Detecting an IO/AO Outlier in a Set of Time Series

Abstract

The analysis of time series is an important area of statistics and it is necessary to understand the nature of outliers, in order to use appropriate methods to detect, or accommodate them. An interesting aspect is the case of detecting an outlier (Type IO or Type AO) in a set of autoregressive time series at the same time point. For example, consider a phenomenon in neighbouring regions. Measurements of the phenomenon in each region is a time series, so a set of series is creating. It is possible, an external factor affecting all regions, to cause unusual values, and then an outlier is appeared in each series of the set at the same time point. Tests for an innovative outlier affecting every member of a set of autoregressive time series at the same time point are developed. In one model, the outliers are represented as independent random effects; likelihood ratio tests are derived for this case and simulated critical values are tabulated. In a second model, assuming that the size of the outlier is the same in each series, a standard regression framework can be used and correlations between the series are introduced. In the case of additive outlier, the outliers are represented only as independent random effects.