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Diagnostic checking for time series models with conditional heteroscedasticity estimated by the least absolute deviation approach. (English) Zbl 1152.62370

Summary: L. Peng and Q. Yao [ibid. 90, 967– 975 (2003)] gave an interesting extension of least absolute deviation estimation to generalised autoregressive conditional heteroscedasticity, GARCH, time series models. The asymptotic distributions of absolute residual autocorrelations and squared residual autocorrelations from the GARCH model estimated by the least absolute deviation method are derived. These results lead to two useful diagnostic tools which can be used to check whether or not a GARCH model fitted by using the least absolute deviation method is adequate. Some simulation experiments give further support to the asymptotic theory and a real data example is also reported.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics
62J20 Diagnostics, and linear inference and regression
62G05 Nonparametric estimation
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