Model checks for the volatility under microstructure noise

TL;DR

This paper introduces new statistical tests for volatility in high-frequency financial data that remain reliable despite microstructure noise, using preaveraging and bootstrap methods.

Contribution

It develops novel tests based on integrated stochastic processes that are robust to microstructure noise, improving over existing methods.

Findings

Tests maintain correct level under microstructure noise

Bootstrap version shows good finite sample performance

Method applicable to high-frequency financial data

Abstract

We consider the problem of testing the parametric form of the volatility for high frequency data. It is demonstrated that in the presence of microstructure noise commonly used tests do not keep the preassigned level and are inconsistent. The concept of preaveraging is used to construct new tests, which do not suffer from these drawbacks. These tests are based on a Kolmogorov-Smirnov or Cramer-von-Mises functional of an integrated stochastic process, for which weak convergence to a (conditional) Gaussian process is established. The finite sample properties of a bootstrap version of the test are illustrated by means of a simulation study.