The speed of convergence of the truncated realized covariance to the integrated covariation between the two Brownian parts of two semimartingales is heavily influenced by the presence of infinite activity jumps with infinite variation. Namely, the two processes small jumps play a crucial role...

In this paper we consider two processes driven by Brownian motions plus drift and jumps with infinite activity. Given discrete observations on a finite time horizon, we study the truncated (threshold) realized covariance \hat{IC} to estimate the integrated covariation IC between the two Brownian...

We introduce a class of nonparametric spot volatility estimators based on delta sequences and conceived to include many of the existing estimators in the field as special cases. The full limit theory is first derived when unevenly sampled observations under infill asymptotics and fixed...

In this paper we consider two semimartingales driven by Wiener processes and (possibly infinite activity) jumps. Given discrete observations we separately estimate the integrated covariation IC from the sum of the co-jumps. The Realized Covariation (RC) approaches the sum of IC with the co-jumps...

We consider dependence structures in multivariate time series that are characterized by deterministic trends. Results from spectral analysis for stationary processes are extended to deterministic trend functions. A regression cross covariance and spectrum are defined. Estimation of these...

In this paper we study a monotone regularized kernel general empirical Bayes method for the estimation of a vector of normal means. This estimator is used to improve upon the kernel methods of Zhang (1997) [12] and Brown and Greenshtein (2009) [5]. We prove an oracle inequality for the regret of...