In this paper, we propose a constancy test for volatility in It processes based on discretely sampled data. The test statistic constitutes an integration of the Ljung–Box test statistic and the kurtosis statistic in the Jarque–Bera test. It is shown that under regularity conditions, the proposed test asymptotically follows a chi-square distribution under the null hypothesis of constant volatility. To evaluate the test, empirical sizes and powers were examined through a simulation study. Analysis of real data including ultra-high frequency transaction data and interest rates was also conducted for illustration. Copyright © 2011 John Wiley & Sons, Ltd.