarding the prediction of cryptocurrency returns, [123] document that machine learning classification algorithms reach about 55-65% predictive accuracy on average at the daily or minute level frequencies. However, our results depart from the latter authors. They attributed the best and consistent results in terms of predictive accuracy to the support vector machines compared to the logistic regression, artificial neural networks, and random forest classification algorithms.
<table><caption>Table 14. Hit rate performance comparison.</caption><thead><tr><th>Full sample/Spot</th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>Hit rate (%) CRYPTO → SPOT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>61.59%</td><td>&lt;50%</td><td>52.74%</td><td>83.84%</td><td>51.83%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>63.72%</td><td>50.30%</td><td>51.83%</td><td>83.54%</td><td>50.61%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>60.06%</td><td>&lt;50%</td><td>53.35%</td><td>85.37%</td><td>51.22%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>57.93%</td><td>&lt;50%</td><td>51.83%</td><td>88.41%</td><td>51.83%</td></tr><tr><td>Full sample/Futures</td><td>AR(1)</td><td>ann</td><td>random</td><td>svm</td><td>knn</td><td>boost</td><td>ridge</td></tr><tr><td>Hit rate (%) CRYPTO → FUT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>73.17%</td><td>50.91%</td><td>57.32%</td><td>70.43%</td><td>50.91%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>66.16%</td><td>&lt;50%</td><td>56.40%</td><td>82.32%</td><td>51.22%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>67.07%</td><td>50.30%</td><td>52.74%</td><td>80.79%</td><td>50.91%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>70.12%</td><td>50.30%</td><td>57.93%</td><td>77.74%</td><td>50.30%</td></tr><tr><td>Sub sample/Crypto-select/Spot</td><td>AR(1)</td><td>ann</td><td>random</td><td>svm</td><td>knn</td><td>boost</td><td>ridge</td></tr><tr><td>Hit rate (%) CRYPTO → SPOT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>58.84%</td><td>50.30%</td><td>55.18%</td><td>85.37%</td><td>50.30%</td></tr><tr><td>Sub sample/Crypto-select/Futures</td><td>AR(1)</td><td>ann</td><td>random</td><td>svm</td><td>knn</td><td>boost</td><td>ridge</td></tr><tr><td>Hit rate (%) CRYPTO → FUT BTC</td><td>&lt;50%</td><td>50.00%</td><td>62.50%</td><td>50.91%</td><td>52.74%</td><td>83.23%</td><td>50.61%</td></tr><tr><td>Sub sample/Tether/Spot</td><td>AR(1)</td><td>ann</td><td>random</td><td>svm</td><td>knn</td><td>boost</td><td>ridge</td></tr><tr><td>Hit rate (%) CRYPTO → SPOT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>60.98%</td><td>50.30%</td><td>54.27%</td><td>84.15%</td><td>50.30%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>58.54%</td><td>50.30%</td><td>53.35%</td><td>86.89%</td><td>50.91%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>61.59%</td><td>50.61%</td><td>52.74%</td><td>84.15%</td><td>50.91%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>58.23%</td><td>&lt;50%</td><td>53.05%</td><td>87.80%</td><td>50.91%</td></tr><tr><td>Sub sample/Tether/Futures</td><td>AR(1)</td><td>ann</td><td>random</td><td>svm</td><td>knn</td><td>boost</td><td>ridge</td></tr><tr><td>Hit rate (%) CRYPTO → FUT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>66.46%</td><td>&lt;50%</td><td>54.88%</td><td>78.05%</td><td>50.61%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>64.33%</td><td>51.22%</td><td>57.32%</td><td>76.52%</td><td>50.91%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>63.41%</td><td>50.30%</td><td>54.88%</td><td>81.10%</td><td>50.30%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>64.02%</td><td>50.30%</td><td>55.18%</td><td>79.88%</td><td>51.22%</td></tr><tr><td>Sub sample/BTC cycle/Spot</td><td>AR(1)</td><td>ann</td><td>random</td><td>svm</td><td>knn</td><td>boost</td><td>ridge</td></tr><tr><td>Hit rate (%) CRYPTO → SPOT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>58.54%</td><td>50.30%</td><td>52.74%</td><td>87.50%</td><td>50.91%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>56.40%</td><td>&lt;50%</td><td>52.13%</td><td>91.16%</td><td>50.30%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>58.84%</td><td>&lt;50%</td><td>51.83%</td><td>89.33%</td><td>&lt;50%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>54.88%</td><td>&lt;50%</td><td>50.91%</td><td>93.90%</td><td>50.30%</td></tr><tr><td>Sub sample/BTC cycle/Futures</td><td>AR(1)</td><td>ann</td><td>random</td><td>svm</td><td>knn</td><td>boost</td><td>ridge</td></tr><tr><td>Hit rate (%) CRYPTO → FUT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>70.73%</td><td>50.30%</td><td>57.01%</td><td>70.73%</td><td>51.22%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>72.87%</td><td>&lt;50%</td><td>54.27%</td><td>72.26%</td><td>51.22%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>66.46%</td><td>&lt;50%</td><td>54.57%</td><td>77.74%</td><td>51.22%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>74.09%</td><td>&lt;50%</td><td>56.10%</td><td>69.51%</td><td>51.52%</td></tr><tr><td>Sub sample/2019/Spot</td><td>AR(1)</td><td>ann</td><td>random</td><td>svm</td><td>knn</td><td>boost</td><td>ridge</td></tr><tr><td>Hit rate (%) CRYPTO → SPOT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>58.54%</td><td>50.30%</td><td>53.66%</td><td>61.89%</td><td>50.91%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>55.49%</td><td>50.91%</td><td>52.13%</td><td>65.55%</td><td>51.22%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>58.54%</td><td>&lt;50%</td><td>52.13%</td><td>64.02%</td><td>50.61%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>57.01%</td><td>50.30%</td><td>52.44%</td><td>64.63%</td><td>50.91%</td></tr><tr><td>Sub sample/2019/Futures</td><td>AR(1)</td><td>ann</td><td>random</td><td>svm</td><td>knn</td><td>boost</td><td>ridge</td></tr><tr><td>Hit rate (%) CRYPTO → FUT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>56.40%</td><td>&lt;50%</td><td>51.83%</td><td>66.77%</td><td>50.30%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>54.57%</td><td>&lt;50%</td><td>52.44%</td><td>68.60%</td><td>50.30%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>54.88%</td><td>&lt;50%</td><td>51.83%</td><td>68.60%</td><td>&lt;50%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>57.01%</td><td>&lt;50%</td><td>52.13%</td><td>66.77%</td><td>&lt;50%</td></tr><tr><td>Sub sample/2020/Spot</td><td>AR(1)</td><td>ann</td><td>random</td><td>svm</td><td>knn</td><td>boost</td><td>sgd</td></tr><tr><td>Hit rate (%) CRYPTO → SPOT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>60.06%</td><td>50.30%</td><td>53.05%</td><td>62.50%</td><td>50.00%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>61.28%</td><td>50.91%</td><td>54.57%</td><td>57.93%</td><td>50.61%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>66.46%</td><td>50.91%</td><td>53.05%</td><td>53.66%</td><td>51.22%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>59.76%</td><td>50.30%</td><td>51.83%</td><td>60.67%</td><td>52.74%</td></tr><tr><td>Sub sample/2020/Futures</td><td>AR(1)</td><td>ann</td><td>random</td><td>svm</td><td>knn</td><td>boost</td><td>sgd</td></tr><tr><td>Hit rate (%) CRYPTO → FUT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>61.28%</td><td>&lt;50%</td><td>52.13%</td><td>61.89%</td><td>&lt;50%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>59.15%</td><td>&lt;50%</td><td>53.66%</td><td>62.50%</td><td>50.30%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>58.54%</td><td>&lt;50%</td><td>52.13%</td><td>64.94%</td><td>&lt;50%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>60.06%</td><td>&lt;50%</td><td>51.83%</td><td>61.59%</td><td>51.83%</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression.
<table><caption>Table 14. Hit rate performance comparison.</caption><thead><tr><th></th><th>AR(1)</th><th>ann</th><th>random</th><th>svm</th><th>knn</th><th>boost</th><th>ridge</th></tr></thead><tbody><tr><td>Full sample/Spot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hit rate (%) CRYPTO → SPOT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>61.59%</td><td>&lt;50%</td><td>52.74%</td><td>83.84%</td><td>51.83%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>63.72%</td><td>50.30%</td><td>51.83%</td><td>83.54%</td><td>50.61%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>60.06%</td><td>&lt;50%</td><td>53.35%</td><td>85.37%</td><td>51.22%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>57.93%</td><td>&lt;50%</td><td>51.83%</td><td>88.41%</td><td>51.83%</td></tr><tr><td>Full sample/Futures</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hit rate (%) CRYPTO → FUT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>73.17%</td><td>50.91%</td><td>57.32%</td><td>70.43%</td><td>50.91%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>66.16%</td><td>&lt;50%</td><td>56.40%</td><td>82.32%</td><td>51.22%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>67.07%</td><td>50.30%</td><td>52.74%</td><td>80.79%</td><td>50.91%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>70.12%</td><td>50.30%</td><td>57.93%</td><td>77.74%</td><td>50.30%</td></tr><tr><td>Sub sample/Crypto-select/Spot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hit rate (%) CRYPTO → SPOT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>58.84%</td><td>50.30%</td><td>55.18%</td><td>85.37%</td><td>50.30%</td></tr><tr><td>Sub sample/Crypto-select/Futures</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hit rate (%) CRYPTO → FUT BTC</td><td>&lt;50%</td><td>50.00%</td><td>62.50%</td><td>50.91%</td><td>52.74%</td><td>83.23%</td><td>50.61%</td></tr><tr><td>Sub sample/Tether/Spot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hit rate (%) CRYPTO → SPOT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>60.98%</td><td>50.30%</td><td>54.27%</td><td>84.15%</td><td>50.30%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>58.54%</td><td>50.30%</td><td>53.35%</td><td>86.89%</td><td>50.91%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>61.59%</td><td>50.61%</td><td>52.74%</td><td>84.15%</td><td>50.91%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>58.23%</td><td>&lt;50%</td><td>53.05%</td><td>87.80%</td><td>50.91%</td></tr><tr><td>Sub sample/Tether/Futures</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hit rate (%) CRYPTO → FUT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>66.46%</td><td>&lt;50%</td><td>54.88%</td><td>78.05%</td><td>50.61%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>64.33%</td><td>51.22%</td><td>57.32%</td><td>76.52%</td><td>50.91%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>63.41%</td><td>50.30%</td><td>54.88%</td><td>81.10%</td><td>50.30%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>64.02%</td><td>50.30%</td><td>55.18%</td><td>79.88%</td><td>51.22%</td></tr><tr><td>Sub sample/BTC cycle/Spot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hit rate (%) CRYPTO → SPOT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>58.54%</td><td>50.30%</td><td>52.74%</td><td>87.50%</td><td>50.91%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>56.40%</td><td>&lt;50%</td><td>52.13%</td><td>91.16%</td><td>50.30%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>58.84%</td><td>&lt;50%</td><td>51.83%</td><td>89.33%</td><td>&lt;50%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>54.88%</td><td>&lt;50%</td><td>50.91%</td><td>93.90%</td><td>50.30%</td></tr><tr><td>Sub sample/BTC cycle/Futures</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hit rate (%) CRYPTO → FUT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>70.73%</td><td>50.30%</td><td>57.01%</td><td>70.73%</td><td>51.22%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>72.87%</td><td>&lt;50%</td><td>54.27%</td><td>72.26%</td><td>51.22%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>66.46%</td><td>&lt;50%</td><td>54.57%</td><td>77.74%</td><td>51.22%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>74.09%</td><td>&lt;50%</td><td>56.10%</td><td>69.51%</td><td>51.52%</td></tr><tr><td>Sub sample/2019/Spot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hit rate (%) CRYPTO → SPOT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>58.54%</td><td>50.30%</td><td>53.66%</td><td>61.89%</td><td>50.91%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>55.49%</td><td>50.91%</td><td>52.13%</td><td>65.55%</td><td>51.22%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>58.54%</td><td>&lt;50%</td><td>52.13%</td><td>64.02%</td><td>50.61%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>57.01%</td><td>50.30%</td><td>52.44%</td><td>64.63%</td><td>50.91%</td></tr><tr><td>Sub sample/2019/Futures</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hit rate (%) CRYPTO → FUT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>56.40%</td><td>&lt;50%</td><td>51.83%</td><td>66.77%</td><td>50.30%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>54.57%</td><td>&lt;50%</td><td>52.44%</td><td>68.60%</td><td>50.30%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>54.88%</td><td>&lt;50%</td><td>51.83%</td><td>68.60%</td><td>&lt;50%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>57.01%</td><td>&lt;50%</td><td>52.13%</td><td>66.77%</td><td>&lt;50%</td></tr><tr><td>Sub sample/2020/Spot</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hit rate (%) CRYPTO → SPOT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>60.06%</td><td>50.30%</td><td>53.05%</td><td>62.50%</td><td>50.00%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>61.28%</td><td>50.91%</td><td>54.57%</td><td>57.93%</td><td>50.61%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>66.46%</td><td>50.91%</td><td>53.05%</td><td>53.66%</td><td>51.22%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>59.76%</td><td>50.30%</td><td>51.83%</td><td>60.67%</td><td>52.74%</td></tr><tr><td>Sub sample/2020/Futures</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Hit rate (%) CRYPTO → FUT BTC</td><td>&lt;50%</td><td>&lt;50%</td><td>61.28%</td><td>&lt;50%</td><td>52.13%</td><td>61.89%</td><td>&lt;50%</td></tr><tr><td>Hit rate (%) STOCKS / BONDS / FX</td><td>&lt;50%</td><td>&lt;50%</td><td>59.15%</td><td>&lt;50%</td><td>53.66%</td><td>62.50%</td><td>50.30%</td></tr><tr><td>Hit rate (%) COMMO</td><td>&lt;50%</td><td>&lt;50%</td><td>58.54%</td><td>&lt;50%</td><td>52.13%</td><td>64.94%</td><td>&lt;50%</td></tr><tr><td>Hit rate (%) ALL</td><td>&lt;50%</td><td>&lt;50%</td><td>60.06%</td><td>&lt;50%</td><td>51.83%</td><td>61.59%</td><td>51.83%</td></tr></tbody></table>

