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

2024/07/11 by Zixuan Liu, Liu, Zixuan, Junmo Song +1
Business, Management and Accounting · Decision Sciences · #Big Data and Business Intelligence #FOS: Computer and information sciences #Forecasting Techniques and Applications #Innovation Diffusion and Forecasting #Methodology (stat.ME)

paper · pdf · doi:10.48550/arxiv.2407.08565

openalex publication_date 2024/07/11 · openalex created_date 2024/07/14 · openalex updated_date 2026/07/28

Abstract

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.

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