We introduce the Realized moMents of Disjoint Increments (ReMeDI) paradigm to measure microstructure noise (the deviation of the observed asset prices from the fundamental values caused by market imperfections). We propose consistent estimators of arbitrary moments of the microstructure noise...

In this paper, we provide non-parametric statistical tools to test stationarity of microstructure noise in general hidden Ito semimartingales, and discuss how to measure liquidity risk using high frequency financial data. In particular, we investigate the impact of non-stationary microstructure...

In this paper, we develop econometric tools to analyze the integrated volatility (IV) of the efficient price and the dynamic properties of microstructure noise in high-frequency data under general dependent noise. We first develop consistent estimators of the variance and autocovariances of...

Aiming at financial applications, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to learn the diffusion coefficient of...

We estimate a general microstructure model of the transitory and permanent impact of order flow on stock prices. Jumps are detected in both the transaction price (observation equation) and fundamental value (state equation). The model's parameters and variances are updated in real time. Prices...

We consider the best quadratic unbiased estimators of the integrated variance in the presence of independent market microstructure noise. We establish the asymptotic normality of a feasible best quadratic unbiased estimator under the assumption of constant volatility and show that it is...

We propose a new estimator for the integrated covariance of two Ito semimartingales observed at a high-frequency. This new estimator, which we call the pre-averaged truncated Hayashi-Yoshida estimator, enables us to separate the sum of the co-jumps from the total quadratic covariation even in...

The aim of this paper is to develop a multi-asset model based on the Hawkes process describing the evolution of assets at high frequency and to study the lead-lag relationship as well as the correlation between the stocks within this framework. Thanks to its strong analytical tractability...