Note: AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression.
### 6.6.2. ML Trading Results Contrasted with HODL Strategy

HODL is a term derived from a misspelling of 'hold' that refers to buy-and-hold strategies in the context of Bitcoin and other cryptocurrencies. (It originated from a famous post on the internet forum 'bitcointalk': https://bitcointalk.org/index.php?topic=375643.0, accessed on 27 May 2021). In the Markowitz world, it is equivalent to the 'buy-and-hold' strategy, which will be used as our benchmark against which ML algorithms compete.

Over the five years (13 January 2015 to 31 December 2020), we set the training period $T_{train} = 4$ - year and the trading period $T_{trade} = 1$ - year. The investor buys 100,000$ worth of Bitcoin at the beginning of the trading session and sells it in the end. His gains are evaluated thanks to the following Rate of Return (RoR) formulation:

$$ \text{RoR} = \frac{\text{net gain from Bitcoin}}{\text{initial investment}}. \qquad (17) $$

The ML algorithms function as automated trading bots, with the following instructions: (i) if the price forecast is equal to the current price, do not take any action; (ii) if the price forecast is below the current price, trigger a sell signal; (iii) if the price forecast is above the current price, initiate a buy signal. By following these instructions, the trader can initiate automated trading (of course, by implementing additional stop-loss rules for his P&L). Transaction fees are ignored, as they are documented to be virtually non-existent. For instance, on 26 October 2020, two back-to-back transactions of 45,671 Bitcoin ($602 million) and 43,185 Bitcoin ($570 million), minutes apart, were sent from a Xapo wallet to two addresses. That corresponds to over $1.1 billion in Bitcoin. The total transaction fee of $3.54 spent was about the price of a Starbucks coffee. (See, e.g., https://decrypt.co/46346/ someone-just-sent-1-billion-in-bitcoin-paid-only-3-in-fees, accessed on 26 October 2020. For real-time mean transaction fees for BTC, see Coinmetrics website: https://network-charts.coinmetrics.io/, accessed on 27 May 2021).

Table 15 compares the profit and loss account (P&L) from the HODL strategy with that of each machine learning algorithm (in the case where the trader follows their price signals) we use all along in this paper. As a trader, we expect a positive RoR and as high as possible.

We observe that the best RoR is achieved by the HODL strategy (26.88%). Looking at our results, depending on the data set used, the best RoR is not always given by the same algorithm. Depending on the dataset we use, the best RoR is provided by (i) an AR(1) for cryptocurrencies (25.55%), (ii) an AR(1) for stocks and bonds (25.55%), (iii) an ANN using commodities (26%), (iv) by Ridge using all the variables (30.47%). There is no segmentation since the best results are obtained as we add financial variables. The cryptocurrency world is not the best trading strategy. ANN using commodities, we have the same result as all (26-26.88%).

Our results stand in sharp contrast with Atsalakis et al. [64] (PATSOS neuro-fuzzy = 37.34%): although the ML algorithms deliver high forecast accuracy, they do not necessarily convert into money (candlestick patterns can be tricky to non-experienced investors). For sensitivity analysis, we run again the trading strategy with coins bought in January 2019 and sold at the end of our study period (aka, December 2020). The results are displayed in Table 16. The latest timeframe chosen tends to exacerbate the forecast statistics due to a heightened speculative situation on cryptocurrency markets, but it does not change the core finding of this section (in favor of the HODL strategy for Bitcoin versus market gains issued from machine learning models).
### 6.6.2. ML Trading Results Contrasted with HODL Strategy

HODL is a term derived from a misspelling of 'hold' that refers to buy-and-hold strategies in the context of Bitcoin and other cryptocurrencies. (It originated from a famous post on the internet forum 'bitcointalk': https://bitcointalk.org/index.php?topic=375643.0, accessed on 27 May 2021). In the Markowitz world, it is equivalent to the 'buy-and-hold' strategy, which will be used as our benchmark against which ML algorithms compete.

Over the five years (13 January 2015 to 31 December 2020), we set the training period $T_{train} = 4$ - year and the trading period $T_{trade} = 1$ - year. The investor buys 100,000$ worth of Bitcoin at the beginning of the trading session and sells it in the end. His gains are evaluated thanks to the following Rate of Return (RoR) formulation:

$$ \text{RoR} = \frac{\text{net gain from Bitcoin}}{\text{initial investment}}. \qquad (17) $$

The ML algorithms function as automated trading bots, with the following instructions: (i) if the price forecast is equal to the current price, do not take any action; (ii) if the price forecast is below the current price, trigger a sell signal; (iii) if the price forecast is above the current price, initiate a buy signal. By following these instructions, the trader can initiate automated trading (of course, by implementing additional stop-loss rules for his P&L). Transaction fees are ignored, as they are documented to be virtually non-existent. For instance, on 26 October 2020, two back-to-back transactions of 45,671 Bitcoin ($602 million) and 43,185 Bitcoin ($570 million), minutes apart, were sent from a Xapo wallet to two addresses. That corresponds to over $1.1 billion in Bitcoin. The total transaction fee of $3.54 spent was about the price of a Starbucks coffee. (See, e.g., https://decrypt.co/46346/ someone-just-sent-1-billion-in-bitcoin-paid-only-3-in-fees, accessed on 26 October 2020. For real-time mean transaction fees for BTC, see Coinmetrics website: https://network-charts.coinmetrics.io/, accessed on 27 May 2021).

