This paper reviews the roles of gamma type kernels in the theory and modelling for Brownian and Lévy semistationary processes. Applications to financial econometrics and the physics of turbulence are pointed out.

In this paper we study the asymptotic behaviour of power and multipower variations of stochastic processes. Processes of the type considered serve in particular, to analyse data of velocity increments of a fluid in a turbulence regime with spot intermittency sigma. The purpose of the present...

We will review the econometrics of non-parametric estimation of the components of the variation of asset prices. This very active literature has been stimulated by the recent advent of complete records of transaction prices, quote data and order books. In our view the interaction of the new data...

This paper looks at some recent work on estimating quadratic variation using realised volatility (RV) - that is sums of M squared returns. When the underlying process is a semimartingale we recall the fundamental result that RV is a consistent estimator of quadratic variation (QV). We express...

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...

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...