Residual Diagnostic Plots for Checking for Model Mis-Specification in Time Series Regression

This paper considers residuals for time series regression. Despite much literature on visual diagnostics for uncorrelated data, there is little on the autocorrelated case. In order to examine various aspects of the fitted time series regression model, three residuals are considered. The fitted regression model can be checked using orthogonal residuals; the time series error model can be analysed using marginal residuals; and the white noise error component can be tested using conditional residuals. When used together, these residuals allow identification of outliers, model mis-specification and mean shifts. Due to the sensitivity of conditional residuals to model mis-specification, it is suggested that the orthogonal and marginal residuals be examined first.