Table 15 compares the profit and loss account (P&L) from the HODL strategy with that of each machine learning algorithm (in the case where the trader follows their price signals) we use all along in this paper. As a trader, we expect a positive RoR and as high as possible.

We observe that the best RoR is achieved by the HODL strategy (26.88%). Looking at our results, depending on the data set used, the best RoR is not always given by the same algorithm. Depending on the dataset we use, the best RoR is provided by (i) an AR(1) for cryptocurrencies (25.55%), (ii) an AR(1) for stocks and bonds (25.55%), (iii) an ANN using commodities (26%), (iv) by Ridge using all the variables (30.47%). There is no segmentation since the best results are obtained as we add financial variables. The cryptocurrency world is not the best trading strategy. ANN using commodities, we have the same result as all (26-26.88%).

Our results stand in sharp contrast with Atsalakis et al. [64] (PATSOS neuro-fuzzy = 37.34%): although the ML algorithms deliver high forecast accuracy, they do not necessarily convert into money (candlestick patterns can be tricky to non-experienced investors). For sensitivity analysis, we run again the trading strategy with coins bought in January 2019 and sold at the end of our study period (aka, December 2020). The results are displayed in Table 16. The latest timeframe chosen tends to exacerbate the forecast statistics due to a heightened speculative situation on cryptocurrency markets, but it does not change the core finding of this section (in favor of the HODL strategy for Bitcoin versus market gains issued from machine learning models).
<table><caption>**Table 15.** Bitcoin Rate of Return (RoR) of ML algorithms against the HODL strategy.</caption><thead><tr><th>Strategy</th><th>Bitcoin RoR</th></tr></thead><tbody><tr><td>HODL</td><td>26.88%</td></tr><tr><td>Cryptos only</td><td></td></tr><tr><td>AR(1)</td><td>25.55%</td></tr><tr><td>ann</td><td>12.26%</td></tr><tr><td>random</td><td>18.93%</td></tr><tr><td>svm</td><td>0.05%</td></tr><tr><td>knn</td><td>19.00%</td></tr><tr><td>boost</td><td>22.47%</td></tr><tr><td>ridge</td><td>21.53%</td></tr><tr><td>Stocks/bonds/fx only</td><td></td></tr><tr><td>AR(1)</td><td>25.55%</td></tr><tr><td>ann</td><td>5.13%</td></tr><tr><td>random</td><td>21.50%</td></tr><tr><td>svm</td><td>0.04%</td></tr><tr><td>knn</td><td>17.48%</td></tr><tr><td>boost</td><td>22.48%</td></tr><tr><td>ridge</td><td>21.48%</td></tr><tr><td>Commodities only</td><td></td></tr><tr><td>AR(1)</td><td>25.55%</td></tr><tr><td>ann</td><td>26.00%</td></tr><tr><td>random</td><td>18.04%</td></tr><tr><td>svm</td><td>0.07%</td></tr><tr><td>knn</td><td>16.77%</td></tr><tr><td>boost</td><td>22.48%</td></tr><tr><td>ridge</td><td>13.00%</td></tr><tr><td>All</td><td></td></tr><tr><td>AR(1)</td><td>25.55%</td></tr><tr><td>ann</td><td>15.20%</td></tr><tr><td>random</td><td>22.75%</td></tr><tr><td>svm</td><td>0.05%</td></tr><tr><td>knn</td><td>24.23%</td></tr><tr><td>boost</td><td>22.37%</td></tr><tr><td>ridge</td><td>30.47%</td></tr></tbody></table>

Note: The RoR is computed for an initial investment of 100,000$ during 13 January 2015–31 December 2020, with three-year initial training period for the ML algorithms, and two-years of paper trading before cashing out. AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression.

Considering the different algorithms, the traditional econometrics AR(1) strategy fares surprisingly well in this context (best results for cryptocurrencies only, stocks/bonds/FX only). We note the stability of the AdaBoost and Random forest strictly after AR(1). ANN comes first (commodities only) due to finding better entry/exit prices in that particular case. Ridge regression performs best for all, being able to find as well an excellent combination of buying/selling points. Unlike other parts of our paper, we cannot say that one machine learning algorithm outperforms the others.

The philosophy of this last small exercise is that: (i) It is challenging to grab daily gains. Many investors report losses to the IRS for tax rebates ('Get rich or die tryin'). (ii) 'REKT': many investors are 'wrecked' by margin trading and leverage on BitMEX (reserved for shrewd FX traders). (iii) Machine Learning algorithms only give trading signals and do not teach how to trade. Traders resort to support and resistance lines, filters, technical indicators in TradingView (a list of trading rules such as Relative Strength Index (RSI), MACD curves, Exponential Moving Averages, Momentum, and their specifications can be
<table><caption>**Table 15.** Bitcoin Rate of Return (RoR) of ML algorithms against the HODL strategy.</caption><thead><tr><th>Strategy</th><th>Bitcoin RoR</th></tr></thead><tbody><tr><td>HODL</td><td>26.88%</td></tr><tr><td>Cryptos only</td><td></td></tr><tr><td>AR(1)</td><td>25.55%</td></tr><tr><td>ann</td><td>12.26%</td></tr><tr><td>random</td><td>18.93%</td></tr><tr><td>svm</td><td>0.05%</td></tr><tr><td>knn</td><td>19.00%</td></tr><tr><td>boost</td><td>22.47%</td></tr><tr><td>ridge</td><td>21.53%</td></tr><tr><td>Stocks/bonds/fx only</td><td></td></tr><tr><td>AR(1)</td><td>25.55%</td></tr><tr><td>ann</td><td>5.13%</td></tr><tr><td>random</td><td>21.50%</td></tr><tr><td>svm</td><td>0.04%</td></tr><tr><td>knn</td><td>17.48%</td></tr><tr><td>boost</td><td>22.48%</td></tr><tr><td>ridge</td><td>21.48%</td></tr><tr><td>Commodities only</td><td></td></tr><tr><td>AR(1)</td><td>25.55%</td></tr><tr><td>ann</td><td>26.00%</td></tr><tr><td>random</td><td>18.04%</td></tr><tr><td>svm</td><td>0.07%</td></tr><tr><td>knn</td><td>16.77%</td></tr><tr><td>boost</td><td>22.48%</td></tr><tr><td>ridge</td><td>13.00%</td></tr><tr><td>All</td><td></td></tr><tr><td>AR(1)</td><td>25.55%</td></tr><tr><td>ann</td><td>15.20%</td></tr><tr><td>random</td><td>22.75%</td></tr><tr><td>svm</td><td>0.05%</td></tr><tr><td>knn</td><td>24.23%</td></tr><tr><td>boost</td><td>22.37%</td></tr><tr><td>ridge</td><td>30.47%</td></tr></tbody></table>

Note: The RoR is computed for an initial investment of 100,000$ during 13 January 2015–31 December 2020, with three-year initial training period for the ML algorithms, and two-years of paper trading before cashing out. AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression.

Considering the different algorithms, the traditional econometrics AR(1) strategy fares surprisingly well in this context (best results for cryptocurrencies only, stocks/bonds/FX only). We note the stability of the AdaBoost and Random forest strictly after AR(1). ANN comes first (commodities only) due to finding better entry/exit prices in that particular case. Ridge regression performs best for all, being able to find as well an excellent combination of buying/selling points. Unlike other parts of our paper, we cannot say that one machine learning algorithm outperforms the others.

The philosophy of this last small exercise is that: (i) It is challenging to grab daily gains. Many investors report losses to the IRS for tax rebates ('Get rich or die tryin'). (ii) 'REKT': many investors are 'wrecked' by margin trading and leverage on BitMEX (reserved for shrewd FX traders). (iii) Machine Learning algorithms only give trading signals and do not teach how to trade. Traders resort to support and resistance lines, filters, technical indicators in TradingView (a list of trading rules such as Relative Strength Index (RSI), MACD curves, Exponential Moving Averages, Momentum, and their specifications can be
found in Shynkevich [120]). For a comprehensive examination of technical trading rules in cryptocurrency markets, see also [124].

<table><caption>**Table 16.** Sensitivity Analysis for Bitcoin Rate of Return (RoR) of ML algorithms against the HODL strategy.</caption><thead><tr><th>Strategy</th><th>Bitcoin RoR</th></tr></thead><tbody><tr><td>HODL</td><td>27.46%</td></tr><tr><td>Cryptos only</td><td></td></tr><tr><td>AR(1)</td><td>26.13%</td></tr><tr><td>ann</td><td>12.79%</td></tr><tr><td>random</td><td>19.55%</td></tr><tr><td>svm</td><td>0.06%</td></tr><tr><td>knn</td><td>19.61%</td></tr><tr><td>boost</td><td>23.06%</td></tr><tr><td>ridge</td><td>22.09%</td></tr><tr><td>Stocks/bonds/fx only</td><td></td></tr><tr><td>AR(1)</td><td>26.13%</td></tr><tr><td>ann</td><td>5.68%</td></tr><tr><td>random</td><td>21.98%</td></tr><tr><td>svm</td><td>0.05%</td></tr><tr><td>knn</td><td>18.06%</td></tr><tr><td>boost</td><td>23.05%</td></tr><tr><td>ridge</td><td>22.06%</td></tr><tr><td>Commodities only</td><td></td></tr><tr><td>AR(1)</td><td>26.13%</td></tr><tr><td>ann</td><td>26.58%</td></tr><tr><td>random</td><td>18.56%</td></tr><tr><td>svm</td><td>0.65%</td></tr><tr><td>knn</td><td>17.36%</td></tr><tr><td>boost</td><td>23.05%</td></tr><tr><td>ridge</td><td>13.61%</td></tr><tr><td>All</td><td></td></tr><tr><td>AR(1)</td><td>26.13%</td></tr><tr><td>ann</td><td>15.81%</td></tr><tr><td>random</td><td>23.32%</td></tr><tr><td>svm</td><td>0.07%</td></tr><tr><td>knn</td><td>24.81%</td></tr><tr><td>boost</td><td>23%</td></tr><tr><td>ridge</td><td>31.05%</td></tr></tbody></table>

Note: The RoR is computed for an initial investment of 100,000 $ during 01 January 2019–31 December 2020, with three-year initial training period for the ML algorithms, and two-years of paper trading before cashing out. AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression.

