A Portmanteau Test for ARMA Processes with Infinite Variance

Abstract

We propose a portmanteau test for autoregressive moving average (ARMA) time series models with infinite variance. Our test is based on the partial autocorrelation function (PACF) of trimmed residuals from the fitted model. The asymptotic null distribution of the test statistic is derived when the innovation has a Pareto-type distribution and the estimators of the ARMA coefficients satisfy certain condition. The effectiveness of our test is established through extensive simulation studies. In general, our test agrees very well with that of Lee and Ng (2010) and under some circumstances it performs even better. Three real world examples are also provided to demonstrate its usage.

KEYWORDS:

• Partial autocorrelation
• Portmanteau test
• Trimmed residuals

Mathematics Subject Classification:

• 62M10
• 62P20

Acknowledgment

The author's are very grateful to the anonymous referees and the editor for reviewing the article. The first author acknowledges support from University of Houston Downtown ORCA fund for carrying out this research.