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Bayesian MCMC analysis of periodic asymmetric power GARCH models

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  • Aknouche, Abdelhakim
  • Demmouche, Nacer
  • Touche, Nassim

Abstract

A Bayesian MCMC estimate of a periodic asymmetric power GARCH (PAP-GARCH) model whose coefficients, power, and innovation distribution are periodic over time is proposed. The properties of the PAP-GARCH model such as periodic ergodicity, finiteness of moments and tail behaviors of the marginal distributions are first examined. Then, a Bayesian MCMC estimate based on Griddy-Gibbs sampling is proposed when the distribution of the innovation of the model is standard Gaussian or standardized Student with a periodic degree of freedom. Selecting the orders and the period of the PAP-GARCH model is carried out via the Deviance Information Criterion (DIC). The performance of the proposed Griddy-Gibbs estimate is evaluated through simulated and real data. In particular, applications to Bayesian volatility forecasting and Value-at-Risk estimation for daily returns on the S&P500 index are considered.

Suggested Citation

  • Aknouche, Abdelhakim & Demmouche, Nacer & Touche, Nassim, 2018. "Bayesian MCMC analysis of periodic asymmetric power GARCH models," MPRA Paper 91136, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:91136
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    More about this item

    Keywords

    Periodic Asymmetric Power GARCH model; probability properties; Griddy-Gibbs estimate; Deviance Information Criterion; Bayesian forecasting; Value at Risk.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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