New Goodness-of-Fit Tests for Time Series Models

TL;DR

This paper introduces new omnibus portmanteau tests for assessing the adequacy of various time series models, including linear and nonlinear structures, using combined autocorrelation measures and asymptotic analysis.

Contribution

It develops novel goodness-of-fit tests based on combined autocorrelation functions, applicable to a wide range of time series models, with proven effectiveness through simulations and real data applications.

Findings

Tests control type I error effectively

Tests show higher power than existing methods in many scenarios

Practical applications demonstrate usefulness for stock return data

Abstract

This article proposes omnibus portmanteau tests for contrasting adequacy of time series models. The test statistics are based on combining the autocorrelation function of the conditional residuals, the autocorrelation function of the conditional squared residuals, and the cross-correlation function between these residuals and their squares. The maximum likelihood estimator is used to derive the asymptotic distribution of the proposed test statistics under a general class of time series models, including ARMA, GARCH, and other nonlinear structures. An extensive Monte Carlo simulation study shows that the proposed tests successfully control the type I error probability and tend to have more power than other competitor tests in many scenarios. Two applications to a set of weekly stock returns for 92 companies from the S&P 500 demonstrate the practical use of the proposed tests.