Equi-spaced sampling is the norm in applied work using high-frequency data. Due to trade intermittency, however, this traditional sampling scheme amounts to implicit random sampling. Under implicit random sampling and on continuous trajectories, we quantify the asymptotic biases of even realized...

In the context of high-frequency financial data it is often assumed that sampling times are exogenous. This entails that financial asset prices, sampled on a grid of trade instants, are independent from the sampling times. We derive statistical tests capable of determining whether or not, and to...

Realized multipower variation, originally introduced to eliminate jumps, can be extremely useful for inference in pure-jump models. The paper shows how to build a simple and precise estimator of the jump activity index of a semimartingale observed at a high frequency by comparing different...

In the context of high-frequency financial data it is often assumed that sampling times are exogenous. This entails that financial asset prices, sampled on a grid of trade instants, are independent from the sampling times. We derive statistical tests capable of determining whether or not, and to...

We provide a set of probabilistic laws for range-based estimation of integrated variance of a continuous semi-martingale. To accomplish this, we exploit the properties of the price range as a volatility proxy and suggest a new method for non-parametric measurement of return variation. Assuming...

In this paper, we develop a penalized realized variance (PRV) estimator of the quadratic variation (QV) of a high-dimensional continuous Itô semimartingale. We adapt the principle idea of regularization from linear regression to covariance estimation in a continuous-time high-frequency setting....