Outliers in a multivariate autoregressive moving-average process

The paper deals with the problem of outliers in a multivariate ARMA-process. The location of the suspicious values is assumed to be known. In order to estimate the parameters, the maximum likelihood method is applied. The estimators are shown to be strong consistent, if the degree of contamination is not too big. Furthermore a test of discordancy for the general linear hypothesis is introduced. On condition that the white noise is multivariate normally distributed, the asymptotic distribution of the test statistic is calculated. Simultaneous treatment of the time series shows some advantages. It is possible to detect outliers, which cannot be determined by a separate investigation of the components.