We note that likelihood inference can be based on an unbiased simulation-based estimator of the likelihood when it is used inside a Metropolis–Hastings algorithm. This result has recently been introduced in statistics literature by Andrieu, Doucet, and Holenstein (2010, <italic>Journal of the Royal...</italic>

Suppose we wish to carry out likelihood based inference but we solely have an unbiased simulation based estimator of the likelihood. We note that unbiasedness is enough when the estimated likelihood is used inside a Metropolis-Hastings algorithm. This result has recently been intro- duced in...

A key ingredient of many particle filters is the use of the sampling importance resampling algorithm (SIR), which transforms a sample of weighted draws from a prior distribution into equally weighted draws from a posterior distribution.  We give a novel analysis of the SIR algorithm and analyse...

Suppose we wish to carry out likelihood based inference but we solely have an unbiased simulation based estimator of the likelihood.  We note that unbiasedness is enough when the estimated likelihood is used inside a Metropolis-Hastings algorithm.  This result has recently been introduced in...

In this paper we will rigourously study some of the properties of continuous time stochastic volatility models. We have five main results, including: the stochastic volatility class can be linked to Cox process based models of tick-by-tick financial data; we characterise the moments,...

Realized kernels use high-frequency data to estimate daily volatility of individual stock prices. They can be applied to either trade or quote data. Here we provide the details of how we suggest implementing them in practice. We compare the estimates based on trade and quote data for the same...

This paper derives the exact distribution of the maximum likelihood estimator of a first-order linear autoregression with an exponential disturbance term. We also 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...

This paper is concerned with the Bayesian estimation of non-linear stochastic differential equations when only discrete observations are available. The estimation is carried out using a tuned MCMC method, in particular a blcked Metropolis-Hastings algorithm, by introducing auxiliary points and...