On the use of mean square error and directional forecast accuracy for model selection: a simulation study

{Monte Carlo simulations are used to determine the weights of a procedure that combines the mean square error and directional forecast accuracy criteria for model selection.} We propose a new simple procedure for model selection based on simultaneously targeting the mean square error and directional forecast accuracy criteria. The procedure combines the two types of accuracy measures using a weighting scheme for the selection of the forecasting models. Monte Carlo analysis under different scenarios serves as a tool that assesses the strength of the procedure. To this end, we consider various time series models as generation mechanisms, such as time-homogeneous univariate and vector autoregressions. We focus on an important but specific aspect of forecast model specification, that is forecast model selection which chooses one out of two rival models, both of them evaluated over a training sample. For the evaluation of the training samples, we use rolling and recursive estimation schemes. The performance of the proposed procedure is quite heterogeneous across designs. However, while finding powerful tools for improving directional accuracy remains a challenge, the new procedure deserves some credits.