The Multiple Outlier Problem in Time Series Analysis

Summary In this paper we consider the multiple outlier problem in time series analysis. The underlying undisturbed time series is assumed to be an autoregressive process. The location of the suspicious values is supposed to be known. We introduce conditional least squares estimators for the parameters. The estimates are shown to be strongly consistent. Using similar arguments as in the theory of linear models, we get a test statistic for the general linear hypothesis. Its asymptotic distribution is derived.