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Biometrika 2005 92(3):691-701; doi:10.1093/biomet/92.3.691
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© 2005 Biometrika Trust

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

Guodong Li and Wai Keung Li

Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong ligd{at}hkusua.hku.hk, hrntlwk{at}hku.hk

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.

Key Words: Absolute residual autocorrelation; Asymptotic distribution; Diagnostic checking; GARCH model; Local least absolute deviation estimator; Squared residual autocorrelation

Received May 2004. Revised December 2004.


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G. Li and W. K. Li
Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity
Biometrika, June 1, 2008; 95(2): 399 - 414.
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