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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)]

MSC:
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
Keywords:
tables; simulations
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References:
[1] Box, Journal of the American Statistical Association 65 pp 1509– (1970)
[2] Beran, Journal of the Royal Statistical Society, Series B 54 pp 749– (1992)
[3] Moulines, Annals of Statistics 27 pp 1415– (1999)
[4] Milhoj, Biometrika 68 pp 177– (1981) · Zbl 0459.62079 · doi:10.1093/biomet/68.1.177
[5] Mandelbrot, SIAM Review 10 pp 422– (1968)
[6] Dahlhaus, Annals of Statistics 17 pp 1749– (1989)
[7] Hosking, Biometrika 68 pp 165– (1981)
[8] Granger, Journal of Time Series Analysis 1 pp 15– (1980) · Zbl 0541.62106
[9] Hong, Econometrica 64 pp 837– (1996)
[10] Deo, Stochastic Processes and Their Applications 85 pp 159– (2000)
[11] Davies, Biometrika 74 pp 95– (1987)
[12] Hurvich, Journal of Time Series Analysis 19 pp 19– (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.