Bayesian MCMC analysis of periodic asymmetric power GARCH models

Abdelhakim Aknouche, Nacer Demmouche and Nassim Touche

MPRA Paper from University Library of Munich, Germany

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.

Keywords: Periodic Asymmetric Power GARCH model; probability properties; Griddy-Gibbs estimate; Deviance Information Criterion; Bayesian forecasting; Value at Risk. (search for similar items in EconPapers)
JEL-codes: C11 C15 C58 (search for similar items in EconPapers)
Date: 2018-05-11
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-ore and nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:91136

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