Heteroscedasticity test of high-frequency data with jumps and microstructure noise

TL;DR

This paper develops a nonparametric test for detecting heteroscedasticity in high-frequency financial data with jumps and noise, revealing volatility variations within trading days.

Contribution

It introduces a new test estimator that accounts for jumps and microstructure noise, with proven convergence properties and practical applicability to real data.

Findings

Test estimator converges to normal under constant volatility.

Rejection of constant volatility hypothesis in nearly half of tested days.

Volatility is higher during opening and closing periods of trading days.

Abstract

In this paper, we are interested in testing if the volatility process is constant or not during a given time span by using high-frequency data with the presence of jumps and microstructure noise. Based on estimators of integrated volatility and spot volatility, we propose a nonparametric way to depict the discrepancy between local variation and global variation. We show that our proposed test estimator converges to a standard normal distribution if the volatility is constant, otherwise it diverges to infinity. Simulation studies verify the theoretical results and show a good finite sample performance of the test procedure. We also apply our test procedure to do the heteroscedasticity test for some real high-frequency financial data. We observe that in almost half of the days tested, the assumption of constant volatility within a day is violated. And this is due to that the stock prices during opening and closing periods are highly volatile and account for a relative large proportion of intraday variation.