Bayesian Estimation Of The Parameters Of The Arch Model With Normal Innovations Using Lindley’S Approximation

Autoregressive conditionally heteroscedastic (ARCH) models are used to analyze empirical financial data and capture various stylized facts in financial econometrics. The procedure that is most commonly used for estimating the unknown parameters of an ARCH model is the maximum likelihood estimation (MLE). In this study, it is assumed that the parameters of the ARCH model are random variables having known prior probability density functions, and therefore they will be estimated using Bayesian methods. The Bayesian estimators are not in a closed form, and thus Lindley’s approximation will be used to estimate them. The Bayesian estimators are derived under squared error loss (SEL) and linear exponential (LINEX) loss functions. An example is given in order to illustrate the findings and furthermore, Monte Carlo simulations are performed in order to compare the ML estimates to the Bayesian ones. Finally, conclusions on the findings are given.