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Biometrika 2008 95(2):399-414; doi:10.1093/biomet/asn014
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© 2008 Biometrika Trust

Articles

Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity

Guodong Li and Wai Keung Li

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

Received for publication 1 January 2006. Revision received 1 November 2007.
  Abstract

We consider a unified least absolute deviation estimator for stationary and nonstationary fractionally integrated autoregressive moving average models with conditional heteroscedasticity. Its asymptotic normality is established when the second moments of errors and innovations are finite. Several other alternative estimators are also discussed and are shown to be less efficient and less robust than the proposed approach. A diagnostic tool, consisting of two portmanteau tests, is designed to check whether or not the estimated models are adequate. The simulation experiments give further support to our model and the results for the absolute returns of the Dow Jones Industrial Average Index daily closing price demonstrate their usefulness in modelling time series exhibiting the features of long memory, conditional heteroscedasticity and heavy tails.

Key Words: ARFIMA • Conditional heteroscedasticity • Heavy tail • GARCH • Least absolute deviation • Long memory


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