Christopher M. Strickland

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. Regressors are included in the model for the latent process in order to allow additional variables to impact on durations. The sampling scheme employed is a hybrid of the Gibbs and Metropolis-Hastings algorithms, with the latent vector sampled in blocks. Candidate draws for the latent process are generated by applying a Kalman filtering and smoothing algorithm to a linear Gaussian approximation of the non-Gaussian state space representation of the model. Monte Carlo sampling experiments demonstrate that the Bayesian method performs better overall than an alternative quasi-maximum likelihood approach. The methodology is illustrated using Australian intraday stock market data, with Bayes factors used to discriminate between different distributional assumptions for durations.

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.

Efficient Bayesian estimation of multivariate state space models

A Bayesian Markov chain Monte Carlo methodology is developed for the estimation of multivariate linear Gaussian state space models. In particular, an efficient simulation smoothing algorithm is proposed that makes use of the univariate representation of the state space model. Substantial gains over existing algorithms in computational efficiency are achieved using the new simulation smoother for the analysis of high dimensional multivariate time series. The methodology is used to analyse a multivariate time series dataset of the Normalised Difference Vegetation Index (NDVI), which is a proxy for the level of live vegetation, for a particular grazing property located in Queensland, Australia.

Comparison of three-dimensional profiles over time

In this paper, we describe an analysis for data collected on a three-dimensional spatial lattice with treatments applied at the horizontal lattice points. Spatial correlation is accounted for using a conditional autoregressive model. Observations are defined as neighbours only if they are at the same depth. This allows the corresponding variance components to vary by depth. We use the Markov chain Monte Carlo method with block updating, together with Krylov subspace methods, for efficient estimation of the model. The method is applicable to both regular and irregular horizontal lattices and hence to data collected at any set of horizontal sites for a set of depths or heights, for example, water column or soil profile data. The model for the three-dimensional data is applied to agricultural trial data for five separate days taken roughly six months apart in order to determine possible relationships over time. The purpose of the trial is to determine a form of cropping that leads to less moist soils in the root zone and beyond. We estimate moisture for each date, depth and treatment accounting for spatial correlation and determine relationships of these and other parameters over time.