Periodic autoregressive stochastic volatility

Abdelhakim Aknouche

MPRA Paper from University Library of Munich, Germany

Abstract: This paper proposes a stochastic volatility model (PAR-SV) in which the log-volatility follows a first-order periodic autoregression. This model aims at representing time series with volatility displaying a stochastic periodic dynamic structure, and may then be seen as an alternative to the familiar periodic GARCH process. The probabilistic structure of the proposed PAR-SV model such as periodic stationarity and autocovariance structure are first studied. Then, parameter estimation is examined through the quasi-maximum likelihood (QML) method where the likelihood is evaluated using the prediction error decomposition approach and Kalman filtering. In addition, a Bayesian MCMC method is also considered, where the posteriors are given from conjugate priors using the Gibbs sampler in which the augmented volatilities are sampled from the Griddy Gibbs technique in a single-move way. As a-by-product, period selection for the PAR-SV is carried out using the (conditional) Deviance Information Criterion (DIC). A simulation study is undertaken to assess the performances of the QML and Bayesian Griddy Gibbs estimates. Applications of Bayesian PAR-SV modeling to daily, quarterly and monthly S&P 500 returns are considered.

Keywords: Periodic stochastic volatility; periodic autoregression; QML via prediction error decomposition and Kalman filtering; Bayesian Griddy Gibbs sampler; single-move approach; DIC. (search for similar items in EconPapers)
JEL-codes: C11 C15 C51 C58 (search for similar items in EconPapers)
Date: 2013-06-01, Revised 2015
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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https://mpra.ub.uni-muenchen.de/83083/1/MPRA_paper_83083.pdf revised version (application/pdf)

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