A Pseudo-Gaussian Test for Comparing Periodic Coefficient Regression Models with Consecutive Periods

This paper addresses the problem of selecting appropriate periods in periodic coefficient regression models where different regressors may exhibit distinct periodic structures. While existing approaches assume a common period across all variables, real-world applications often involve multiple periodicities. We propose a pseudo-Gaussian test for comparing a periodic regression model with variable-specific periods S_j against a model with periods S_j+1, providing a formal framework for local refinement of period specifications. The test is developed within a small T, large n asymptotic framework using uniform local asymptotic normality (ULAN), and we derive the least squares estimator for model parameters under the null hypothesis. Extensive simulation studies demonstrate the test's validity and power across symmetric and asymmetric error distributions, as well as its superiority compared to the likelihood ration test. Comparisons with AIC and BIC reveal competitive performance in period selection. An application to real meteorological data illustrates how the proposed test can be used sequentially to identify optimal periods, with the results corroborated by RMSE-based model selection. The method offers a flexible and robust tool for model diagnostics in settings with complex periodic structures.