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...

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...

This paper looks at some recent work on estimating quadratic variation using realised variance (RV) - that is sums of M squared returns. This econometrics has been motivated by the advent of the common availability of high frequency financial return data. When the underlying process is a...

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...

Limit distribution results on realised 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,...

This paper shows that realised power variation and its extension we introduce here called realised bipower variation is somewhat robust to rare jumps. We show realised bipower variation estimates integrated variance in SV models --- thus providing a model free and consistent alternative to...

The availability of intra-day data on the prices of speculative assets means that we can use quadratic variation like measures of activity in financial markets, called realised volatility, to study the stochastic properties of returns. Here we provide a statistical basis for realised volatility...

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 studies in some detail a class of high frequency based volatility (HEAVY) models.  These models are direct models of daily asset return volatility based on realized measures constructed from high frequency data.  Our analysis identifies that the models have momentum and mean...

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...