Empirical processes for non ergodic data are investigated under uniform distance. Some CLTs, both uniform and non uniform, are proved. In particular, conditions for Bn = n^(1/2) (µn - bn) and Cn = n^(1/2) (µn - an) to converge in distribution are given, where µn is the empirical measure, an...

This paper deals with empirical processes of the type Cn(B) = n^(1/2) {µn(B) - P(Xn+1 in B | X1, . . . ,Xn)} , where (Xn) is a sequence of random variables and µn = (1/n)SUM(i=1,..,n) d(Xi) the empirical measure. Conditions for supB|Cn(B)| to converge stably (in particular, in distribution)...

In this paper we present two new tests for the parametric form of the variance function in difusion processes dXt = b(t;Xt)+ó(t;Xt)dWt: Our approach is based on two stochastic processes of the integrated volatility. We prove weak convergence of these processes to centered processes whose...

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...

This paper presents a Hayashi-Yoshida type estimator for the covariation matrix of continuous Itô semimartingales observed with noise. The coordinates of the multivariate process are assumed to be observed at highly frequent nonsynchronous points. The estimator of the covariation matrix is...

We develop a new parametric estimation procedure for option panels observed with error which relies on asymptotic approximations assuming an ever increasing set of observed option prices in the moneyness-maturity (cross-sectional) dimension, but with a fixed time span. We develop consistent...

We will focus on estimating the integrated covariance of two diffusion processes observed in a nonsynchronous manner. The observation data is contaminated by some noise, which is possibly correlated with the returns of the diffusion processes, while the sampling times also possibly depend on the...

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