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Improved multivariate portmanteau test. (English) Zbl 1300.62062
Summary: A new portmanteau diagnostic test for vector autoregressive moving average (VARMA) models that is based on the determinant of the standardized multivariate residual autocorrelations is derived. The new test statistic may be considered an extension of the univariate portmanteau test statistic suggested by D. Peña and J. Rodríguez [J. Am. Stat. Assoc. 97, No. 458, 601–610 (2002; Zbl 1073.62554)]. The asymptotic distribution of the test statistic is derived as well as a chi-square approximation. However, the Monte-Carlo test is recommended unless the series is very long. Extensive simulation experiments demonstrate the usefulness of this test as well as its improved power performance compared to widely used previous multivariate portmanteau diagnostic check. Two illustrative applications are given.

MSC:
62M07 Non-Markovian processes: hypothesis testing
62H15 Hypothesis testing in multivariate analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
Software:
FinTS
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