Michael K. Pitt

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This paper provides methods for carrying out likelihood based inference for diffusion driven models, for example discretely observed multivariate diffusions, continuous time stochas-tic volatility models and counting process models. The diffusions can potentially be non-stationary. Although our methods are sampling based, making use of Markov chain Monte(More)
In this paper we provide a unified methodology in order to conduct likelihood-based inference on the unknown parameters of a general class of discrete-time stochastic volatility models, characterized by both a leverage effect and jumps in returns. Given the non-linear/non-Gaussian state-space form, approximating the likelihood for the parameters is(More)
In this paper we develop likelihood based inferential methods for a novel class of (potentially non-stationary) diffusion driven state space models. Examples of models in this class are continuous time stochastic volatility models and counting process models. Although our methods are sampling based, making use of Markov chain Monte Carlo methods to sample(More)
We show that for a general state space model the general auxiliary particle filter evaluates a simulated likelihood that is an unbiased estimate of the true likelihood. This generalizes the unbiasedness result for the standard particle filter by Del Moral (2004) and justifies the use of auxiliary particle filter to carry out Bayesian inference in state(More)
This paper provides methods for carrying out likelihood based inference on non-linear observed and partially observed non-linear diffusions. The diffusions can potentially be non-stationary. The methods are based on innovative Markov chain Monte Carlo methods combined with an augmentation strategy. We study the performance of the methods as the degree of(More)
In this paper, we p r o vide a method for modelling stationary time series. We allow t h e family of marginal densities for the observations to be speciied. Our approach is to construct the model with a speciied marginal family and build the dependence structure around it. We show that the resulting time series is linear with a simple autocorrelation(More)