Bitcoin currently being in a bear market since the 19k$ price spike, our paper trading P&L challenges the thirst to be a millionaire ('When Lambo?') often found in the trading forums of the crypto-sphere, such as Reddit, where beginner day-traders dream of driving the most expensive sportscars—Lamborghinis.

## 7. Conclusions

Machine learning algorithms attempt to find natural patterns in data to enhance decision-making. Machine learning typically prescribes a vast collection of high-dimensional models attempting to predict quantities of interest to solve problems in computational finance while imposing regularization methods.
found in Shynkevich [120]). For a comprehensive examination of technical trading rules in cryptocurrency markets, see also [124].

<table><caption>**Table 16.** Sensitivity Analysis for Bitcoin Rate of Return (RoR) of ML algorithms against the HODL strategy.</caption><thead><tr><th>Strategy</th><th>Bitcoin RoR</th></tr></thead><tbody><tr><td>HODL</td><td>27.46%</td></tr><tr><td>Cryptos only</td><td></td></tr><tr><td>AR(1)</td><td>26.13%</td></tr><tr><td>ann</td><td>12.79%</td></tr><tr><td>random</td><td>19.55%</td></tr><tr><td>svm</td><td>0.06%</td></tr><tr><td>knn</td><td>19.61%</td></tr><tr><td>boost</td><td>23.06%</td></tr><tr><td>ridge</td><td>22.09%</td></tr><tr><td>Stocks/bonds/fx only</td><td></td></tr><tr><td>AR(1)</td><td>26.13%</td></tr><tr><td>ann</td><td>5.68%</td></tr><tr><td>random</td><td>21.98%</td></tr><tr><td>svm</td><td>0.05%</td></tr><tr><td>knn</td><td>18.06%</td></tr><tr><td>boost</td><td>23.05%</td></tr><tr><td>ridge</td><td>22.06%</td></tr><tr><td>Commodities only</td><td></td></tr><tr><td>AR(1)</td><td>26.13%</td></tr><tr><td>ann</td><td>26.58%</td></tr><tr><td>random</td><td>18.56%</td></tr><tr><td>svm</td><td>0.65%</td></tr><tr><td>knn</td><td>17.36%</td></tr><tr><td>boost</td><td>23.05%</td></tr><tr><td>ridge</td><td>13.61%</td></tr><tr><td>All</td><td></td></tr><tr><td>AR(1)</td><td>26.13%</td></tr><tr><td>ann</td><td>15.81%</td></tr><tr><td>random</td><td>23.32%</td></tr><tr><td>svm</td><td>0.07%</td></tr><tr><td>knn</td><td>24.81%</td></tr><tr><td>boost</td><td>23%</td></tr><tr><td>ridge</td><td>31.05%</td></tr></tbody></table>

Note: The RoR is computed for an initial investment of 100,000 $ during 01 January 2019–31 December 2020, with three-year initial training period for the ML algorithms, and two-years of paper trading before cashing out. AR(1) stands for the autoregressive model of order one; ann for the Artificial Neural Network model; random for the Random forest model; svm for the Support Vector Machine model; knn for the k-Nearest neighbor model; boost for the Adaboost model; and ridge for the Ridge regression.

Bitcoin currently being in a bear market since the 19k$ price spike, our paper trading P&L challenges the thirst to be a millionaire ('When Lambo?') often found in the trading forums of the crypto-sphere, such as Reddit, where beginner day-traders dream of driving the most expensive sportscars—Lamborghinis.

## 7. Conclusions

Machine learning algorithms attempt to find natural patterns in data to enhance decision-making. Machine learning typically prescribes a vast collection of high-dimensional models attempting to predict quantities of interest to solve problems in computational finance while imposing regularization methods.
In a seminal paper, Zhao and Hastie [8] warns us against the pitfalls of ‘black-box’ machine learning models and urge us to make proper use of (i) a good predictive model, (ii) a sound selection of the dataset, and (iii) visualization tools to ensure the quality of the research work.

This paper addresses the following central research questions: How far the is use of machine learning techniques useful to forecast daily movements of the price of Bitcoin? How strong is the relationship between cryptocurrencies and traditional financial assets? How to perform a trading strategy based on cryptocurrencies? We overcome the risks of machine learning in predicting Bitcoin spot and futures prices by documenting: (i) either the AdaBoost or Random forest algorithms perform as the ‘best’ machine learning models among the six considered and could be implemented in a banking institution’s internal computing system for Bitcoin forecastability. (ii) A financial market approach favors price relationships between asset classes (cryptocurrencies, stocks, bonds, foreign exchange, and commodities) for the dataset’s quality. (iii) We implement a myriad of visualization tools (e.g., Louvain clustering, self-organizing map, t-distributed SNE, Sieve diagrams, and multidimensional scaling) to strengthen our findings.

During the period under study, the key takeaway is that Bitcoin appears as a problematic asset to forecast, subject to frequent price swings, as highlighted by the latest end-of-year 2020 run-up. From our empirical results, Bitcoin appears segmented from traditional financial and commodity markets. It seems to react more to the information content stemming from other cryptocurrencies, enhancing the forecast accuracy of Bitcoin. Whatever the period in which we work (full period, sub-sample periods), the best result is achieved during the full period (lowest MAPE = 0.15).

Across the trading strategies, we have documented that (i) machine learning algorithms (configured as bots following buy/sell signals) do not teach how to trade, (ii) the buy-and-hold strategy appears the best, which incites owners of Bitcoin to ‘hodl’. Because of the variability of the forecasting results, it is necessary to let cool heads prevail before investing in Bitcoin with private individuals’ money. Wealthy clients from investment banks can have access to Bitcoin funds in special entities such as Morgan Stanley, for individuals with “an aggressive risk tolerance” and a net worth of $2 million held by the firm. (See CNBC (2021) at https://www.cnbc.com/2021/03/17/bitcoin-morgan-stanley-is-the-first-big-us-bank-to-offer-wealthy-clients-access-to-bitcoin-funds.html, accessed on 17 March 2021). Such clients are especially waiting for the approval of ETF funds by the U.S. SEC led by the new appointment of Mr. Gary Gensler, a professor in the digital economy from MIT. The SEC’s cryptocurrency commissioner, Ms. Hester Peirce (dubbed “crypto mom”), has long advocated a Bitcoin ETF. The argument behind the use of cryptocurrencies lies in the modernization of the financial system, whereby assets worth billion dollars can be transferred securely and quasi-instantly (compared to the SWIFT/IBAN system) between agents. Transaction fees are recorded to be minimal. It is possible to follow the transactions in real-time on blockchain.com. For example, one timestamp 6 April 2021 13:22 (UTC) records $1,783,170,000 exchanged through Bitcoin for a transaction fee of $45.45. At the time of writing, only Canada has approved the opening of ETFs on Bitcoin (such as Purpose Investment, Evolve Funds Group, or CI Galaxy). (See Coindesk (2021) at https://www.coindesk.com/third-bitcoin-etf-expected-to-launch-in-canada-this-week, accessed on 8 March 2021).

Overall, we believe that Bitcoin remains a difficult beast to tame for a modeler, and that the debate on its pricing and forecasting accuracy remains open. We wish to insist here on the speculative nature of investing in Bitcoin, which remains an artificial mechanism without an underlying (unless it can be considered that the proof-of-work algorithm is a receivable underlying in financial derivatives markets?). It remains hard to gauge the fundamental value of Bitcoin from an economist’s standpoint, hence the challenge attached to any attempt at forecasting.

As avenues for future research, we would like to stress that our method can be extended to alt-coins, with a specific interest obviously for Ethereum, Litecoin, or Ripple. (i.e.,
In a seminal paper, Zhao and Hastie [8] warns us against the pitfalls of ‘black-box’ machine learning models and urge us to make proper use of (i) a good predictive model, (ii) a sound selection of the dataset, and (iii) visualization tools to ensure the quality of the research work.

This paper addresses the following central research questions: How far the is use of machine learning techniques useful to forecast daily movements of the price of Bitcoin? How strong is the relationship between cryptocurrencies and traditional financial assets? How to perform a trading strategy based on cryptocurrencies? We overcome the risks of machine learning in predicting Bitcoin spot and futures prices by documenting: (i) either the AdaBoost or Random forest algorithms perform as the ‘best’ machine learning models among the six considered and could be implemented in a banking institution’s internal computing system for Bitcoin forecastability. (ii) A financial market approach favors price relationships between asset classes (cryptocurrencies, stocks, bonds, foreign exchange, and commodities) for the dataset’s quality. (iii) We implement a myriad of visualization tools (e.g., Louvain clustering, self-organizing map, t-distributed SNE, Sieve diagrams, and multidimensional scaling) to strengthen our findings.

During the period under study, the key takeaway is that Bitcoin appears as a problematic asset to forecast, subject to frequent price swings, as highlighted by the latest end-of-year 2020 run-up. From our empirical results, Bitcoin appears segmented from traditional financial and commodity markets. It seems to react more to the information content stemming from other cryptocurrencies, enhancing the forecast accuracy of Bitcoin. Whatever the period in which we work (full period, sub-sample periods), the best result is achieved during the full period (lowest MAPE = 0.15).

