Bayesian Estimation of Flexible Multivariate Econometric Models
This thesis focuses on the development of Bayesian models and their application to multivariate econometric data. These models are flexible and are therefore potentially very highly-parameterised. This is accounted for by either assuming sparse model structures, by employing shrinkage priors, by averaging over a subset of parsimonious sub-models or by a combination of these techniques. All inference is obtained from the posterior density and evaluated using computationally intensive Markov chain Monte Carlo (MCMC) estimation. The models are applied to interesting datasets from econometrics and finance and the empirical results of this thesis represent major contributions to the applied literature in their own right.
The thesis is largely based on three separate but broadly related papers. The first is concerned with semiparametric regression models with components that are linear combinations of basis functions. A linearly constrained Gaussian prior, with a potentially rank-deficient precision matrix, is developed for regularisation of the basis coefficients. This prior also identifies the additive model and enables component selection. Non-degenerate priors are assumed for the shrinkage parameters enabling the development of fast and efficient sampling schemes. These sampling schemes and the overall efficacy of the approach are shown to be highly competitive when compared to alternative contemporary methodologies in a simulated environment. The potential of the approach in high dimensional settings is demonstrated by estimating two seemingly unrelated regression models for the analysis of electricity load. Both of these models require the selection and estimation of a largenumber of components that capture the influence of meteorological variables on electricity load. Selecting some of these components as null has a meaningful impact on the results.
In the second paper, a vector autoregression model with skew t distributed disturbances is applied to the forecasting of intraday electricity spot prices. The model is specified par-simoniously by assuming that the inverse scale matrix and the matrix of autoregressive coefficients are sparse. Forecasts from four nested sub-models are evaluated using metrics that include the cumulative rank probability score. The major contribution here is to rigorously analyse an important econometric application, through a combination of contemporary modelling techniques. All aspects of the model can be estimated jointly by exploiting the modular nature of MCMC.
In the third paper, methods are developed for skew selection in two popular skew t distributions. Here, skew selection refers to the simultaneous determination of whether each margin is symmetric or asymmetric. A major contribution here is the development of a prior that is uniform over the values of the skew coefficient. The prior is proper thus enabling skew selection through the introduction of indicator variables in a similar vein to the Bayesian variable selection literature. This prior also provides an elegant solution to the identification problems that arise in the limiting skew normal case. The skew selection methodology is shown to be effective in a simulated setting. Three econometric applications demonstrate the potential of the approach; a simple model for pre-filtered returns of three exchange rates, a three factor model for financial stock returns and a longitudinal vector autoregression for intraday electricity spot prices. In all applications skew selection is insightful.
Notwithstanding these separate contributions, this thesis also contributes to Bayesian models and methods in a general sense. The literature on Bayesian model averaging is refined and expanded. Novel sampling schemes are introduced that are fast and efficient, thus enriching MCMC methodology. The advantages that arise from choosing appropriate priors and from exploiting the modularity of MCMC are highlighted throughout, vindicating a Bayesian approach. The techniques developed in this thesis substantially improve the analysis of a variety of interesting applications. In particular, a number of contributions are made to the empirical understanding of electricity markets using longitudinal models.
Associate Professor Michael Smith and Dr Richard Gerlach.