Robust Testing Serial Correlation in AR(1) Processes in the Presence of a Single Additive Outlier

Abstract

The effect of a single additive outlier on the test of serial correlation in first order autoregressive processes is presented. We show that the test based on the least square estimator is highly sensitive to a single additive outlier: if the outlier is large then both the size and the power of the test are close to zero! A test based on the median of ratios of consecutive observations (Hurwicz, L. (1950). Least-Squares Bias in Time Series. In: Koopmas, T. C., ed. Statistical Inference in Dynamic Economic Models. Wiley.) and a test based on the normalized median of products of two consecutive observations (Haddad, John N. (2000). On robust estimation in the first-order autoregressive process. Communication in Statistics, Theory and Methods 29(1.1):45–54.) are discussed. A thorough simulation study as well as some theoretical considerations allow us to conclude that both are reasonably robust.