Across the trading strategies, we have documented that (i) machine learning algorithms (configured as bots following buy/sell signals) do not teach how to trade, (ii) the buy-and-hold strategy appears the best, which incites owners of Bitcoin to ‘hodl’. Because of the variability of the forecasting results, it is necessary to let cool heads prevail before investing in Bitcoin with private individuals’ money. Wealthy clients from investment banks can have access to Bitcoin funds in special entities such as Morgan Stanley, for individuals with “an aggressive risk tolerance” and a net worth of $2 million held by the firm. (See CNBC (2021) at https://www.cnbc.com/2021/03/17/bitcoin-morgan-stanley-is-the-first-big-us-bank-to-offer-wealthy-clients-access-to-bitcoin-funds.html, accessed on 17 March 2021). Such clients are especially waiting for the approval of ETF funds by the U.S. SEC led by the new appointment of Mr. Gary Gensler, a professor in the digital economy from MIT. The SEC’s cryptocurrency commissioner, Ms. Hester Peirce (dubbed “crypto mom”), has long advocated a Bitcoin ETF. The argument behind the use of cryptocurrencies lies in the modernization of the financial system, whereby assets worth billion dollars can be transferred securely and quasi-instantly (compared to the SWIFT/IBAN system) between agents. Transaction fees are recorded to be minimal. It is possible to follow the transactions in real-time on blockchain.com. For example, one timestamp 6 April 2021 13:22 (UTC) records $1,783,170,000 exchanged through Bitcoin for a transaction fee of $45.45. At the time of writing, only Canada has approved the opening of ETFs on Bitcoin (such as Purpose Investment, Evolve Funds Group, or CI Galaxy). (See Coindesk (2021) at https://www.coindesk.com/third-bitcoin-etf-expected-to-launch-in-canada-this-week, accessed on 8 March 2021).

Overall, we believe that Bitcoin remains a difficult beast to tame for a modeler, and that the debate on its pricing and forecasting accuracy remains open. We wish to insist here on the speculative nature of investing in Bitcoin, which remains an artificial mechanism without an underlying (unless it can be considered that the proof-of-work algorithm is a receivable underlying in financial derivatives markets?). It remains hard to gauge the fundamental value of Bitcoin from an economist’s standpoint, hence the challenge attached to any attempt at forecasting.

As avenues for future research, we would like to stress that our method can be extended to alt-coins, with a specific interest obviously for Ethereum, Litecoin, or Ripple. (i.e.,
the “main” alt-coins, as listed on https://coinmarketcap.com/, accessed on 27 May 2021). Having forecast the spot and futures prices of Bitcoin in this article, it might be interesting to look at the spreads between the two next. Indeed, with the “democratization” of ML among institutional investors, we can imagine that there will be more significant volumes of trading and arbitrage between the two markets, but the differences in performance between the two were due for a certain time. reflect distinct populations of participants.

**Author Contributions:** Conceptualization, J.C. and D.G.; methodology, J.C. and D.G.; software, J.C.; validation, J.C., D.G. and S.G.; data curation, J.C.; writing—original draft preparation, J.C. and D.G.; writing—review and editing, J.C., D.G. and S.G.; supervision, D.G.; project administration, J.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data is publicly available on Coinbase: https://www.coinbase.com/fr/ accessed on 27 May 2021, Fred: https://fred.stlouisfed.org/ accessed on 27 May 2021.

**Acknowledgments:** For useful comments on earlier drafts, we thank Sofiane Aboura and Laurent Gauthier. The authors also wish to thank conference participants at the University of Geneva's MAF (Mathematical and Statistical Methods for Actuarial Sciences and Finance) in November 2020, at the 1st Research Day of the Macro-Finance Axis (Research Lab LED, University Paris 8) in April 2021, as well as at the RIFED Global Virtual Conference on Fintech, Business Ecosystem & Economic Development in June 2021.

**Conflicts of Interest:** The authors declare no conflict of interest.

## References

1. Misheva, B.H.; Osterrieder, J.; Hirsa, A.; Kulkarni, O.; Lin, S.F. Explainable AI in Credit Risk Management. arXiv 2021, arXiv:2103.00949.

2. Bussmann, N.; Giudici, P.; Marinelli, D.; Papenbrock, J. Explainable machine learning in credit risk management. Comput. Econ. 2021, 57, 203–216. [CrossRef]

3. Islam, S.R.; Eberle, W.; Bundy, S.; Ghafoor, S.K. Infusing domain knowledge in ai-based “black box” models for better explainability with application in bankruptcy prediction. arXiv 2019, arXiv:1905.11474.

4. Cohen, G. Forecasting Bitcoin Trends Using Algorithmic Learning Systems. Entropy 2020, 22, 838. [CrossRef] [PubMed]

5. Li, Y.; Zheng, Z.; Dai, H.N. Enhancing Bitcoin Price Fluctuation Prediction Using Attentive LSTM and Embedding Network. Appl. Sci. 2020, 10, 4872. [CrossRef]

6. Livieris, I.E.; Kiriakidou, N.; Stavroyiannis, S.; Pintelas, P. An Advanced CNN-LSTM Model for Cryptocurrency Forecasting. Electronics 2021, 10, 287. [CrossRef]

7. Chen, T.H.; Chen, M.Y.; Du, G.T. The determinants of bitcoin's price: Utilization of GARCH and machine learning approaches. Comput. Econ. 2021, 57, 267–280. [CrossRef]

8. Zhao, Q.; Hastie, T. Causal interpretations of black-box models. J. Bus. Econ. Stat. 2021, 39, 272–281. [CrossRef]

9. Farrell, M.H.; Liang, T.; Misra, S. Deep neural networks for estimation and inference. Econometrica 2021, 89, 181–213. [CrossRef]

10. De Prado, M.M.L. Machine Learning for Asset Managers; Cambridge University Press: Cambridge, UK, 2020.

11. Abadie, A.; Kasy, M. Choosing among regularized estimators in empirical economics: The risk of machine learning. Rev. Econ. Stat. 2019, 101, 743–762. [CrossRef]

12. Athey, S.; Imbens, G.W. Machine learning methods that economists should know about. Annu. Rev. Econ. 2019, 11, 685–725. [CrossRef]

13. Nakamoto, S. Bitcoin: A Peer-to-Peer Electronic Cash System; White Paper; Bitcoin.org: New York, NY, USA 2009.

14. Reuters. Bitcoin Hits $1 Trillion Market Cap, Surges to Fresh All-Time Peak. Technical Report. Available online: https://www.reuters.com/article/us-crypto-currency-bitcoin-idUSKBN2AJ0GC (accessed on 19 February 2021).

15. Abedifar, P.; Giudici, P.; Hashem, S.Q. Heterogeneous market structure and systemic risk: Evidence from dual banking systems. J. Financ. Stab. 2017, 33, 96–119. [CrossRef]

16. Ahelegbey, D.F.; Billio, M.; Casarin, R. Bayesian graphical models for structural vector autoregressive processes. J. Appl. Econom. 2016, 31, 357–386. [CrossRef]

17. Billio, M.; Getmansky, M.; Lo, A.W.; Pelizzon, L. Econometric measures of connectedness and systemic risk in the finance and insurance sectors. J. Financ. Econ. 2012, 104, 535–559. [CrossRef]
the “main” alt-coins, as listed on https://coinmarketcap.com/, accessed on 27 May 2021). Having forecast the spot and futures prices of Bitcoin in this article, it might be interesting to look at the spreads between the two next. Indeed, with the “democratization” of ML among institutional investors, we can imagine that there will be more significant volumes of trading and arbitrage between the two markets, but the differences in performance between the two were due for a certain time. reflect distinct populations of participants.

**Author Contributions:** Conceptualization, J.C. and D.G.; methodology, J.C. and D.G.; software, J.C.; validation, J.C., D.G. and S.G.; data curation, J.C.; writing—original draft preparation, J.C. and D.G.; writing—review and editing, J.C., D.G. and S.G.; supervision, D.G.; project administration, J.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data is publicly available on Coinbase: https://www.coinbase.com/fr/ accessed on 27 May 2021, Fred: https://fred.stlouisfed.org/ accessed on 27 May 2021.

**Acknowledgments:** For useful comments on earlier drafts, we thank Sofiane Aboura and Laurent Gauthier. The authors also wish to thank conference participants at the University of Geneva's MAF (Mathematical and Statistical Methods for Actuarial Sciences and Finance) in November 2020, at the 1st Research Day of the Macro-Finance Axis (Research Lab LED, University Paris 8) in April 2021, as well as at the RIFED Global Virtual Conference on Fintech, Business Ecosystem & Economic Development in June 2021.

**Conflicts of Interest:** The authors declare no conflict of interest.

## References

1. Misheva, B.H.; Osterrieder, J.; Hirsa, A.; Kulkarni, O.; Lin, S.F. Explainable AI in Credit Risk Management. *arXiv* 2021, arXiv:2103.00949.

2. Bussmann, N.; Giudici, P.; Marinelli, D.; Papenbrock, J. Explainable machine learning in credit risk management. *Comput. Econ.* 2021, 57, 203–216. [CrossRef]

3. Islam, S.R.; Eberle, W.; Bundy, S.; Ghafoor, S.K. Infusing domain knowledge in ai-based “black box” models for better explainability with application in bankruptcy prediction. *arXiv* 2019, arXiv:1905.11474.

