Bayesian Model Estimation and Selection for the Weekly Colombian Exchange Rate

This document reviews and applies recently developed techniques for Bayesian estimation and model selection in the context of Time Series modeling for Stochastic Volatility. After the literature review on Generalized Conditional Autoregressive models, Stochastic Volatility models, and the relevant results on Markov Chain Monte Carlo methods (MCMC), an example applying such techniques is shown. The methodology is used with a series of Weekly Colombian-USA Exchange Rate on seven different models. The GARCH model, which uses Type-IV Pearson distribution, is favored for the selecting technique, Reversible Jump MCMC, over other models, including Stochastic Volatility Models with a Student-t distribution. ∗This work is based on the Master Report presented to The University of Texas at Austin as a requirement for my degree of Master of Science in statistics. I would like to thank Dr. Edward George for his guidance, his advice, and his patience. However, any mistakes that remain are my own. Needless to say, I am very thankful to the Colombian Central Bank for its financial support during my studies at UT.