*4.1. Simulation Study*

While, as mentioned before, the bias and MSE were acceptable overall, with consistent estimates for the AR parameter and threshold, it can be noticed that the estimates for Gamma parameters were more volatile. This is possibly due to the profile likelihood methodology adopted for estimation, which increases the complexity in estimating the Gamma parameters.

Additionally, as the simulation study was constructed in such a way that the true model was within the set of candidate models, the BIC would select the true model with probability tending to one and, thus, outperformed the AIC. However, in practice, the true model may not reside within the candidate set, and the AIC may give a better result, ye<sup>t</sup> may also choose a more complicated model (as mentioned above), while the BIC would prefer a simpler model. Therefore, in terms of forecasting MSE, both criteria are considered, in practice, for model selection.
