New Tests for Regression Error Autocorrelation

• Activity Number: 174
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Alexander Thomas*+ and Mark Inlow
• Companies: Rose-Hulman Institute of Technology and Rose-Hulman Institute of Technology
• Keywords: autocorrelation ; regression ; time series ; Durbin-Watson ; Breusch-Godfrey ; Fourier analysis

Abstract

There are various procedures for testing for regression error autocorrelation, perhaps the most important being the Durbin-Watson (D-W) and Breusch-Godfrey (B-G) tests. A shortcoming of these two tests is that neither is an omnibus test: D-W tests for nonzero autocorrelation at lag 1 and B-G tests for nonzero autocorrelation from lag 1 up to some pre-specified lag p. In this paper we present new tests for regression models with non-stochastic predictors which are omnibus in the sense of having power against autocorrelation at all lags. These tests are based on a generalized discrete Fourier analysis using maximally smooth orthonormal sequences which are orthogonal to the regression model space. The corresponding Fourier coefficients are IID normal(0,sigma) under the null, facilitating construction of exact omnibus tests for autocorrelation by various approaches, e.g., data-driven smooth test methodology. Preliminary simulation results show our new tests have power comparable to that of the D-W and B-G tests against AR(1) and AR(p) alternatives, respectively, in spite of being omnibus procedures.