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On the squared residual autocorrelations in nonlinear time series with conditional heteroskedasticity. (English) Zbl 0807.62070

Summary: Time series with a changing conditional variance have been found useful in many applications. Residual autocorrelations from traditional autoregressive moving-average models have been found useful in model diagnostic checking. By analogy, squared residual autocorrelations from fitted conditional heteroskedastic time series models would be useful in checking the adequacy of such models.
A general class of squared residual autocorrelations is defined and their asymptotic distribution is obtained. The result leads to some useful diagnostic tools for statisticians using conditional heteroskedastic time series models. Some simulation results and an illustrative example are also reported.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics
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