Econometrica: Nov 2021, Volume 89, Issue 6

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

https://doi.org/10.3982/ECTA15593
p. 2787-2825

Rui Da, Dacheng Xiu

We conduct inference on volatility with noisy high‐frequency data. We assume the observed transaction price follows a continuous‐time Itô‐semimartingale, contaminated by a discrete‐time moving‐average noise process associated with the arrival of trades. We estimate volatility, defined as the quadratic variation of the semimartingale, by maximizing the likelihood of a misspecified moving‐average model, with its order selected based on an information criterion. Our inference is uniformly valid over a large class of noise processes whose magnitude and dependence structure vary with sample size. We show that the convergence rate of our estimator dominates n1/4 as noise vanishes, and is determined by the selected order of noise dependence when noise is sufficiently small. Our implementation guarantees positive estimates in finite samples.



Log In To View Full Content

Supplemental Material

Supplement to "When Moving-Average Models Meet High-Frequency Data: Uniform Inference on Volatility"

This supplement contains lemmas supporting Appendix A and proofs of Corollary 1 and Proposition 1.

Read More View PDF


Supplement to "When Moving-Average Models Meet High-Frequency Data: Uniform Inference on Volatility"

This zip file contains the replication files for the manuscript.

Read More View ZIP



Back