Detection of autoregressive errors in periodic coefficients regression models

This paper proposes a pseudo-Gaussian test for detecting autoregressive errors in periodic regression models. The test is constructed based on uniform local asymptotic normality (ULAN) results. Monte Carlo simulation studies confirm the validity and effectiveness of the proposed test under both symmetric and asymmetric error distributions, and demonstrate its superiority over the classical Durbin–Watson and Breusch-Godfrey tests. In addition, applications to real data illustrate the practical advantages of the proposed approach compared with the periodic regression model introduced by Regui et al. (Citation2024) and the linear regression model with autoregressive errors proposed by Durbin and Watson (Citation1950).