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 error of certain types and can also handle non-synchronous trading. It is the first estimator...

Motivated by features of low latency data in financial econometrics we study in detail integervalued Lévy processes as the basis of price processes for high frequency econometrics. We propose using models built out of the difference of two subordinators. We apply these models in practice to low...

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...

In this paper we introduce and study a regularizing one-to-one mapping from the class of one-dimensional Lévy measures into itself. This mapping appeared implicitly in our previous paper [O.E. Barndorff-Nielsen, S. Thorbjørnsen, A connection between free and classical infinite divisibility,...

We develop the asymptotic theory for the realised power variation of the processes X=[phi]-G, where G is a Gaussian process with stationary increments. More specifically, under some mild assumptions on the variance function of the increments of G and certain regularity conditions on the path of...

Using bivariate Lévy processes, stationary and self-similar processes, with prescribed one-dimensional marginal laws of type G, are constructed. The self-similar processes are obtained from the stationary by the Lamperti transformation. In the case of square integrability the arbitrary spectral...

Upsilon transformations satisfying certain regularity conditions are shown to generate semigroups of such transformations. This is based on a general commutativity property of the Upsilon transformations, and uses log infinite divisibility. The existence of random integral representations of...

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

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 error of certain types and can also handle non-synchronous trading. It is the first estimator...

type="main" xml:id="sjos12056-abs-0001" <title type="main">ABSTRACT</title>This paper introduces a new continuous-time framework for modelling serially correlated count and integer-valued data. The key component in our new model is the class of integer-valued trawl processes, which are serially correlated, stationary,...