Likelihood-based estimation of latent generalised ARCH structures
	
Gabriele Fiorentini
	
IPSC-JRC and University of Alicante, TP361, Via E.Fermi 1,
I-21020 Ispra (VA), Italy
	
Enrique Sentana
	
CEMFI, Casado del Alisal 5, E-28014 Madrid, Spain

and

Neil Shephard
Nuffield College, Oxford OX1 1NF, U.K.
	
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.
	
Keywords: Bayesian inference; Dynamic Heteroskedasticity;
Factor models; Markov chain Monte Carlo; Simulated EM algorithm; Volatility.