Understanding the dynamic mechanisms of some key financial and economic quantities plays a central role in an array of decision making processes such as risk management, portfolio allocation, and more generally managerial planning in response to macroeconomic forecasts. This thesis develops Bayesian inferential methodologies for dynamic hierarchically specified models relevant to certain empirical economic and financial settings. The new models are flexible and are therefore able to accommodate non-standard distributional shapes as well as nonlinear relationships between variables. Bayesian inference is obtained by sampling from the relevant posterior densities using Markov Chain Monte Carlo (MCMC) simulation techniques. In addition, the thesis also develops a novel portfolio optimisation method for high-dimensional portfolio selection problems.