Bayesian estimation of stochastic volatility models based on OU processes with marginal Gamma law

Sylvia Frühwirth-Schnatter, Leopold Soegner

Research output: Contribution to journalArticle

Abstract

This paper discusses practical Bayesian estimation of stochastic volatility models based on OU processes with marginal Gamma laws. Estimation is based on a parameterization which is derived from the Rosiński representation, and has the advantage of being a non-centered parameterization. The parameterization is based on a marked point process, living on the positive real line, with uniformly distributed marks. We define a Markov chain Monte Carlo (MCMC) scheme which enables multiple updates of the latent point process, and generalizes single updating algorithm used earlier. At each MCMC draw more than one point is added or deleted from the latent point process. This is particularly useful for high intensity processes. Furthermore, the article deals with superposition models, where it discuss how the identifiability problem inherent in the superposition model may be avoided by the use of a Markov prior. Finally, applications to simulated data as well as exchange rate data are discussed.

Original languageEnglish (US)
Pages (from-to)159-179
Number of pages21
JournalAnnals of the Institute of Statistical Mathematics
Volume61
Issue number1
DOIs
StatePublished - Mar 1 2009

Fingerprint

Stochastic Volatility Model
Bayesian Estimation
Parameterization
Latent Process
Point Process
Model-based
Markov Chain Monte Carlo
Superposition
Marked Point Process
Identifiability
Exchange rate
Real Line
Updating
Update
Generalise
Model

Keywords

  • Data augmentation
  • Identification
  • Marked point processes
  • Markov chain Monte Carlo

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Bayesian estimation of stochastic volatility models based on OU processes with marginal Gamma law. / Frühwirth-Schnatter, Sylvia; Soegner, Leopold.

In: Annals of the Institute of Statistical Mathematics, Vol. 61, No. 1, 01.03.2009, p. 159-179.

Research output: Contribution to journalArticle

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