Missing observation analysis for matrix-variate time series data

Bayesian inference is developed for matrix-variate dynamic linear models (MV-DLMs), in order to allow missing observation analysis, of any sub-vector or sub-matrix of the observation time series matrix. We propose modifications of the inverted Wishart and matrix t distributions, replacing the scalar degrees of freedom by a diagonal matrix of degrees of freedom. The MV-DLM is then re-defined and modifications of the updating algorithm for missing observations are suggested

Posterior mean and variance approximation for regression and time series problems

This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models that are defined only by specifying means and variances, are constructed based upon second-order conditional independence in order to facilitate posterior updating and prediction of required distributional quantities. Such models are formulated particularly for multivariate regression and time series analysis with unknown observational variance-covariance components. The similarities and differences of these models with the Bayes linear approach are established. Several subclasses of important models, including regression and time series models with errors following multivariate t, inverted multivariate t and Wishart distributions, are discussed in detail. Two numerical examples consisting of simulated data and of US investment and change in inventory data illustrate the proposed methodology

A note on state-space representations of locally stationary wavelet time series

In this note we show that the locally stationary wavelet process can be decomposed into a sum of signals, each of which follows a moving average process with time-varying parameters. We then show that such moving average processes are equivalent to state space models with stochastic design components. Using a simple simulation step, we propose a heuristic method of estimating the above state space models and then we apply the methodology to foreign exchange rates data

On observational variance learning for multivariate Bayesian time series and related models

This thesis is concerned with variance learning in multivariate dynamic linear models (DLMs). Three new models are developed in this thesis. The first one is a dynamic regression model with no distributional assumption of the unknown variance matrix. The second is an extension of a known model that enables comprehensive treatment of any missing observations. For this purpose new distributions that replace the inverse Wishart and matrix T and that allow conjugacy are introduced. The third model is the general multivariate DLM without any precise assumptions of the error sequences and of the unknown variance matrix. We find analytic updatings of the first two moments based on weak assumptions that are satisfied for the usual models. Missing observations and time varying variances are considered in detail for every model. For the first time, deterministic and stochastic variance laws for the general multivariate DLM are presented. Also, by introducing a new distribution that replaces the matrix-beta of a previous work, we prove results on stochastic changes in variance that are in line with missing observation analysis and variance intervention

Bayesian inference of multivariate rotated GARCH models with skew returns

Bayesian inference is proposed for volatility models, targeting financial returns, which exhibit high kurtosis and slight skewness. Rotated GARCH models are considered which can accommodate the multivariate standard normal, Student t, generalised error distributions and their skewed versions. Inference on the model parameters and prediction of future volatilities and cross-correlations are addressed by Markov chain Monte Carlo inference. Bivariate simulated data is used to assess the performance of the method, while two sets of real data are used for illustration: the first is a trivariate data set of financial stock indices and the second is a higher dimensional data set for which a portfolio allocation is performed