We develop the asymptotic theory for the realised power variation of the processes X = f • 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 condition on the path of...

This paper provides limit distribution results for power variation, that is sums of powers of absolute increments, for certain types of time-changed Brownian motion and $\alpha $-stable processes. Special cases of these processes are stochastic volatility models used extensively in financial...

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 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...

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...

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...

How to measure and model volatility is an important issue in finance. Recent research uses high frequency intraday data to construct ex post measures of daily volatility. This paper uses a Bayesian model averaging approach to forecast realized volatility. Candidate models include autoregressive...

The paper evaluates the performance of several recently proposed change-point tests applied to conditional variance dynamics and conditional distributions of asset returns. These are CUSUM-type tests for beta-mixing processes and EDF-based tests for the residuals of such nonlinear dependent...

Historical and sequential CUSUM change-point tests for strongly dependent nonlinear processes are studied. These tests are used to monitor the conditional variance of asset returns and to provide early information regarding instabilities or disruptions in financial risk. Data-driven monitoring...