Likelihood-based estimation of latent generalised ARCH

Gabriele Fiorentini: Università di Firenze, Viale Morgagni 59, I-50134 Firenze, Italy fiorentini@ds.unifi.it

Enrique Sentana: CEMFI, Casado del Alisal 5, E-28014 Madrid, Spain sentana@cemfi.es

Neil Shephard: Nuffield College, Oxford OX1 1NF, U.K. neil.shephard@nuf.ox.ac.uk

Abstract

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 of a classical estimator via the simulated EM algorithm or a Bayesian solution in O(T) computational operations, where T denotes the sample size. We assess the performance of our proposed algorithm in the context of both artificial examples and an empirical application to 26 UK sectorial stock returns, and compare it to existing approximate solutions.

GARCH models are commonly used as latent processes in econometrics, financial economics and macroeconomics. Yet no exact likelihood analysis of these models has been

Keywords: Bayesian inference; Dynamic Heteroskedasticity; Factor models; Markov chain

Appeared in Econometrica, 2004, 72, 1481-1517

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