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Bayesian Inference for Time Series with Stable Innovations

Author

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  • Zuqiang Qiou
  • Nalini Ravishanker

Abstract

This paper describes Bayesian inference for a linear time series model with stable innovations. An advantage of the Bayesian approach is that it enables the simultaneous estimation of the parameters characterizing the stable law and the parameters of the linear autoregressive moving‐average model. Our approach uses a Metropolis–Hastings algorithm to generate samples from the joint posterior distribution of all the parameters and subsequent inference is based on these samples. We illustrate our approach using data simulated from three linear processes with stable innovations and a real data set

Suggested Citation

  • Zuqiang Qiou & Nalini Ravishanker, 1998. "Bayesian Inference for Time Series with Stable Innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(2), pages 235-249, March.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:2:p:235-249
    DOI: 10.1111/1467-9892.00088
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    Cited by:

    1. Peters, G.W. & Sisson, S.A. & Fan, Y., 2012. "Likelihood-free Bayesian inference for α-stable models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3743-3756.
    2. John P. Nolan & Nalini Ravishanker, 2009. "Simultaneous prediction intervals for ARMA processes with stable innovations," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(3), pages 235-246.
    3. Pai, Jeffrey & Ravishanker, Nalini, 2015. "Fast approximate likelihood evaluation for stable VARFIMA processes," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 160-168.
    4. Sampaio, Jhames M. & Morettin, Pedro A., 2020. "Stable Randomized Generalized Autoregressive Conditional Heteroskedastic Models," Econometrics and Statistics, Elsevier, vol. 15(C), pages 67-83.
    5. Marco J. Lombardi & Giorgio Calzolari, 2008. "Indirect Estimation of α-Stable Distributions and Processes," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 193-208, March.
    6. repec:dau:papers:123456789/6326 is not listed on IDEAS
    7. Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, vol. 172(2), pages 235-247.

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