Measuring influence in dynamic regression models

Abstract

This article presents a methodology to build measures of influence in regression models with time series data. We introduce statistics that measure the influence of each observation on the parameter estimates and on the forecasts. These statistics take into account the autocorrelation of the sample. The first statistic can be decomposed to measure the change in the univariate ARIMA parameters, the transfer function parameters and the interaction between both. For independent data they reduce to the D statistics considered by Cook in the standard regression modelo These statistics can be easily computed using standard time series software. Their performance is analyzed in an example in which they seem to be useful to identify important events, such as additive outliers and trend shifts, in time series data.