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

Guodong LI, Wai Keung LI

Research output: Contribution to journalArticles

27 Citations (Scopus)

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. Copyright © 2008 Biometrika Trust.
Original languageEnglish
Pages (from-to)399-414
JournalBiometrika
Volume95
Issue number2
DOIs
Publication statusPublished - Jun 2008

Citation

Li, G., & Li, W. K. (2008). Least absolute deviation estimation for fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity. Biometrika, 95(2), 399-414. doi: 10.1093/biomet/asn014

Keywords

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

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