# Do Cryptocurrency Prices Camouflage Latent Economic Effects? A Bayesian Hidden Markov Approach +
## 3 The Empirical Application
### Results: The Logistic Regression Model  
We report the in-sample performance for the logistic regression model in Table 3 for every threshold and for both cryptocurrencies. Even though the in-sample performance--based on the large number of incorrect point estimates of the series--is poor, we see that when the threshold \(\alpha\) increases, the in-sample performance is improved. \begin{table}
\begin{tabular}{l l l l} \hline \hline  & \multicolumn{3}{c}{**Explanatory Variables**} \\ \hline
**Description** & **Symbol** & **Transformation** & **Retrieved from** \\ \hline US dollars to Euros exchange rate & USD/EUR & Normalized & investing.com \\ US dollars to GBP exchange rate & USD/GBP & Normalized & investing.com \\ US dollars to Japanese Yen exchange rate & USD/JPY & Normalized & investing.com \\ US dollars to Chinese Yuan exchange rate & USD/CNY & Normalized & investing.com \\ Russel 2000 index & R2000 & Normalized & finance.yahoo.com \\ Standard \& Poor’s 500 index & SP500 & Normalized & finance.yahoo.com \\ NASDAQ Composite index & NASDAQ & Normalized & finance.yahoo.com \\ Dow Jones Industrial Average & DOW & Normalized & finance.yahoo.com \\ Crude Oil Futures price & OIL & Normalized & finance.yahoo.com \\ Price of Gold & GOLD & Normalized & finance.yahoo.com \\ CBOE Volatility index & VIX & Normalized & finance.yahoo.com \\ Equity market Economic Uncertainty index & EUI & None & fred.stlouisfed.org \\ Hash Rate & HR & Percentage of change & quandl.com/etherscan.io \\ Average Block Size & AVS & Percentage of change & quandl.com/etherscan.io \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of explanatory variables along with the applied transformations and the online resources. The Hash Rate (HR) and Average Block Size (AVS) have been retrieved [55] for Bitcoin and from [56] for Ether. \begin{table}
\begin{tabular}{l l l l l l l l l l l l l l l l} \hline
**Variables** & USD/EUR & USD/GBP & USD/JPY & USD/CNY & R2000 & **SP900** & **NASDAQ** & **DOW** & **OIL** & **GOLD** & **VX** & **EUI** & **HR** & **AVS** \\ \hline
**USD/EUR** & 1.0 & 0.63 & 0.6 & 0.54 & 0.16 & 0.25 & 0.26 & 0.2 & \(-0.82\) & \(-0.33\) & 0.08 & 0.13 & 0.01 & \(-0.02\) \\
**USD/GBP** & 0.63 & 1.0 & 0.92 & \(-0.07\) & 0.66 & 0.73 & 0.73 & 0.71 & \(-0.56\) & \(-0.18\) & \(-0.09\) & 0.18 & \(-0.01\) & \(-0.02\) \\
**USD/JPY** & 0.6 & 0.92 & 1.0 & \(-0.09\) & 0.55 & 0.66 & 0.65 & 0.64 & \(-0.54\) & \(-0.31\) & \(-0.03\) & 0.23 & 0.00 & \(-0.01\) \\
**USD/CNY** & 0.54 & \(-0.07\) & \(-0.08\) & 1.0 & \(-0.06\) & \(-0.08\) & \(-0.06\) & \(-0.1\) & \(-0.42\) & \(-0.21\) & 0.12 & \(-0.05\) & 0.00 & \(-0.02\) \\
**B200** & 0.16 & 0.66 & 0.55 & \(-0.06\) & 1.0 & 0.95 & 0.95 & \(-0.08\)  
In Tables 4 and 5, we report the posterior probabilities of inclusion \(\pi_{k}\), \(k=1,\ldots,K\) of the \(K\) explanatory variables for the studied logistic models for the BTC and ETH binary series, respectively. For both coins, we observe that the studied covariated set does not affect nor predict the probability of positive return, i.e., \(Y_{t}-Y_{t-1}\geq 0\). \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multicolumn{6}{c}{**Posterior Probabilities of Inclusion**} \\ \hline Predictors & \multicolumn{6}{c}{Return’s magnitude} \\ \hline  & \(\alpha=0\%\) & \(\alpha=1\%\) & \(\alpha=2\%\) & \(\alpha=3\%\) & \(\alpha=4\%\) & \(\alpha=5\%\) \\ \hline USD/EUR & 0 & 0 & 0 & 0 & **1.00** & **0.65** \\ USD/GBP & 0 & 0 & 0 & 0 & 0 & 0 \\ USD/JPY & 0 & 0 & 0 & 0 & 0 & 0 \\ USD/CNY & 0 & 0.01 & 0 & 0 & 0 & 0.02 \\ R2000 & 0 & 0.01 & 0.02 & **1.00** & **1.00** & **0.72** \\ SP500 & 0 & 0. 3 & 0.02 & 0 & 0.01 & 0.02 \\ NASDAQ & 0 & 0.03 & 0.07 & 0 & 0 & 0 \\ DOW & 0 & 0.08 & 0.03 & 0 & 0 & 0 \\ OIL & 0 & 0.07 & **0.77** & 0 & 0.01 & 0.01 \\ GOLD & 0 & 0.11 & **0.80** & 0.01 & 0.02 & 0.07 \\ VIX & 0 & 0 & 0 & 0.3 & 0 & 0 \\ EUI & 0 & 0 & 0 & 0 & 0 & 0 \\ HR & 0 & 0 & 0 & 0 & 0 & 0 \\ AVS & 0 & 0 & 0 & 0 & 0.01 & 0.15 \\ \hline \hline \end{tabular}
\end{table}