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Improved Peňa-Rodriguez portmanteau test. (English) Zbl 1157.62493

Summary: Several problems with the diagnostic check suggested by D. Peňa and J. Rodriguez [A powerful portmanteau test of lack of fit for time series. J. Am. Stat. Assoc. 97, No. 458, 601–610 (2002; Zbl 1073.62554)] are noted and an improved Monte-Carlo version of this test is suggested. It is shown that quite often the test statistic recommended by Peňa and Rodriguez 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 Peňa and Rodriguez 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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
65C05 Monte Carlo methods
62E20 Asymptotic distribution theory in statistics

Citations:

Zbl 1073.62554

Software:

bootlib
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Full Text: DOI arXiv

References:

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