4. Cohen, G. Forecasting Bitcoin Trends Using Algorithmic Learning Systems. *Entropy* 2020, 22, 838. [CrossRef] [PubMed]

5. Li, Y.; Zheng, Z.; Dai, H.N. Enhancing Bitcoin Price Fluctuation Prediction Using Attentive LSTM and Embedding Network. *Appl. Sci.* 2020, 10, 4872. [CrossRef]

6. Livieris, I.E.; Kiriakidou, N.; Stavroyiannis, S.; Pintelas, P. An Advanced CNN-LSTM Model for Cryptocurrency Forecasting. *Electronics* 2021, 10, 287. [CrossRef]

7. Chen, T.H.; Chen, M.Y.; Du, G.T. The determinants of bitcoin's price: Utilization of GARCH and machine learning approaches. *Comput. Econ.* 2021, 57, 267–280. [CrossRef]

8. Zhao, Q.; Hastie, T. Causal interpretations of black-box models. *J. Bus. Econ. Stat.* 2021, 39, 272–281. [CrossRef]

9. Farrell, M.H.; Liang, T.; Misra, S. Deep neural networks for estimation and inference. *Econometrica* 2021, 89, 181–213. [CrossRef]

10. De Prado, M.M.L. *Machine Learning for Asset Managers*; Cambridge University Press: Cambridge, UK, 2020.

11. Abadie, A.; Kasy, M. Choosing among regularized estimators in empirical economics: The risk of machine learning. *Rev. Econ. Stat.* 2019, 101, 743–762. [CrossRef]

12. Athey, S.; Imbens, G.W. Machine learning methods that economists should know about. *Annu. Rev. Econ.* 2019, 11, 685–725. [CrossRef]

13. Nakamoto, S. *Bitcoin: A Peer-to-Peer Electronic Cash System*; White Paper; Bitcoin.org: New York, NY, USA 2009.

14. Reuters. Bitcoin Hits $1 Trillion Market Cap, Surges to Fresh All-Time Peak. Technical Report. Available online: https://www.reuters.com/article/us-crypto-currency-bitcoin-idUSKBN2AJ0GC (accessed on 19 February 2021).

15. Abedifar, P.; Giudici, P.; Hashem, S.Q. Heterogeneous market structure and systemic risk: Evidence from dual banking systems. *J. Financ. Stab.* 2017, 33, 96–119. [CrossRef]

16. Ahelegbey, D.F.; Billio, M.; Casarin, R. Bayesian graphical models for structural vector autoregressive processes. *J. Appl. Econom.* 2016, 31, 357–386. [CrossRef]

17. Billio, M.; Getmansky, M.; Lo, A.W.; Pelizzon, L. Econometric measures of connectedness and systemic risk in the finance and insurance sectors. *J. Financ. Econ.* 2012, 104, 535–559. [CrossRef]
18. Baumöhl, E. Are cryptocurrencies connected to forex? A quantile cross-spectral approach. *Financ. Res. Lett.* **2019**, *29*, 363–372.
[CrossRef]

19. Dahir, A.M.; Mahat, F.; Noordin, B.A.A.; Ab Razak, N.H. Dynamic connectedness between Bitcoin and equity market information across BRICS countries: Evidence from TVP-VAR connectedness approach. *Int. J. Manag. Financ.* **2019**, *16*, 357–371. [CrossRef]

20. Le, T.L.; Abakah, E.J.A.; Tiwari, A.K. Time and frequency domain connectedness and spill-over among fintech, green bonds and cryptocurrencies in the age of the fourth industrial revolution. *Technol. Forecast. Soc. Chang.* **2021**, *162*, 120382. [CrossRef] [PubMed]

21. Mensi, W.; Sensoy, A.; Aslan, A.; Kang, S.H. High-frequency asymmetric volatility connectedness between Bitcoin and major precious metals markets. *N. Am. J. Econ. Financ.* **2019**, *50*, 101031. [CrossRef]

22. Cao, L.; Gu, Q. Dynamic support vector machines for non-stationary time series forecasting. *Intell. Data Anal.* **2002**, *6*, 67–83.
[CrossRef]

23. Kurbatsky, V.G.; Sidorov, D.N.; Spiraev, V.A.; Tomin, N.V. Forecasting nonstationary time series based on Hilbert-Huang transform and machine learning. *Autom. Remote. Control* **2014**, *75*, 922–934. [CrossRef]

24. Wang, X.; Han, M. Online sequential extreme learning machine with kernels for nonstationary time series prediction. *Neurocomputing* **2014**, *145*, 90–97. [CrossRef]

25. Rosenblatt, F. Perceptron simulation experiments. *Proc. IRE 1960*, *48*, 301–309. [CrossRef]

26. Russell, S.J.; Norvig, P. *Artificial Intelligence: A Modern Approach*; Pearson Education Limited: Kuala Lumpur, Malaysia, 2016.

27. Iworiso, J.; Vrontos, S. On the Directional Predictability of Equity Premium Using Machine Learning Techniques. *J. Forecast.* **2020**, *39*, 449–469. [CrossRef]

28. Foley, S.; Karlsen, J.R.; Putninš, T.J. Sex, drugs, and bitcoin: How much illegal activity is financed through cryptocurrencies? *Rev. Financ. Stud.* **2019**, *32*, 1798–1853. [CrossRef]

29. Easley, D.; O'Hara, M.; Basu, S. From mining to markets: The evolution of bitcoin transaction fees. *J. Financ. Econ.* **2019**, *134*, 91–109. [CrossRef]

30. Prat, J.; Walter, B. An equilibrium model of the market for bitcoin mining. *J. Political Econ.* **2021**, [CrossRef]

31. Makarov, I.; Schoar, A. Trading and arbitrage in cryptocurrency markets. *J. Financ. Econ.* **2020**, *135*, 293–319. [CrossRef]

32. Cheng, S.F.; De Franco, G.; Jiang, H.; Lin, P. Riding the blockchain mania: public firms' speculative 8-K disclosures. *Manag. Sci.* **2019**, *65*, 5901–5913.

33. Wei, Y.; Dukes, A. Cryptocurrency Adoption with Speculative Price Bubbles. *Mark. Sci.* **2021**, *40*, 241–260. [CrossRef]

34. Pagnotta, E. Decentralizing Money: Bitcoin Prices and Blockchain Security. *Rev. Financ. Stud.* **2020**. [CrossRef]

35. Fantazzini, D.; Nigmatullin, E.; Sukhanovskaya, V.; Ivliev, S. *Everything You Always Wanted to Know about Bitcoin Modelling but Were Afraid to Ask*; MPRA Paper No. 71946; MPRA: Munich, Germany, 2016; 50p.

36. Briere, M.; Oosterlinck, K.; Szafarz, A. Virtual currency, tangible return: Portfolio diversification with bitcoin. *J. Asset Manag.* **2015**, *16*, 365–373. [CrossRef]

37. Aslanidis, N.; Bariviera, A.F.; Martínez-Ibañez, O. An analysis of cryptocurrencies conditional cross correlations. *Financ. Res. Lett.* **2019**, *31*, 130–137. [CrossRef]

38. Caporale, G.M.; Zekokh, T. Modelling volatility of cryptocurrencies using Markov-Switching GARCH models. *Res. Int. Bus. Financ.* **2019**, *48*, 143–155. [CrossRef]

39. Bariviera, A.F.; Basgall, M.J.; Hasperué, W.; Naiouf, M. Some stylized facts of the Bitcoin market. *Phys. A Stat. Mech. Appl.* **2017**, *484*, 82–90. [CrossRef]

40. Alvarez-Ramirez, J.; Rodriguez, E.; Ibarra-Valdez, C. Long-range correlations and asymmetry in the Bitcoin market. *Phys. A Stat. Mech. Appl.* **2018**, *492*, 948–955. [CrossRef]

41. Begušić, S.; Kostanjčar, Z.; Stanley, H.E.; Podobnik, B. Scaling properties of extreme price fluctuations in Bitcoin markets. *Phys. A Stat. Mech. Appl.* **2018**, *510*, 400–406. [CrossRef]

42. Khuntia, S.; Pattanayak, J. Adaptive long memory in volatility of intra-day bitcoin returns and the impact of trading volume. *Financ. Res. Lett.* **2020**, *32*, 101077. [CrossRef]

43. Al-Yahyaee, K.H.; Mensi, W.; Yoon, S.M. Efficiency, multifractality, and the long-memory property of the Bitcoin market: A comparative analysis with stock, currency, and gold markets. *Financ. Res. Lett.* **2018**, *27*, 228–234. [CrossRef]

44. Phillip, A.; Chan, J.; Peiris, S. On long memory effects in the volatility measure of Cryptocurrencies. *Financ. Res. Lett.* **2019**, *28*, 95–100. [CrossRef]

45. Mensi, W.; Al-Yahyaee, K.H.; Kang, S.H. Structural breaks and double long memory of cryptocurrency prices: A comparative analysis from Bitcoin and Ethereum. *Financ. Res. Lett.* **2019**, *29*, 222–230. [CrossRef]

46. Su, C.W.; Li, Z.Z.; Tao, R.; Si, D.K. Testing for Multiple Bubbles in Bitcoin Markets: A. *Econ. Bull.* **2017**, *36*, 843–850.

47. Guegan, D.; Frunza, M. Is the Bitcoin Rush Over? In *Handbook: Cryptofinance and Mechanism of Exchange*; Springer: Berlin, Germany, 2018.

