# Do Cryptocurrency Prices Camouflage Latent Economic Effects? A Bayesian Hidden Markov Approach +
## 3 The Empirical Application
### Results: The NHPG Model
The change of the sample sizes has a significant impact on the distribution of the unobserved process. Figure 6: Mean posterior out-of-sample predictions (gray line) for \(L=30\) days both for the (**a**) ETH and (**b**) BTC log-transformed price series (blue line). While the predictions for ETH are better than those for BTC, both are not satisfactory as they frequently miss the direction of price movement. The BTC predictions are essentially the same for both the 2016–2019 and 2013–2019 data sets (the second not shown here). probabilities are marked with bold. These variables make up the median probability model (MPM). Although the BTC and ETH are correlated [15], the variables that affect the series (by means of the MPM) are not the same. The MPM of ETH consists of 7 covariates: the USD/EUR, USD/GBP and USD/CNY exchange rates, Russel 2000, S&P 500, Dow Jones, NASDAQ indices. The MPM of BTC additionally contains the USD/JPY exchange rate and VIX. This difference on the exchange rates indicates that ETH is more geographically restricted. Moreover, the hash rate (HR) and Average Block size is insignificant for both cryptocurrencies. Regarding the extended BTC dataset, we find that Gold and Crude Oil future prices are also significant. Furthermore, it is worth mentioning that all the effects are linear in BTC series and hence the transition probabilities of hidden states are homogeneous (constant through time). This is in difference with ETH price series where S&P 500 and USD/GBP affects the series also non-linearly. The inclusion of these two variables in the transition probabilities equation results to the non-constant transition probabilities and consequently indicates that the Non-Homogeneous Hidden Markov model is promising in the understanding of cryptocurrencies price formation. The non-constant transition probabilities along with the fact that there exist other variables with non-negligible posterior probabilities of inclusion (above 0.3), imply that the are other drives that drive changes in the underlying process that go beyond the financial aspects that have been considered in the present setting. Finally, we observe that even though the number of statistical important variables is large, for both coins, the forecasting performance of this model is very modest. This is an indication that non-traditional financial and economic variables need to be considered. To sum up, even though we observe a large number of statistical significant explanatory variables, the insufficient forecasting performance of the NHPG model confirms that the cryptocurrencies are still decoupled from the mainstream financial and economic assets [57]. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multicolumn{4}{c}{**Posterior Probabilities of Inclusion**} \\ \hline \hline \multicolumn{4}{c}{Data Sets} \\ \hline Predictors & BTC & BTC & ETH \\ \hline Sample period & 1/2014-11/2019 & 1/2017-11/2019 & 1/2017-11/2019 \\ \hline USD/EUR & **1.00** & **0** & **1.00** & **0.12** \\ USD/GBP & **1.00** & **0** & **1.00** & **0.97** & **0.54** \\ USD/JPY & **1.00** & **0** & **1.00** & 0 & 0.06 \\ USD/CNY & **1.00** & **0** & **1.00** & **0** & **1.00** & **0.11** \\ R2000 & **1.00** & **0.06** & **1.00** & **0.01** & **1.00** & **0.26** \\ SP500 & **1.00** & **0.08** & **1.00** & **0** & **1.00** & **0.63** \\ VIX & **1.00** & **0.07** & **0.70** & **0.08** & 0 & 0.12 \\ DOW & **1.00** & **0.06** & **0.90** & **0.01** & **1.00** & **0.32** \\ NASDAQ & **1.00** & **0.06** & **1.00** & **0.01** & **1.00** & **0.34** \\ GOLD & **1.00** & **0.02** & 0.32 & 0.05 & 0 & 0.45 \\ CO & **1.00** & **0.01** & 0.24 & 0.01 & 0.00 & 0.08 \\ EUI & 0 0.01 & 0 0.01 & 0 0 & 0 \\ HR & 0 0.02 & 0 0 & 0 & 0.01 \\ AVS & 0 0.02 & 0 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Posterior probabilities of inclusion of the explanatory variables. The first value in each cell is the posterior probability of inclusion in the mean equation and the second the probability of inclusion in the transition probabilities of the underlying Markov process.