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, a method is introduced for approximating the likelihood for the unknown parameters of a state space model. The approximation converges to the true likelihood as the simulation size goes to infinity. In addition, the approximating likelihood is continuous as a function of the unknown parameters under rather general conditions. The approach(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 recent years, numerous volatility-based derivative products have been engineered. This has led to interest in constructing conditional predictive densities and confidence intervals for integrated volatility. In this paper, we propose nonparametric estimators of the aforementioned quantities, based on model free volatility estimators. We establish(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)