Periodic autoregressive stochastic volatility
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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.
KeywordsPeriodic stochastic volatility Periodic autoregression QML via prediction error decomposition and Kalman filtering Bayesian Griddy Gibbs sampler Single-move approach DIC
Mathematics Subject ClassificationPrimary 62M10 Secondary 60F99
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.
- Bollerslev T, Ghysels E (1996) Periodic autoregressive conditional heteroskedasticity. J. Bus. Econ. Stat. 14:139–151Google Scholar
- Breidt FJ (1997) A threshold autoregressive stochastic volatility. http://citeseer.ist.psu.edu/103850.html
- Chan CC, Grant AL (2014) Issues in comparing stochastic volatility models using the deviance information criterion. CAMA Working Paper 51/2014. Australian National UniversityGoogle Scholar
- Ghysels E, Harvey AC, Renault E (1996) Stochastic volatility. In: Rao CR, Maddala GS (eds) Statistical Methods in Finance. North-Holland, AmsterdamGoogle Scholar
- Osborn DR, Savva CS, Gill L (2008) Periodic dynamic conditional correlations between stock markets in Europe and the US. J Financ Econ 6:307–325Google Scholar
- Taylor SJ (1982) Financial returns modelled by the product of two stochastic processes—a study of daily sugar prices, 1961–1979. In: Anderson OD (ed) Time series analysis: theory and practice. North-Holland, Amsterdam, pp 203–226Google Scholar
- Tsiakas I (2006) Periodic stochastic volatility and fat tails. J Financ Econ 4:90–135Google Scholar