The identification of multiple outliers in arima models

Abstract

The presence of outliers causes biases in the estimation of ARIMA models. In this work we present a procedure for detecting outliers and obtaining a robust estimator of the parameters in univariate ARIMA time series models. There are three main problems in the existing procedures for detecting outliers in ARIMA time series models. The first one is the confusion between level shifts and innovative outliers when a level shift is present in a time series. The procedure ineludes a possible solution to avoid this problem based on not comparing the statistics for level shifts and innovative outliers together, because the critical values under the null hypothesis of no outliers can be quite different. The second problem is the biased estimation of the initial parameter values. In the existing procedures, this initial estimation is done under the hypotheses of no outliers in the data, which may lead to begin the search for outliers using a very biased set of parameters and, therefore, these procedures may fail. In order to solve this problem, we use two measures of influence in the first stage of the proposed procedure; one measure for individually influential observations, and an additional measure for level shifts and sequences of outliers. The third problem is masking. This problem appears when there is a sequence of additive outliers, because the usual one by one outlier identification method may fail in the identification of sorne of the members of the group. The proposed procedure seems to solve the aforementioned problems and obtains food parameter estimates when the time series has isolated outliers and/or multiple adjacent outliers. The performance of the proposed procedure is analyzed and an example is shown.