Bayesian inference in autoregressive Conditional Heteroscedasticity models: A Monte Carlo assessment

In recent decades, ARCH (Autoregressive Conditional Heteroscedasticity) models have become widely popular in modelling the volatility dynamics of financial time-series. This dissertation investigates the finite-sample performance of Bayesian and frequentist estimators for three ARCH-type econometric models commonly used in the empirical literature. Our investigation focuses on the versatility of the Bayesian framework to accommodate non-sample information relevant to the theoretical consistency of these models. In particular, the Bayesian approach enables the econometrician to explicitly entertain the appropriate parameter inequality constraints that guarantee the prediction of non-negative conditional variances, as well as the covariance stationarity of the process of interest. Our findings suggest that the Bayesian point and interval estimators of the parameters generally perform competitively, and quite often outperform their common sampling theory counterparts. Under the appropriate positivity and stationarity constraints, posterior means an medians frequently exhibit lower mean squared error than the maximum likelihood estimator. Similarly, Bayesian credible and highest posterior density intervals often enjoy greater finite-sample probability content than asymptotic confidence intervals. Based on strictly sampling-theory performance criteria, the evidence provides compelling support in favor of the Bayesian framework.