Tests of Seasonal and Non-Seasonal Serial Correlation

Donald Andrews (), Xuemei Liu and Werner Ploberger
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Xuemei Liu: Dept. of Statistics, Yale University

No 1124, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This paper considers tests for seasonal and non-seasonal serial correlation in time series and in the errors of regression models. The problem of testing for white noise against multiplicative seasonal ARMA(l,l)-ARMA(l,l) alternatives is investigated. This testing problem is non-standard due to nuisance parameters that appear under the alternative but not under the null hypothesis. The likelihood ratio (LR), sup Lagrange multiplier (LM), and exponential average LM and LR tests are considered and are shown to be asymptotically admissible for multiplicative seasonal ARMA(l,l)-ARMA(l,l) alternatives. In addition, they are shown to be consistent against all (weakly stationary strong mixing) non-white noise alternatives. Simulation results compare the tests to several tests in the literature. The exponential average test, Exp-LR_{infinity}, is found to be the best test overall. It performs substantially better than the Box-Pierce, Durbin-Watson, and Wallis tests.

Keywords: Autoregressive moving average model; consistent test; Lagrange multiplier test; likelihood ratio test; multiplicative seasonal ARMA model; nonstandard testing problem; seasonality; test of white noise. (search for similar items in EconPapers)
Pages: 35 pages
Date: 1996-05
Note: CFP 971.
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Published in Biometrika, 85, 1998

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