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Non-Gaussian processes of Ornstein-Uhlenbeck type, or OU processes for short, offer the possibility of capturing important distributional deviations from Gaussianity and for flexible modelling of dependence structures. This paper develops this potential, drawing on and extending powerful results from probability theory for applications in statistical… (More)

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, under the assumption of a rather general stochastic volatility model, we derive the moments and the asymptotic… (More)

This paper shows that realised power variation and its extension called realised bipower variation that we introduce here is somewhat robust to rare jumps. We demonstrate that in special cases realised bipower variation estimate integrated variance in stochastic volatility models, thus providing a model free and consistent alternative to realised variance.… (More)

- Ole E. Barndorff-Nielsen
- Finance and Stochastics
- 1997

In this paper we provide an asymptotic distribution theory for some non-parametric tests of the hypothesis that asset prices have continuous sample paths. We study the behaviour of the tests using simulated data and see that certain versions of the tests have good finite sample behaviour. We also apply the tests to exchange rate data and show that the null… (More)

This paper analyses multivariate high frequency financial data using realised covariation. We provide a new asymptotic distribution theory for standard methods such as regression, correlation analysis and covariance. It will be based on a fixed interval of time (e.g. a day or week), allowing the number of high frequency returns during this period to go to… (More)

This paper reviews some recent work in which Lévy processes are used to model and analyse time series from financial econometrics. A main feature of the paper is the use of positive OrnsteinUhlenbeck (OU) type processes inside stochastic volatility processes. The basic probability theory associated with such models is discussed in some detail.

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 which has these three properties which are all essential for… (More)

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 semimartingale we recall the fundamental result that RV is a… (More)

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.