48. Geuder, J.; Kinateder, H.; Wagner, N.F. Cryptocurrencies as financial bubbles: The case of Bitcoin. *Financ. Res. Lett.* **2019**, *31*, 179–184 [CrossRef]

49. Guesmi, K.; Saadi, S.; Abid, I.; Ftiti, Z. Portfolio diversification with virtual currency: Evidence from bitcoin. *Int. Rev. Financ. Anal.* **2019**, *63*, 431–437. [CrossRef]

50. Dyhrberg, A.H. Hedging capabilities of bitcoin. Is it the virtual gold? *Financ. Res. Lett.* **2016**, *16*, 139–144. [CrossRef]
18. Baumöhl, E. Are cryptocurrencies connected to forex? A quantile cross-spectral approach. *Financ. Res. Lett.* **2019**, *29*, 363–372.
[CrossRef]

19. Dahir, A.M.; Mahat, F.; Noordin, B.A.A.; Ab Razak, N.H. Dynamic connectedness between Bitcoin and equity market information across BRICS countries: Evidence from TVP-VAR connectedness approach. *Int. J. Manag. Financ.* **2019**, *16*, 357–371. [CrossRef]

20. Le, T.L.; Abakah, E.J.A.; Tiwari, A.K. Time and frequency domain connectedness and spill-over among fintech, green bonds and cryptocurrencies in the age of the fourth industrial revolution. *Technol. Forecast. Soc. Chang.* **2021**, *162*, 120382. [CrossRef] [PubMed]

21. Mensi, W.; Sensoy, A.; Aslan, A.; Kang, S.H. High-frequency asymmetric volatility connectedness between Bitcoin and major precious metals markets. *N. Am. J. Econ. Financ.* **2019**, *50*, 101031. [CrossRef]

22. Cao, L.; Gu, Q. Dynamic support vector machines for non-stationary time series forecasting. *Intell. Data Anal.* **2002**, *6*, 67–83.
[CrossRef]

23. Kurbatsky, V.G.; Sidorov, D.N.; Spiraev, V.A.; Tomin, N.V. Forecasting nonstationary time series based on Hilbert-Huang transform and machine learning. *Autom. Remote. Control* **2014**, *75*, 922–934. [CrossRef]

24. Wang, X.; Han, M. Online sequential extreme learning machine with kernels for nonstationary time series prediction. *Neurocomputing* **2014**, *145*, 90–97. [CrossRef]

25. Rosenblatt, F. Perceptron simulation experiments. *Proc. IRE 1960*, *48*, 301–309. [CrossRef]

26. Russell, S.J.; Norvig, P. *Artificial Intelligence: A Modern Approach*; Pearson Education Limited: Kuala Lumpur, Malaysia, 2016.

27. Iworiso, J.; Vrontos, S. On the Directional Predictability of Equity Premium Using Machine Learning Techniques. *J. Forecast.* **2020**, *39*, 449–469. [CrossRef]

28. Foley, S.; Karlsen, J.R.; Putninš, T.J. Sex, drugs, and bitcoin: How much illegal activity is financed through cryptocurrencies? *Rev. Financ. Stud.* **2019**, *32*, 1798–1853. [CrossRef]

29. Easley, D.; O'Hara, M.; Basu, S. From mining to markets: The evolution of bitcoin transaction fees. *J. Financ. Econ.* **2019**, *134*, 91–109. [CrossRef]

30. Prat, J.; Walter, B. An equilibrium model of the market for bitcoin mining. *J. Political Econ.* **2021**, [CrossRef]

31. Makarov, I.; Schoar, A. Trading and arbitrage in cryptocurrency markets. *J. Financ. Econ.* **2020**, *135*, 293–319. [CrossRef]

32. Cheng, S.F.; De Franco, G.; Jiang, H.; Lin, P. Riding the blockchain mania: public firms' speculative 8-K disclosures. *Manag. Sci.* **2019**, *65*, 5901–5913.

33. Wei, Y.; Dukes, A. Cryptocurrency Adoption with Speculative Price Bubbles. *Mark. Sci.* **2021**, *40*, 241–260. [CrossRef]

34. Pagnotta, E. Decentralizing Money: Bitcoin Prices and Blockchain Security. *Rev. Financ. Stud.* **2020**. [CrossRef]

35. Fantazzini, D.; Nigmatullin, E.; Sukhanovskaya, V.; Ivliev, S. *Everything You Always Wanted to Know about Bitcoin Modelling but Were Afraid to Ask*; MPRA Paper No. 71946; MPRA: Munich, Germany, 2016; 50p.

36. Briere, M.; Oosterlinck, K.; Szafarz, A. Virtual currency, tangible return: Portfolio diversification with bitcoin. *J. Asset Manag.* **2015**, *16*, 365–373. [CrossRef]

37. Aslanidis, N.; Bariviera, A.F.; Martínez-Ibañez, O. An analysis of cryptocurrencies conditional cross correlations. *Financ. Res. Lett.* **2019**, *31*, 130–137. [CrossRef]

38. Caporale, G.M.; Zekokh, T. Modelling volatility of cryptocurrencies using Markov-Switching GARCH models. *Res. Int. Bus. Financ.* **2019**, *48*, 143–155. [CrossRef]

39. Bariviera, A.F.; Basgall, M.J.; Hasperué, W.; Naiouf, M. Some stylized facts of the Bitcoin market. *Phys. A Stat. Mech. Appl.* **2017**, *484*, 82–90. [CrossRef]

40. Alvarez-Ramirez, J.; Rodriguez, E.; Ibarra-Valdez, C. Long-range correlations and asymmetry in the Bitcoin market. *Phys. A Stat. Mech. Appl.* **2018**, *492*, 948–955. [CrossRef]

41. Begušić, S.; Kostanjčar, Z.; Stanley, H.E.; Podobnik, B. Scaling properties of extreme price fluctuations in Bitcoin markets. *Phys. A Stat. Mech. Appl.* **2018**, *510*, 400–406. [CrossRef]

42. Khuntia, S.; Pattanayak, J. Adaptive long memory in volatility of intra-day bitcoin returns and the impact of trading volume. *Financ. Res. Lett.* **2020**, *32*, 101077. [CrossRef]

43. Al-Yahyaee, K.H.; Mensi, W.; Yoon, S.M. Efficiency, multifractality, and the long-memory property of the Bitcoin market: A comparative analysis with stock, currency, and gold markets. *Financ. Res. Lett.* **2018**, *27*, 228–234. [CrossRef]

44. Phillip, A.; Chan, J.; Peiris, S. On long memory effects in the volatility measure of Cryptocurrencies. *Financ. Res. Lett.* **2019**, *28*, 95–100. [CrossRef]

45. Mensi, W.; Al-Yahyaee, K.H.; Kang, S.H. Structural breaks and double long memory of cryptocurrency prices: A comparative analysis from Bitcoin and Ethereum. *Financ. Res. Lett.* **2019**, *29*, 222–230. [CrossRef]

46. Su, C.W.; Li, Z.Z.; Tao, R.; Si, D.K. Testing for Multiple Bubbles in Bitcoin Markets: A. *Econ. Bull.* **2017**, *36*, 843–850.

47. Guegan, D.; Frunza, M. Is the Bitcoin Rush Over? In *Handbook: Cryptofinance and Mechanism of Exchange*; Springer: Berlin, Germany, 2018.

48. Geuder, J.; Kinateder, H.; Wagner, N.F. Cryptocurrencies as financial bubbles: The case of Bitcoin. *Financ. Res. Lett.* **2019**, *31*, 179–184 [CrossRef]

49. Guesmi, K.; Saadi, S.; Abid, I.; Ftiti, Z. Portfolio diversification with virtual currency: Evidence from bitcoin. *Int. Rev. Financ. Anal.* **2019**, *63*, 431–437. [CrossRef]

50. Dyhrberg, A.H. Hedging capabilities of bitcoin. Is it the virtual gold? *Financ. Res. Lett.* **2016**, *16*, 139–144. [CrossRef]
51. Polasik, M.; Piotrowska, A.I.; Wisniewski, T.P.; Kotkowski, R.; Lightfoot, G. Price fluctuations and the use of Bitcoin: An empirical inquiry. *Int. J. Electron. Commer.* **2015**, *20*, 9–49. [CrossRef]

52. Bouri, E.; Molnár, P.; Azzi, G.; Roubaud, D.; Hagfors, L.I. On the hedge and safe haven properties of Bitcoin: Is it really more than a diversifier? *Financ. Res. Lett.* **2017**, *20*, 192–198. [CrossRef]

53. Selmi, R.; Mensi, W.; Hammoudeh, S.; Bouoiyour, J. Is Bitcoin a hedge, a safe haven or a diversifier for oil price movements? A comparison with gold. *Energy Econ.* **2018**, *74*, 787–801. [CrossRef]

54. Kurka, J. Do cryptocurrencies and traditional asset classes influence each other? *Financ. Res. Lett.* **2019**, *31*, 38–46. [CrossRef]

55. Zargar, F.N.; Kumar, D. Informational inefficiency of Bitcoin: A study based on high-frequency data. *Res. Int. Bus. Financ.* **2019**, *47*, 344–353. [CrossRef]

56. Fang, L.; Bouri, E.; Gupta, R.; Roubaud, D. Does global economic uncertainty matter for the volatility and hedging effectiveness of Bitcoin? *Int. Rev. Financ. Anal.* **2019**, *61*, 29–36. [CrossRef]

57. Gillaizeau, M.; Jayasekera, R.; Maaitah, A.; Mishra, T.; Parhi, M.; Volokitina, E. Giver and the receiver: Understanding spillover effects and predictive power in cross-market Bitcoin prices. *Int. Rev. Financ. Anal.* **2019**, *63*, 86–104. [CrossRef]

58. Wołk, K. Advanced social media sentiment analysis for short-term cryptocurrency price prediction. *Expert Syst.* **2020**, *37*, e12493. [CrossRef]

59. Shen, D.; Urquhart, A.; Wang, P. Does twitter predict Bitcoin? *Econ. Lett.* **2019**, *174*, 118–122. [CrossRef]

60. Philippas, D.; Rjiba, H.; Guesmi, K.; Goutte, S. Media attention and Bitcoin prices. *Financ. Res. Lett.* **2019**, *30*, 37–43. [CrossRef]

61. Guégan, D.; Renault, T. Does investor sentiment on social media provide robust information for Bitcoin returns predictability? *Financ. Res. Lett.* **2021**, *38*, 101494. [CrossRef]

62. Dey, A.K.; Akcora, C.G.; Gel, Y.R.; Kantarcioglu, M. On the role of local blockchain network features in cryptocurrency price formation. *Can. J. Stat.* **2020**, *48*, 561–581. [CrossRef]

63. Nicola, G.; Cerchiello, P.; Aste, T. Information network modeling for US banking systemic risk. *Entropy* **2020**, *22*, 1331. [CrossRef]

64. Atsalakis, G.S.; Atsalaki, I.G.; Pasiouras, F.; Zopounidis, C. Bitcoin price forecasting with neuro-fuzzy techniques. *Eur. J. Oper. Res.* **2019**, *276*, 770–780. [CrossRef]

