*Robustness Check*

In this section, we perform the forecasting exercises by including different univariate models. We report the results for different possible benchmark models. We consider the following two univariate models: an autoregressive model with one lag (AR(1)) and an autoregressive model with the first three lags (AR(3)) based on the BIC criterion.

Table 7 reports the point and density forecasting for the AR(1) and AR(3) versus the benchmark model considered in Section 5. All models are run by using the usual Bayesian priors for 5000 iterations. Furthermore, we perform the root mean square error (RMSE) and the CRPS for the four main cryptocurrencies. As stated in Table 7, the results for the point and density forecasting are qualitatively similar to multivariate benchmark case, VAR(3).


**Table 7.** Point (RMSE) and Density forecasting (CRPS) for Bayesian AR(1), AR(3) and VAR(3).
