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Laplace mixture autoregressive models

Author

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  • Nguyen, Hien D.
  • McLachlan, Geoffrey J.
  • Ullmann, Jeremy F.P.
  • Janke, Andrew L.

Abstract

Autoregressive (AR) models are an important tool in the study of time series data. However, the standard AR model only allows for unimodal marginal and conditional densities, and cannot capture conditional heteroscedasticity. Previously, the Gaussian mixture AR (GMAR) model was considered to remedy these shortcomings by using a Gaussian mixture conditional model. We introduce the Laplace mixture (LMAR) model that utilizes a Laplace mixture conditional model, as an alternative to the GMAR model. We characterize the LMAR model and provide conditions for stationarity. An MM (minorization–maximization) algorithm is then proposed for maximum pseudolikelihood (MPL) estimation of an LMAR model. Conditions for asymptotic inference and a rule for model selection for the MPL estimator are considered. An example analysis of data arising from the calcium imaging of a zebrafish brain is performed.

Suggested Citation

  • Nguyen, Hien D. & McLachlan, Geoffrey J. & Ullmann, Jeremy F.P. & Janke, Andrew L., 2016. "Laplace mixture autoregressive models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 18-24.
    • Handle: RePEc:eee:stapro:v:110:y:2016:i:c:p:18-24
    DOI: 10.1016/j.spl.2015.11.006
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    References listed on IDEAS

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    1. C. S. Wong & W. K. Li, 2000. "On a mixture autoregressive model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 95-115.
    2. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Laplace mixture of linear experts," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 177-191.
    3. Small, Kenneth A. & Ng, Chen Feng, 2014. "Optimizing road capacity and type," Economics of Transportation, Elsevier, vol. 3(2), pages 145-157.
    4. Song, Weixing & Yao, Weixin & Xing, Yanru, 2014. "Robust mixture regression model fitting by Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 128-137.
    5. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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    1. Arifatus Solikhah & Heri Kuswanto & Nur Iriawan & Kartika Fithriasari, 2021. "Fisher’s z Distribution-Based Mixture Autoregressive Model," Econometrics, MDPI, vol. 9(3), pages 1-35, June.

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