Bayesian inference for volatility models in financial time series
The aim of the thesis is to study the two principal volatility models used in ¯nancial time series, and to perform inference using a Bayesian approach. The ¯rst model is the Deterministic Time-Varying volatility represented by Autoregressive Conditional Heteroscedastic (ARCH) models. The second model is the Stochastic Time Varying volatility or Stochastic Volatility (SV) model. The thesis concentrates on using Financial Foreign Exchange (FX) data including time series for four Asian countries of Thailand, Singapore, Japan and Hong Kong, and FX data sets from other countries. The time period this particular FX data set covers includes the recent biggest crisis in Asian ¯nancial markets in 1997. The analysis involves exploring high frequency ¯nancial FX data where the sets of data used are the daily and hourly opening FX rates. The key development of the thesis is the implementation of changepoint models to allow for non-stationarity in the volatility process. The changepoint approach has only rarely been implemented for volatility data. In this thesis, the changepoint model for SVtype volatility structures is formulated. The variable dimensional nature of the inference problem, that is, that the number as well as the locations of the volatility changepoints are unknown, is acknowledged and incorporated, as are the potential leptokurtic nature of ¯nancial returns. The Bayesian computational approach used for making inference about the model parameters is Markov Chain Monte Carlo (MCMC). Another contribution of this thesis is the study of reparameterizations of parameters in both ARCH and SV models. The objective is to improve the performance of the MCMC method.