I discuss models which allow the local level model, which rationalised exponentially weighted moving averages, to have a time-varying signal/noise ratio.  I call this a martingale component model.  This makes the rate of discounting of data local.  I show how to handle such models...

We propose a new measure of risk, based entirely on downward moves measured using high frequency data.  Realised semivariances are shown to have important predictive qualities for future market volatility.  The theory of these new measures is spelt out, drawing on some new results from...

Here we assume that the logarithmic asset price is given by a semimartingale. Jacod (2006) has derived an infeasible central limit theorem for the realised variance in such a general framework. However, here we focus on constructing a feasible limit theorem. We propose a new estimator for the...

In this paper we review some recent work on limit results on realised power variation, that is sums of powers of absolute increments of various semimartingales. A special case of this analysis is realised variance and its probability limit, quadratic variation. Such quantities often appear in...

In this paper we study the reliability of the mixed normal asymptotic distribution of realised variance error, which we have previously derived using the theory of realised power variation. Our experiments suggest that the asymptotics is reliable when we work with the logarithmic transform of...

This paper provides limit distribution results for power variation, that is sums of powers of absolute increments, for certain types of time-changed Brownian motion and $alpha $-stable processes. Special cases of these processes are stochastic volatility models used extensively in financial...

We use high frequency financial data to proxy, via the realised variance, each days financial variability. Based on a semiparametric stochastic volatility process, a limit theory shows you can represent the proxy as a true underlying variability plus some measurement noise with known...