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A New Approach to ANOVA Methods for Autocorrelated Data

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  • Robert Lund
  • Gang Liu
  • Qin Shao

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.]

Suggested Citation

  • Robert Lund & Gang Liu & Qin Shao, 2016. "A New Approach to ANOVA Methods for Autocorrelated Data," The American Statistician, Taylor & Francis Journals, vol. 70(1), pages 55-62, February.
    • Handle: RePEc:taf:amstat:v:70:y:2016:i:1:p:55-62
    DOI: 10.1080/00031305.2015.1093026
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    References listed on IDEAS

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    1. De Iorio, Maria & Muller, Peter & Rosner, Gary L. & MacEachern, Steven N., 2004. "An ANOVA Model for Dependent Random Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 205-215, January.
    2. Shao, Q. & Ni, P.P., 2004. "Least-squares estimation and ANOVA for periodic autoregressive time series," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 287-297, September.
    3. Michael Robbins & Colin Gallagher & Robert Lund & Alexander Aue, 2011. "Mean shift testing in correlated data," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(5), pages 498-511, September.
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    1. M. Azimmohseni & M. Khalafi & M. Kordkatuli, 2019. "Time series analysis of covariance based on linear transfer function models," Statistical Inference for Stochastic Processes, Springer, vol. 22(1), pages 1-16, April.

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