We propose a multivariate realised kernel to estimate the ex-post covariation of log-prices. We show this new consistent estimator is guaranteed to be positive semi-definite and is robust to measurement noise of certain types and can also handle non-synchronous trading. It is the first estimator...

We consider kernel-based estimators of integrated variances in the presence of independent market microstructure effects. We derive the bias and variance properties for all regular kernel-based estimators and derive a lower bound for their asymptotic variance. Further we show that the...

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 that this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend...

This paper shows how to use realised kernels to carry out efficient feasible inference on the ex-post variation of underlying equity prices in the presence of simple models of market frictions. The issue is subtle with only estimators which have symmetric weights delivering consistent estimators...

In this paper we provide a systematic study of the robustness of probability limits and central limit theory for realised multipower variation when we add finite activity and infinite activity jump processes to an underlying Brownian semimartingale.

In this paper we provide an asymptotic analysis of generalised bipower measures of the variation of price processes in financial economics. These measures encompass the usual quadratic variation, power variation and bipower variations which have been highlighted in recent years in financial...

In this note we show that the feasible central limit theory for realised volatility and realised covariation recently developed by Barndorff-Nielsen and Shephard applies under arbitrary diffusion based leverage effects. Results from a simulation experiment suggest that the feasible version of...

We propose a new measure of risk, based entirely on downwards 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...

In this brief note we review some of our recent results on the use of high frequency financial data to estimate objects like integrated variance in stochastic volatility models. Interesting issues include multipower variation, jumps and market microstructure effects.