A mixture‐distribution factor model for multivariate outliers

Abstract

Summary The aim of the paper is to go beyond the detection of outliers in multivariate time series, and to find regularities in the effect of special events on the series. The tool is a factor model in which the direction of every column of the loading matrix is identified, in contrast with Gaussian factor models, where only the span of the whole loading matrix is identified. Under asymptotics for rare and influential stochastic outliers, it is shown that the outliers' location is estimated consistently, and outliers are consistently classified into the factor components that have generated them. The direction, but not the length, of every column of the loading matrix is also estimated consistently. Inference on the directions, which underlies the interpretation of the factor structure, is asymptotically Gaussian under conditions that include Gaussianity of the innovations after accounting for the outliers. The model, augmented with a VAR specification for the conditional mean, provides a statistically acceptable and historically meaningful description of bond rates series for Denmark, Germany and the Netherlands.