Ordinary and proper location M-estimates for autoregressive-moving average models

Abstract

SUMMARY 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 autoregressive 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.