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In this paper, we are interested in testing if the volatility process isconstant or not during a given time span by using high-frequency data with thepresence of jumps and microstructure noise. Based on estimators of integratedvolatility and spot volatility, we propose a nonparametric way to depict thediscrepancy between local variation and global variation. We show that ourproposed test estimator converges to a standard normal distribution if thevolatility is constant, otherwise it diverges to infinity. Simulation studiesverify the theoretical results and show a good finite sample performance of thetest procedure. We also apply our test procedure to do the heteroscedasticitytest for some real high-frequency financial data. We observe that in almosthalf of the days tested, the assumption of constant volatility within a day isviolated. And this is due to that the stock prices during opening and closingperiods are highly volatile and account for a relative large proportion ofintraday variation.

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