Information matrix test for normality of innovations in stationary time series models

This study focuses on the problem of testing for normality of innovations in stationary time series models.To achieve this, we introduce an information matrix (IM) based test. While the IM test was originally developed to test for model misspecification, our study addresses that the test can also be used to test for the normality of innovations in various time series models. We provide sufficient conditions under which the limiting null distribution of the test statistics exists. As applications, a first-order threshold moving average model, GARCH model and double autoregressive model are considered. We conduct simulations to evaluate the performance of the proposed test and compare with other tests, and provide a real data analysis.