JSM 2004 - Toronto

Abstract #301055

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Activity Number: 192
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Bayesian Statistical Science
Abstract - #301055
Title: Stochastic Volatility Models for Ordinal-valued Time Series
Author(s): Claudia Czado*+ and Gernot Mueller
Companies: Munich University of Technology and Munich University of Technology
Address: Center for Mathematical Sciences, D-85747 Garching, 85747, Germany
Keywords: MCMC ; stochastic volatility ; time series ; intraday financial data ; transformation group
Abstract:

Our aim is to model the intraday development of stock prices changes. We introduce a model for ordinal observations that are considered to be realizations of discretized versions of latent continuous variables. For these latent variables we assume a stochastic volatility (SV) model. MCMC methods for SV models have been considered in Chib, Nardari, and Shephard. To estimate the model parameters we consider an MCMC algorithm which, however, exhibits a bad convergence behavior. Therefore we develop a GM-MGMC (grouped move multigrid Monte Carlo) sampler, where additional grouped move (GM) steps (Liu and Sabatti 2000) are used. We show that these GM steps lead to a fundamental improvement in convergence. Finally, we fit the model to price changes of the IBM stock in January 2001.

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