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A generalized portmanteau goodness-of-fit test for time series models. (English) Zbl 1072.62088
Summary: We present a goodness-of-fit test for time series models based on the discrete spectral average estimator. Unlike current tests of goodness of fit, the asymptotic distribution of our test statistic allows the null hypothesis to be either a short- or long-range dependence model. Our test is in the frequency domain, is easy to compute, and does not require the calculation of residuals from the fitted model. This is especially advantageous when the fitted model is not a finite-order autoregressive model. The test statistic is a frequency domain analogue of the test of Y. Hong [Econometrica 64, No. 4, 837–864 (1996; Zbl 0960.62559)], which is a generalization of the G. E. P. Box and D. A. Pierce [J. Am. Stat. Assoc. 65, 1509–1526 (1970; Zbl 0224.62041)] test statistic. A simulation study shows that our test has power comparable to that of Hong’s test and superior to that of another frequency domain test by A. Milhoj [Biometrika 68, 177–187 (1981; Zbl 0459.62079)]

62M15 Inference from stochastic processes and spectral analysis
62M07 Non-Markovian processes: hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics
tables; simulations
Full Text: DOI
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