Improved Pena-Rodriguez Portmanteau Test

TL;DR

This paper improves the Pena-Rodriguez portmanteau test for time series by introducing a Monte-Carlo version that is more reliable and powerful, especially for small sample sizes, and demonstrates its effectiveness through simulations and examples.

Contribution

An improved Monte-Carlo version of the Pena-Rodriguez portmanteau test that addresses its limitations and enhances diagnostic power for time series analysis.

Findings

Monte-Carlo test is more powerful than the original Pena-Rodriguez test.

The Monte-Carlo test outperforms the Ljung-Box test in simulations.

The new method is effective for series with less than 1000 observations.

Abstract

Several problems with the diagnostic check suggested by Pena and Rodriguez [2002. A powerful portmanteau test of lack of fit for time series. J. Amer. Statist. Assoc. 97, 601-610.] are noted and an improved Monte-Carlo version of this test is suggested. It is shown that quite often the test statistic recommended by Pena and Rodriguez [2002. A powerful portmanteau test of lack of fit for time series. J. Amer. Statist. Assoc. 97, 601-610.] may not exist and their asymptotic distribution of the test does not agree with the suggested gamma approximation very well if the number of lags used by the test is small. It is shown that the convergence of this test statistic to its asymptotic distribution may be quite slow when the series length is less than 1000 and so a Monte-Carlo test is recommended. Simulation experiments suggest the Monte-Carlo test is usually more powerful than the test given by Pena and Rodriguez [2002. A powerful portmanteau test of lack of fit for time series. J. Amer. Statist. Assoc. 97, 601-610.] and often much more powerful than the Ljung-Box portmanteau test. Two illustrative examples of enhanced diagnostic checking with the Monte-Carlo test are given.