Robust and Powerful Serial Correlation Tests with New Robust Estimates in ARX Models

• Activity Number: 124
• Type: Contributed
• Date/Time: Monday, August 4, 2003 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Pierre Duchesne*+
• Companies: HEC Montreal
• Keywords: serial correlation ; weighted portmanteau statistic ; spectral density ; additive outliers ; time series ; robustness

Abstract

We consider robust serial correlation tests in autoregressive models with exogenous variables (ARX). Since the least squares estimators are not robust when outliers are present, a new family of estimators is introduced. They provide resistant estimators that are less sensible to abnormal observations in the output variable of the dynamic model. We show that the new robust estimators are consistent and we can consider robust and powerful tests of serial correlation in ARX models based on these estimators. The new one-sided tests of serial correlation are obtained in extending Hong's (1996) approach in a framework resistant to outliers. They are based on a weighted sum of robust squared residual autocorrelations and on any robust and sqrt(n)-consistent estimators. Our approach generalizes Li's (1988) test statistic, that can be interpreted as a test using the truncated uniform kernel. However, many kernels deliver a higher power. This is confirmed in a simulation study, where we investigate the finite sample properties of the new robust serial correlation tests in comparison to some commonly used robust and nonrobust tests.