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WEIGHTED LEAST ABSOLUTE DEVIATIONS ESTIMATION FOR ARMA MODELS WITH INFINITE VARIANCE

Published online by Cambridge University Press:  14 May 2007

Jiazhu Pan ,
Hui Wang  and
Qiwei Yao
Jiazhu Pan
Affiliation:
Peking University London School of Economics
Hui Wang
Affiliation:
Peking University
Qiwei Yao
Affiliation:
Peking University London School of Economics
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Abstract

For autoregressive moving average (ARMA) models with infinite variance innovations, quasi-likelihood-based estimators (such as Whittle estimators) suffer from complex asymptotic distributions depending on unknown tail indices. This makes statistical inference for such models difficult. In contrast, the least absolute deviations estimators (LADE) are more appealing in dealing with heavy tailed processes. In this paper, we propose a weighted least absolute deviations estimator (WLADE) for ARMA models. We show that the proposed WLADE is asymptotically normal, is unbiased, and has the standard root-n convergence rate even when the variance of innovations is infinity. This paves the way for statistical inference based on asymptotic normality for heavy-tailed ARMA processes. For relatively small samples numerical results illustrate that the WLADE with appropriate weight is more accurate than the Whittle estimator, the quasi-maximum-likelihood estimator (QMLE), and the Gauss–Newton estimator when the innovation variance is infinite and that the efficiency loss due to the use of weights in estimation is not substantial.The authors thank the two referees for their valuable suggestions. The work was partially supported by an EPSRC research grant (UK) and the Natural Science Foundation of China (grant 10471005).

Type
Research Article
Information
Econometric Theory , Volume 23 , Issue 5 , October 2007 , pp. 852 - 879
Copyright
© 2007 Cambridge University Press

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