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Finite Mixture Modeling of Gaussian Regression Time Series with Application to Dendrochronology

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Listed:
  • Semhar Michael

    (South Dakota State University)

  • Volodymyr Melnykov

    (The University of Alabama)

Abstract

Finite mixture modeling is a popular statistical technique capable of accounting for various shapes in data. One popular application of mixture models is model-based clustering. This paper considers the problem of clustering regression autoregressive moving average time series. Two novel estimation procedures for the considered framework are developed. The first one yields the conditional maximum likelihood estimates which can be used in cases when the length of times series is substantial. Simple analytical expressions make fast parameter estimation possible. The second method incorporates the Kalman filter and yields the exact maximum likelihood estimates. The procedure for assessing variability in obtained estimates is discussed. We also show that the Bayesian information criterion can be successfully used to choose the optimal number of mixture components and correctly assess time series orders. The performance of the developed methodology is evaluated on simulation studies. An application to the analysis of tree ring data is thoroughly considered. The results are very promising as the proposed approach overcomes the limitations of other methods developed so far.

Suggested Citation

  • Semhar Michael & Volodymyr Melnykov, 2016. "Finite Mixture Modeling of Gaussian Regression Time Series with Application to Dendrochronology," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 412-441, October.
    • Handle: RePEc:spr:jclass:v:33:y:2016:i:3:d:10.1007_s00357-016-9216-4
    DOI: 10.1007/s00357-016-9216-4
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    References listed on IDEAS

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    1. Melnykov, Volodymyr & Melnykov, Igor, 2012. "Initializing the EM algorithm in Gaussian mixture models with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1381-1395.
    2. Leisch, Friedrich, 2004. "FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i08).
    3. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    4. Watson, Mark W. & Engle, Robert F., 1983. "Alternative algorithms for the estimation of dynamic factor, mimic and varying coefficient regression models," Journal of Econometrics, Elsevier, vol. 23(3), pages 385-400, December.
    5. Khalili, Abbas & Chen, Jiahua, 2007. "Variable Selection in Finite Mixture of Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1025-1038, September.
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    Cited by:

    1. Douglas L. Steinley, 2018. "Editorial," Journal of Classification, Springer;The Classification Society, vol. 35(1), pages 1-4, April.
    2. Volodymyr Melnykov & Xuwen Zhu, 2019. "Studying crime trends in the USA over the years 2000–2012," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 325-341, March.
    3. Douglas L. Steinley, 2018. "Editorial," Journal of Classification, Springer;The Classification Society, vol. 35(2), pages 195-197, July.
    4. Douglas L. Steinley, 2018. "Editorial," Journal of Classification, Springer;The Classification Society, vol. 35(3), pages 391-393, October.

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