In this paper we introduce a decomposition of the joint distribution of price changes of assets recorded trade--by--trade. Our decomposition means that we can model the dynamics of price changes using quite simple and interpretable models which are easily extended in a great number of...

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...

In a recent paper we have introduced the class of realised kernel estimators of the increments of quadratic variation in the presence of noise. We showed this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend our...

A local level model has a deterministic level when the signal-to-noise ratio q is zero. In this paper we investigate the properties of the maximum likelihood estimator of q, paying particular attention to the case where its true value is zero. These properties are shown to be crucially dependent...

Limit distribution results on realized power variation, that is, sums of absolute powers of increments of a process, are derived for certain types of semimartingale with continuous local martingale component, in particular for a class of flexible stochastic volatility models. The theory covers,...