Time series modelling and in particular multivariate time series have received considerable attention in the literature over the past 20 years. Time series data are met in almost all subject areas, such as in economics, engineering, medicine and genetics, to name but a few. One of the key problems of multivariate time series analysis is the estimation of the covariance matrix of the data, as this holds important information of the co-evolution and correlation of the component time series data of interest. The aim of this book is to provide an account of the recent developments on this subject area and subsequently to develop methodology for tackling the problem of variance estimation in time series. The book introduces the basic modelling framework for state space time series models and then it provides estimation algorithms, within the Bayesian paradigm, for several classes of models. The book is aimed at both masters/Ph.D. students in a numerate discipline (such as statistics, mathematics, economics, engineering, computer science, and physics) and postdoctoral researchers interested in time series methods.