Periodic autoregressive stochastic volatility

Article

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 in finite samples while 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 

Mathematics Subject Classification

Primary 62M10 Secondary 60F99 

Notes

Acknowledgments

I am deeply grateful to the Editor-In-Chief Prof. Marc Hallin, an Associate Editor and two Referees for their careful reading, helpful comments and useful suggestions that have greatly helped me in substantially improving the earlier version of the manuscript.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of Science and Technology Houari BoumedieneAlgiersAlgeria
  2. 2.Mathematics Department, College of ScienceQassim UniversityQassimSaudi Arabia

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