This paper presents new results on the Edgeworth expansion for high frequency functionals of continuous diffusion processes. We derive asymptotic expansions for weighted functionals of the Brownian motion and apply them to provide the Edgeworth expansion for power variation of diffusion...

This paper presents a goodness-of-fit test for the volatility function of a SDE driven by a Gaussian process with stationary and centered increments. Under rather weak assumptions on the Gaussian process, we provide a procedure for testing whether the unknown volatility function lies in a given...

In this paper we present a test for the maximal rank of the matrix-valued volatility process in the continuous Itô semimartingale framework. Our idea is based upon a random perturbation of the original high frequency observations of an Itô semimartingale, which opens the way for rank testing....

High-profile universities often face public criticism for undermining academic merit and promoting social elitism through their admissions-process. In this paper, we develop an empirical test for whether access to selective universities is meritocratic. If so, then the academic potential of...

This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of the BSS model. We review the limit theory discussed in...

This paper presents the asymptotic theory for non-degenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The...

This paper establishes uniform consistency results for nonparametric kernel density and regression estimators when time series regressors concerned are nonstationary null recurrent Markov chains. Under suitable regularity conditions, we derive uniform convergence rates of the estimators. Our...

This paper introduces the concept of stochastic volatility of volatility in continuous time and, hence, extends standard stochastic volatility (SV) models to allow for an additional source of randomness associated with greater variability in the data. We discuss how stochastic volatility of...

Novel transition-based misspeci?cation tests of semiparametric and fully parametric univariate diffusion models based on the estimators developed in Kristensen (Journal of Econometrics, 2010) are proposed. It is demonstrated that transition-based tests in general lack power in detecting local...

This paper presents a generalized pre-averaging approach for estimating the integrated volatility. This approach also provides consistent estimators of other powers of volatility – in particular, it gives feasible ways to consistently estimate the asymptotic variance of the estimator of the...