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A Bayes algorithm for model compatibility and comparison of ARMA(p,q) models

Author

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  • Tripathi Praveen Kumar

    (Department of Mathematics and Statistics, Banasthali Vidyapith, Rajasthan, India .)

  • Sen Rijji

    (Department of Statistics, Behala College, Calcutta University, India .)

  • Upadhyay S. K.

    (Department of Statistics, Banaras Hindu University, Varanasi, India .)

Abstract

The paper presents a Bayes analysis of an autoregressive-moving average model and its components based on exact likelihood and weak priors for the parameters where the priors are defined so that they incorporate stationarity and invertibility restrictions naturally. A Gibbs-Metropolis hybrid scheme is used to draw posterior-based inferences for the models under consideration. The compatibility of the models with the data is examined using the Ljung-Box-Pierce chi-square-based statistic. The paper also compares different compatible models through the posterior predictive loss criterion in order to recommend the most appropriate one. For a numerical illustration of the above, data on the Indian gross domestic product growth rate at constant prices are considered. Differencing the data once prior to conducting the analysis ensured their stationarity. Retrospective short-term predictions of the data are provided based on the final recommended model. The considered methodology is expected to offer an easy and precise method for economic data analysis.

Suggested Citation

  • Tripathi Praveen Kumar & Sen Rijji & Upadhyay S. K., 2021. "A Bayes algorithm for model compatibility and comparison of ARMA(p,q) models," Statistics in Transition New Series, Statistics Poland, vol. 22(2), pages 95-123, June.
    • Handle: RePEc:vrs:stintr:v:22:y:2021:i:2:p:95-123:n:3
    DOI: 10.21307/stattrans-2021-018
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    References listed on IDEAS

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    1. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
    2. Ludlow, Jorge & Enders, Walter, 2000. "Estimating non-linear ARMA models using Fourier coefficients," International Journal of Forecasting, Elsevier, vol. 16(3), pages 333-347.
    3. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
    4. Frank R. Kleibergen & Henk Hoek, 2000. "Bayesian Analysis of ARMA Models," Tinbergen Institute Discussion Papers 00-027/4, Tinbergen Institute.
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