Dependent microstructure noise and integrated volatility estimation from high-frequency data

Abstract

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 noise using a variant of realized volatility. Next, we employ these estimators to adapt the pre-averaging method and derive consistent estimators of the IV, which converge stably to a mixed Gaussian distribution at the optimal rate n 1/4 . To improve the finite sample performance, we propose a multi-step approach that corrects the finite sample bias, which turns out to be crucial in applications. Our extensive simulation studies demonstrate the excellent performance of our multi-step estimators. In an empirical study, we analyze the dependence structures of microstructure noise and provide intuitive economic interpretations; we also illustrate the importance of accounting for both the serial dependence in noise and the finite sample bias when estimating IV.

A ReMeDI for Microstructure Noise

“…Note that χ has unit variance. We set , motivated by the empirical studies in Aït‐Sahalia, Mykland, and Zhang (2011) and Li, Laeven, and Vellekoop (2020).…”

“…Thus, to correct the bias, we need an estimate of the QV. But the estimation of QV in the presence of dependent noise is not trivial; see a discussion in Li, Laeven, and Vellekoop (2020). In a simulation context, we can obtain the QV and thus can give the LA estimators the privilege to make the bias correction, which is, of course, not feasible in practice.…”

“…Several recent papers explore richer microstructure models by allowing for autocorrelated noise. The estimators of the second moments of noise in Da and Xiu (2019) and Li, Laeven, and Vellekoop (2020) are by‐products of the integrated volatility estimators in the presence of autocorrelated noise. In a recent seminal paper, Jacod, Li, and Zheng (2017) introduced the first feasible procedure, called the local averaging (LA) method, to estimate arbitrary moments of microstructure noise using high‐frequency data.…”

Robust Estimation of Integrated Volatility

“…Assumption (N-v) implies r can be arbitrarily large, thus (23) holds since v > 3. The rest of the proof of (21) follows from the proof of Lemma A.1 in Li et al (2020). 22follows from the condition E |χ i | r < ∞, r > 4 and the limit distribution (21); that is, convergence in distribution implies convergence in moments when some higher order moments of χ are bounded, see, e.g., Theorem 4.5.2 in Chung (2001).…”

When Moving‐Average Models Meet High‐Frequency Data: Uniform Inference on Volatility

“…They implement the estimator and demonstrate its desirable performance in extensive simulations with various noise models. Related work that discusses serially dependent noise also include Kalnina and Linton (2008), Bandi and Russell (2008), Aït‐Sahalia, Mykland, and Zhang (2011), Hautsch and Podolskij (2013), Bibinger, Hautsch, Malec, and Reiß (2019), and Li, Laeven, and Vellekoop (2020). Their assumptions on noise, however, are more restrictive than in our setting.…”