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Diagnostic checking integer-valued ARCH\((p)\) models using conditional residual autocorrelations. (English) Zbl 1464.62200

Summary: Time series of counts are commonly observed in real-world applications. The integer-valued ARCH\((p)\) models are able to describe integer-valued processes and offer the potential to be widely applied in practice in future. This paper develops an asymptotic theory for (partial) autocorrelations of the conditional residuals from the integer-valued ARCH\((p)\) model. Based on the above results, we propose five portmanteau test statistics, which are very useful in checking the adequacy of a fitted integer-valued ARCH specification. The asymptotic distributions of the statistics are derived and their finite sample properties are studied in detail through Monte Carlo simulations. Finally, we illustrate the results analyzing two empirical examples.

MSC:

62-08 Computational methods for problems pertaining to statistics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G10 Nonparametric hypothesis testing
62E20 Asymptotic distribution theory in statistics
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