IDEAS home Printed from https://ideas.repec.org/a/taf/amstat/v70y2016i1p55-62.html
   My bibliography  Save this article

A New Approach to ANOVA Methods for Autocorrelated Data

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00031305.2015.1093026
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00031305.2015.1093026?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "On the stick–breaking representation of normalized inverse Gaussian priors," DEM Working Papers Series 008, University of Pavia, Department of Economics and Management.
    2. Pati, Debdeep & Dunson, David B. & Tokdar, Surya T., 2013. "Posterior consistency in conditional distribution estimation," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 456-472.
    3. Mahsa Samsami & Ralf Wagner, 2021. "Investment Decisions with Endogeneity: A Dirichlet Tree Analysis," JRFM, MDPI, vol. 14(7), pages 1-19, July.
    4. Abel Rodriguez & Enrique ter Horst, 2008. "Measuring expectations in options markets: An application to the SP500 index," Papers 0901.0033, arXiv.org.
    5. Villani, Mattias & Kohn, Robert & Giordani, Paolo, 2009. "Regression density estimation using smooth adaptive Gaussian mixtures," Journal of Econometrics, Elsevier, vol. 153(2), pages 155-173, December.
    6. Fuentes-García, Ruth & Mena, Ramsés H. & Walker, Stephen G., 2009. "A nonparametric dependent process for Bayesian regression," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1112-1119, April.
    7. Michael W. Robbins & Colin M. Gallagher & Robert B. Lund, 2016. "A General Regression Changepoint Test for Time Series Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 670-683, April.
    8. Weixuan Zhu & Fabrizio Leisen, 2015. "A multivariate extension of a vector of two-parameter Poisson-Dirichlet processes," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(1), pages 89-105, March.
    9. Michael L. Pennell & David B. Dunson, 2008. "Nonparametric Bayes Testing of Changes in a Response Distribution with an Ordinal Predictor," Biometrics, The International Biometric Society, vol. 64(2), pages 413-423, June.
    10. Jie Shen & Colin M. Gallagher & QiQi Lu, 2014. "Detection of multiple undocumented change-points using adaptive Lasso," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1161-1173, June.
    11. Trippa, Lorenzo & Muliere, Pietro, 2009. "Bayesian nonparametric binary regression via random tessellations," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2273-2280, November.
    12. Bruno Scarpa & David B. Dunson, 2009. "Bayesian Hierarchical Functional Data Analysis Via Contaminated Informative Priors," Biometrics, The International Biometric Society, vol. 65(3), pages 772-780, September.
    13. Hatjispyros, Spyridon J. & Nicoleris, Theodoros & Walker, Stephen G., 2016. "Random density functions with common atoms and pairwise dependence," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 236-249.
    14. George Karabatsos & Stephen Walker, 2009. "A Bayesian Nonparametric Approach to Test Equating," Psychometrika, Springer;The Psychometric Society, vol. 74(2), pages 211-232, June.
    15. Yushu Shi & Purushottam Laud & Joan Neuner, 2021. "A dependent Dirichlet process model for survival data with competing risks," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(1), pages 156-176, January.
    16. Inés M. Varas & Jorge González & Fernando A. Quintana, 2020. "A Bayesian Nonparametric Latent Approach for Score Distributions in Test Equating," Journal of Educational and Behavioral Statistics, , vol. 45(6), pages 639-666, December.
    17. Bassetti, Federico & Casarin, Roberto & Leisen, Fabrizio, 2014. "Beta-product dependent Pitman–Yor processes for Bayesian inference," Journal of Econometrics, Elsevier, vol. 180(1), pages 49-72.
    18. Chen, Kunzhi & Shen, Weining & Zhu, Weixuan, 2023. "Covariate dependent Beta-GOS process," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    19. Jared S. Murray & Jerome P. Reiter, 2016. "Multiple Imputation of Missing Categorical and Continuous Values via Bayesian Mixture Models With Local Dependence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1466-1479, October.
    20. Song, Junmo & Baek, Changryong, 2019. "Detecting structural breaks in realized volatility," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 58-75.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:amstat:v:70:y:2016:i:1:p:55-62. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UTAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.