A New Approach to ANOVA Methods for Autocorrelated Data

Robert Lund, Gang Liu and Qin Shao

The American Statistician, 2016, vol. 70, issue 1, 55-62

Abstract: This article reexamines ANOVA problems for autocorrelated data. Using linear prediction techniques for stationary time series, a new test statistic that assesses a null hypothesis of equal means is proposed and investigated. Our test statistic mimics the classical F -type ratio form used with independent data, but substitutes estimated prediction residuals in for the errors. This simple tactic departs from past studies that adjust the quadratic forms in the numerator and denominator in the F ratio for autocorrelation. One of the advantages is that our statistic retains the classical null hypothesis F distribution (now as a limit) with the customary degrees of freedom. The statistic is shown to perform well in simulations. Asymptotic proofs are given in the case of autoregressive random errors; a sports application is supplied.[Received December 2014. Revised August 2015.]

Date: 2016
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DOI: 10.1080/00031305.2015.1093026

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