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A Bayes analysis of autoregressive model having functional-coefficients and its application on exchange rate data

Author

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  • Praveen Kumar Tripathi

    (Banasthali Vidyapith)

  • Manika Agarwal

    (Banasthali Vidyapith)

  • Satyanshu K. Upadhyay

    (Banaras Hindu University)

Abstract

The paper provides a Bayes analysis, based on free-knot spline technique, of the popular autoregressive model having functional-coefficients. The model was initially proposed by Chen and Tsay (1993). The technique of polynomial splines of different orders is used to approximate the functional-coefficients. A sample based approach using the Gibbs sampler algorithm with intermediate Metropolis steps is adopted to draw the posterior estimates for the parameters involved. Additionally, the technique of reversible jump Markov chain Monte Carlo is incorporated to update the location and number of knots in the polynomial spline. The paper then proceeds with the motive of obtaining both retrospective and prospective predictions based on the selected model. The complete procedure is illustrated by both simulated and a real dataset representing the exchange rate of Indian rupees relative to the US dollars.

Suggested Citation

  • Praveen Kumar Tripathi & Manika Agarwal & Satyanshu K. Upadhyay, 2024. "A Bayes analysis of autoregressive model having functional-coefficients and its application on exchange rate data," METRON, Springer;Sapienza Università di Roma, vol. 82(3), pages 363-391, December.
    • Handle: RePEc:spr:metron:v:82:y:2024:i:3:d:10.1007_s40300-024-00275-6
    DOI: 10.1007/s40300-024-00275-6
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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. Lindstrom, Mary J., 2002. "Bayesian estimation of free-knot splines using reversible jumps," Computational Statistics & Data Analysis, Elsevier, vol. 41(2), pages 255-269, December.
    3. Hai-Bin Wang & Ping Wu, 2015. "Bayesian Inference of Autoregressive and Functional-Coefficient Moving Average Models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(3), pages 453-467, February.
    4. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    5. Grégoire, Gérard & Hamrouni, Zouhir, 2002. "Change Point Estimation by Local Linear Smoothing," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 56-83, October.
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