65. Jang, H.; Lee, J. An empirical study on modeling and prediction of bitcoin prices with bayesian neural networks based on blockchain information. *IEEE Access* **2017**, *6*, 5427–5437. [CrossRef]

66. Mallqui, D.C.; Fernandes, R.A. Predicting the direction, maximum, minimum and closing prices of daily Bitcoin exchange rate using machine learning techniques. *Appl. Soft Comput.* **2019**, *75*, 596–606. [CrossRef]

67. Nakano, M.; Takahashi, A.; Takahashi, S. Bitcoin technical trading with artificial neural network. *Phys. A Stat. Mech. Appl.* **2018**, *510*, 587–609. [CrossRef]

68. Sun, X.; Liu, M.; Sima, Z. A novel cryptocurrency price trend forecasting model based on LightGBM. *Financ. Res. Lett.* **2020**, *32*, 101084. [CrossRef]

69. Giudici, P.; Polinesi, G. Crypto price discovery through correlation networks. *Ann. Oper. Res.* **2021**, *299*, 443–457. [CrossRef]

70. Jay, P.; Kalariya, V.; Parmar, P.; Tanwar, S.; Kumar, N.; Alazab, M. Stochastic neural networks for cryptocurrency price prediction. *IEEE Access* **2020**, *8*, 82804–82818. [CrossRef]

71. Tibshirani, R. Regression shrinkage and selection via the lasso. *J. R. Stat. Soc. Ser. B (Methodol.)* **1996**, *58*, 267–288. [CrossRef]

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73. Fan, J.; Li, R. Variable selection via nonconcave penalized likelihood and its oracle properties. *J. Am. Stat. Assoc.* **2001**, *96*, 1348–1360. [CrossRef]

74. Zou, H. The adaptive lasso and its oracle properties. *J. Am. Stat. Assoc.* **2006**, *101*, 1418–1429. [CrossRef]

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76. Hastie, T.; Tibshirani, R.; Friedman, J. *The Elements of Statistical Learning: Data Mining, Inference, and Prediction*; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2009.

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78. Epprecht, C.; Guegan, D.; Veiga, Á. *Comparing Variable Selection Techniques for Linear Regression: Lasso and Autometrics*; Centre D'économie de la Sorbonne: Paris, France, 2013.

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82. Windisch, D. Loading deep networks is hard: The pyramidal case. *Neural Comput.* **2005**, *17*, 487–502. [CrossRef]

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52. Bouri, E.; Molnár, P.; Azzi, G.; Roubaud, D.; Hagfors, L.I. On the hedge and safe haven properties of Bitcoin: Is it really more than a diversifier? *Financ. Res. Lett.* **2017**, *20*, 192–198. [CrossRef]

53. Selmi, R.; Mensi, W.; Hammoudeh, S.; Bouoiyour, J. Is Bitcoin a hedge, a safe haven or a diversifier for oil price movements? A comparison with gold. *Energy Econ.* **2018**, *74*, 787–801. [CrossRef]

54. Kurka, J. Do cryptocurrencies and traditional asset classes influence each other? *Financ. Res. Lett.* **2019**, *31*, 38–46. [CrossRef]

55. Zargar, F.N.; Kumar, D. Informational inefficiency of Bitcoin: A study based on high-frequency data. *Res. Int. Bus. Financ.* **2019**, *47*, 344–353. [CrossRef]

56. Fang, L.; Bouri, E.; Gupta, R.; Roubaud, D. Does global economic uncertainty matter for the volatility and hedging effectiveness of Bitcoin? *Int. Rev. Financ. Anal.* **2019**, *61*, 29–36. [CrossRef]

57. Gillaizeau, M.; Jayasekera, R.; Maaitah, A.; Mishra, T.; Parhi, M.; Volokitina, E. Giver and the receiver: Understanding spillover effects and predictive power in cross-market Bitcoin prices. *Int. Rev. Financ. Anal.* **2019**, *63*, 86–104. [CrossRef]

58. Wołk, K. Advanced social media sentiment analysis for short-term cryptocurrency price prediction. *Expert Syst.* **2020**, *37*, e12493. [CrossRef]

59. Shen, D.; Urquhart, A.; Wang, P. Does twitter predict Bitcoin? *Econ. Lett.* **2019**, *174*, 118–122. [CrossRef]

60. Philippas, D.; Rjiba, H.; Guesmi, K.; Goutte, S. Media attention and Bitcoin prices. *Financ. Res. Lett.* **2019**, *30*, 37–43. [CrossRef]

61. Guégan, D.; Renault, T. Does investor sentiment on social media provide robust information for Bitcoin returns predictability? *Financ. Res. Lett.* **2021**, *38*, 101494. [CrossRef]

62. Dey, A.K.; Akcora, C.G.; Gel, Y.R.; Kantarcioglu, M. On the role of local blockchain network features in cryptocurrency price formation. *Can. J. Stat.* **2020**, *48*, 561–581. [CrossRef]

63. Nicola, G.; Cerchiello, P.; Aste, T. Information network modeling for US banking systemic risk. *Entropy* **2020**, *22*, 1331. [CrossRef]

64. Atsalakis, G.S.; Atsalaki, I.G.; Pasiouras, F.; Zopounidis, C. Bitcoin price forecasting with neuro-fuzzy techniques. *Eur. J. Oper. Res.* **2019**, *276*, 770–780. [CrossRef]

65. Jang, H.; Lee, J. An empirical study on modeling and prediction of bitcoin prices with bayesian neural networks based on blockchain information. *IEEE Access* **2017**, *6*, 5427–5437. [CrossRef]

66. Mallqui, D.C.; Fernandes, R.A. Predicting the direction, maximum, minimum and closing prices of daily Bitcoin exchange rate using machine learning techniques. *Appl. Soft Comput.* **2019**, *75*, 596–606. [CrossRef]

67. Nakano, M.; Takahashi, A.; Takahashi, S. Bitcoin technical trading with artificial neural network. *Phys. A Stat. Mech. Appl.* **2018**, *510*, 587–609. [CrossRef]

68. Sun, X.; Liu, M.; Sima, Z. A novel cryptocurrency price trend forecasting model based on LightGBM. *Financ. Res. Lett.* **2020**, *32*, 101084. [CrossRef]

69. Giudici, P.; Polinesi, G. Crypto price discovery through correlation networks. *Ann. Oper. Res.* **2021**, *299*, 443–457. [CrossRef]

70. Jay, P.; Kalariya, V.; Parmar, P.; Tanwar, S.; Kumar, N.; Alazab, M. Stochastic neural networks for cryptocurrency price prediction. *IEEE Access* **2020**, *8*, 82804–82818. [CrossRef]

71. Tibshirani, R. Regression shrinkage and selection via the lasso. *J. R. Stat. Soc. Ser. B (Methodol.)* **1996**, *58*, 267–288. [CrossRef]

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73. Fan, J.; Li, R. Variable selection via nonconcave penalized likelihood and its oracle properties. *J. Am. Stat. Assoc.* **2001**, *96*, 1348–1360. [CrossRef]

74. Zou, H. The adaptive lasso and its oracle properties. *J. Am. Stat. Assoc.* **2006**, *101*, 1418–1429. [CrossRef]

75. Zhao, P.; Yu, B. On model selection consistency of Lasso. *J. Mach. Learn. Res.* **2006**, *7*, 2541–2563.

76. Hastie, T.; Tibshirani, R.; Friedman, J. *The Elements of Statistical Learning: Data Mining, Inference, and Prediction*; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2009.

77. Tibshirani, R. Regression shrinkage and selection via the lasso: A retrospective. *J. R. Stat. Soc. Ser. B (Stat. Methodol.)* **2011**, *73*, 273–282. [CrossRef]

78. Epprecht, C.; Guegan, D.; Veiga, Á. *Comparing Variable Selection Techniques for Linear Regression: Lasso and Autometrics*; Centre D'économie de la Sorbonne: Paris, France, 2013.

79. Maclin, R.; Shavlik, J.W. Combining the predictions of multiple classifiers: Using competitive learning to initialize neural networks. *IJCAI* **1995**, *95*, 524–531.

80. Vapnik, V.N. An overview of statistical learning theory. *IEEE Trans. Neural Netw.* **1999**, *10*, 988–999. [CrossRef] [PubMed]

81. Scholkopf, B. Support vector machines: a practical consequence of learning theory. *IEEE Intell. Syst.* **1998**, *13*, 4.

82. Windisch, D. Loading deep networks is hard: The pyramidal case. *Neural Comput.* **2005**, *17*, 487–502. [CrossRef]

83. Hinton, G.E.; Salakhutdinov, R.R. Reducing the dimensionality of data with neural networks. *Science* **2006**, *313*, 504–507. [CrossRef] [PubMed]

84. Schmidhuber, J. Deep learning in neural networks: An overview. *Neural Netw.* **2015**, *61*, 85–117. [CrossRef]

85. Ho, T.K. The random subspace method for constructing decision forests. *IEEE Trans. Pattern Anal. Mach. Intell.* **1998**, *20*, 832–844.

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102. Baur, D.G.; Dimpfl, T. Price discovery in bitcoin spot or futures? *J. Futur. Mark.* **2019**, *39*, 803–817. [CrossRef]

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110. Kapar, B.; Olmo, J. An analysis of price discovery between Bitcoin futures and spot markets. *Econ. Lett.* **2019**, *174*, 62–64. [CrossRef]

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118. Griffin, J.M.; Shams, A. Is Bitcoin really untethered? *J. Financ.* **2020**, *75*, 1913–1964. [CrossRef]

119. Kraken, I.R.D. *Born to Run: December 2020 Market Recap & Outlook*; Technical Report; Ordo AB Crypto, Blockchain Consulting & Cryptocurrency Financial Services Information: San Francisco, CA, USA, 2020.

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