A TRIMMED MEAN OF LOCATION OF AN AR(INFINITY) STATIONARY PROCESS

This paper concerns the problem of estimating the location of a stationary infinite order autoregressive process. Since time series often contains atypical observations called 'outliers', which may affect estimates of parameters derived by classical methods and lead to incorrect inferences, a trimmed mean is considered as a robust estimator for the location. The main result of this paper is to show that under certain conditions the trimmed mean can be represented as an average of a bounded strictly stationary process. Based on the result, a weakly consistent estimator is constructed for the asymptotic variance of the trimmed mean.