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Biometrika 1986 73(3):679-686; doi:10.1093/biomet/73.3.679
© 1986 by Biometrika Trust
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Ordinary and proper location M-estimates for autoregressive-moving average models

CHIN-HUI LEE and R. DOUGLAS MARTIN

Department of Statistics, University of Washington Seattle, Washington 98195, U.S.A.

Proper location M-estimates for a model with non-Gaussian autoregressive-moving average type errors are genuine maximum likelihood type estimates, whereas ordinary location M-estimates are those introduced by P. Huber for independent and identically distributed errors. The relative behaviour of ordinary location M-estimates and proper location M-estimates is studied for situations with dependent errors of purely autoregress ive and purely moving average type. It is shown through asymptotic calculations and finite-sample size Monte Carlo studies that although ordinary location M-estimates are adequate for weak dependency structure, they can be quite inefficient compared with proper M-estimates of location when the non-Gaussian errors have a moderate to strong dependency structure.

Key Words: ARMA model • Location M-estimate • Robustness • Time series


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