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...

This paper derives the exact distribution of the maximum likelihood estimator of a first order linear autoregression with exponential innovations. We show that even if the process is stationary, the estimator is $T$-consistent, where $T$ is the sample size. In the unit root case the estimator is...

This paper looks at the problem of performing likelihood inference for limited dependent processes. Throughout we use simulation to carry out either classical inference through a simulated score method (simulated EM algorithm) or Bayesian analysis. A common theme is to develop computationally...

Neil Shephard has brought together a set of classic and central papers that have contributed to our understanding of financial volatility. They cover stocks, bonds and currencies and range from 1973 up to 2001. Shephard, a leading researcher in the field, provides a substantial introduction in...

In this paper we replace the Gaussian errors in the standard Gaussian, linear state space model with stochastic volatility processes. This is called a GSSF-SV model. We show that conventional MCMC algorithms for this type of model are ineffective, but that this problem can be removed by...

In this paper, Markov chain Monte Carlo sampling methods are exploited to provide a unified, practical likelihood-based framework for the analysis of stochastic volatility models. A highly effective method is developed that samples all the unobserved volatilities at once using an approximating...

This paper is concerned with the fitting and comparison of high dimensional multivariate time series models with time varying correlations. The models considered here combine features of the classical factor model with those of the univariate stochastic volatility model. Specifically, a set of...

This paper is concerned with simulation based inference in generalized models of stochastic volatility defined by heavy-tailed student-t distributions (with unknown degrees of freedom) and covariate effects in the observation and volatility equations and a jump component in the observation...