ARMA-GARCH models: Bayes estimation versus MLE, and Bayes non-stationarity test

We compare small-sample properties of Bayes estimation and Maximum likelihood estimation (MLE) of ARMA-GARCH models. Our Monte Carlo experiments indicate that in small sample, the Bayes estimator beats the MLE. We also develop a Bayes method of testing strict stationarity and ergodicity of the conditional variance in the GARCH(1,1) process, near epoch dependence (NED), and finiteness of unconditional moments of the GARCH(1,1) process by using a Markov chain Monte Carlo (MCMC) method We apply this method to test these properties in the ARMA-GARCH models of weekly foreign exchange rates.