Mixed Portmanteau Tests for Simultaneous Linear and Nonlinear Dependency in Time Series

Omnibus portmanteau tests, for detecting simultaneous linear and nonlinear dependence structures in time series, are proposed. The tests are based on combining the autocorrelation function of the conditional residuals, the autocorrelation function of the conditional square residuals, and the cross-correlation function between the conditional residuals and their squares. The quasi maximum likelihood estimate is used to derive the asymptotic distribution as a chi-squared distribution under a general class of time series models including ARMA, arch, and other linear and nonlinear models. The simulation results show that the proposed tests successfully control the Type I error probability and tend to be more powerful than other tests in many cases. The efficacy of the proposed tests is demonstrated through the analysis of Facebook Inc., daily log returns.