Diagnostic checking for time series models with conditional heteroscedasticity estimated by the least absolute deviation approach

Authors: Li, Guodong; Li, Wai Keung

Source: Biometrika, Volume 92, Number 3, 1 September 2005 , pp. 691-701(11)

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Abstract:

The recent paper by Peng & Yao (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 in this paper. 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.

Keywords: Absolute residual autocorrelation; Asymptotic distribution; Diagnostic checking

Document Type: Research article

DOI: http://dx.doi.org/10.1093/biomet/92.3.691

Publication date: 2005-09-01