Financial Time Series Analysis of SV Model by Hybrid Monte Carlo

We apply the hybrid Monte Carlo (HMC) algorithm to the financial time sires analysis of the stochastic volatility (SV) model for the first time. The HMC algorithm is used for the Markov chain Monte Carlo (MCMC) update of volatility variables of the SV model in the Bayesian inference. We compute parameters of the SV model from the artificial financial data and compare the results from the HMC algorithm with those from the Metropolis algorithm. We find that the HMC decorrelates the volatility variables faster than the Metropolis algorithm. We also make an empirical analysis based on the Yen/Dollar exchange rates.Comment: 8 pages, 3 figures, to be published in LNC

Stochastic volatility models for ordinal valued time series with application to finance

In this paper we introduce two stochastic volatility models where the response variable takes on only finite many ordered values. Corresponding time series occur in high-frequency finance when the stocks are traded on a coarse grid. For parameter estimation we develop an e±cient Grouped Move Multigrid Monte Carlo (GM-MGMC) sampler. We apply both models to price changes of the IBM stock in January, 2001 at the NYSE. Dependencies of the price change process on covariates are quantified and compared with theoretical considerations on such processes. We also investigate whether this data set requires modeling with a heavy-tailed Student-t distribution

Bayesian Analysis of the Stochastic Conditional Duration Model

A Bayesian Markov Chain Monte Carlo methodology is developed for estimating the stochastic conditional duration model. The conditional mean of durations between trades is modelled as a latent stochastic process, with the conditional distribution of durations having positive support. The sampling scheme employed is a hybrid of the Gibbs and Metropolis Hastings algorithms, with the latent vector sampled in blocks. The suggested approach is shown to be preferable to the quasi-maximum likelihood approach, and its mixing speed faster than that of an alternative single-move algorithm. The methodology is illustrated with an application to Australian intraday stock market data.Transaction data, Latent factor model, Non-Gaussian state space model, Kalman filter and simulation smoother.

Parameterisation and Efficient MCMC Estimation of Non-Gaussian State Space Models

The impact of parameterisation on the simulation efficiency of Bayesian Markov chain Monte Carlo (MCMC) algorithms for two non-Gaussian state space models is examined. Specifically, focus is given to particular forms of the stochastic conditional duration (SCD) model and the stochastic volatility (SV) model, with four alternative parameterisations of each model considered. A controlled experiment using simulated data reveals that relationships exist between the simulation efficiency of the MCMC sampler, the magnitudes of the population parameters and the particular parameterisation of the state space model. Results of an empirical analysis of two separate transaction data sets for the SCD model, as well as equity and exchange rate data sets for the SV model, are also reported. Both the simulation and empirical results reveal that substantial gains in simulation efficiency can be obtained from simple reparameterisations of both types of non-Gaussian state space models.Bayesian methodology, stochastic volatility, durations, non-centred in location, non-centred in scale, inefficiency factors.