“…Thus, rolling estimation of the models through the post-sample window and up to March 2022 delivers 40 1-month-ahead forecasts, 39 2-month, 38 3-month, 37 4-month, 36 5-month, and 35 6-month forecasts, whose RMSE are reported in Table 5, for all processes considered. These results reveal that structural VAR and Markov forecasts are equally good and even better than naive predictions for almost all Hypotheses in the Johansen test are nested and a "*" indicates the first non-rejection where one should stop when reading from left to right (see Johansen, 1992;Kirikos, 1996). The null hypothesis in the Engle-Granger test (Engle & Granger, 1987) is that the series are not cointegrated and the number in parenthesis next to the τ-statistic is the p-value.…”