Autocorrelation Effects on Least-Squares Intervention Analysis of Short Time Series

Abstract

Several issues regarding the effects of autocorrelated errors on Type I error in ordinary least-squares models are clarified. Although autocorrelated errors have a large effect on both omnibus F tests and tests on individual intervention effect coefficients in many applications, there are exceptions that have not been pointed out previously. It is demonstrated that under certain conditions, distortion in Type I error is far less than is predicted by asymptotic theory. It is shown that these exceptions occur because the effect of autocorrelated errors is dependent on (a) the type of parameters (e.g., level change and/or slope change) required in the model, (b) the number of variables in the design matrix, and (c) the sample size. Because existing time-series methods perform poorly with small samples, this may be a useful finding in some situations; however, a better general solution is to use a recently developed small-sample method.