GARCH models are commonly used as latent processes in econometrics, financial economics and macroeconomics. Yet no exact likelihood analysis of these models has been provided so far. In this paper we outline the issues and suggest a Markov chain Monte Carlo algorithm which allows the calculation...

We provide numerically reliable analytical expressions for the score of conditionally heteroskedastic dynamic regression models when the conditional distribution is multivariate $t$. We also derive one-sided and 2-sided LM tests for multivariate normality versus multivariate $t$ based on the...

We develop generalised indirect inference procedures that handle equality and inequality constraints on the auxiliary model parameters. We obtain expressions for the optimal weighting matrices, and discuss as examples an MA(1) estimated as AR(1), an AR(1) estimated as MA(1), and a log-normal...