Comparing Forecast Predictive Accuracy Approaches for Finite Samples

• Activity Number: 108 - Innovations in Testing and Inference
• Type: Contributed
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): William John Best* and Jane L Harvill
• Companies: Baylor University and Baylor University
• Keywords: Prediction; Vector Time Series; Hotelling T^2; Bootstrap

Abstract

We investigate a modification of the Mariano-Preve (2012) $chi^2$ test for equal predictive ability of three or more forecasting models. Under the proposed modification, the null distribution of the Wald-type test statistic is asymptotically Hotelling $T^2$. The modified version of the test is empirically shown to outperform the $\chi^2$ version. Monte Carlo simulations indicate improved empirical size for series of moderate lengths. For series of small length the empirical size is larger than nominal, but is an improvement over the $\chi^2$. A finite sample correction factor is moderately successful in correcting the size of the test. To preserve the integrity of the power the test, a size-adjustment is applied. The powers of both the $\chi^2$ and Hotelling $T^2$ approaches increase with series length. Finally, a bootstrap approach is proposed to correct the size of the test for series that have a short length.