Abstract: Traditional tests for conditional heteroscedasticity are based on testing for significant autocorrelations of squared or absolute observations. In the context of high frequency time series of financial returns, these autocorrelations are often positive and very persistent, although their magnitude is usually very small. Moreover, the sample autocorrelations are severely biased towards zero, especially if the volatility is highly persistent. Consequently, the power of the traditional tests is often very low. In this paper, we propose a new test that takes into account not only the magnitude of the sample autocorrelations but also possible patterns among them. This additional information makes the test more powerful in situations of empirical interest. The asymptotic distribution of the new statistic is derived and its finite sample properties are analyzed by means of Monte Carlo experiments. The performance of the new test is compared with various alternative tests. Finally, we illustrate the results analyzing several time series of financial returns.
Key words and phrases: Autocorrelations of non-linear transformations, GARCH, long-memory, McLeod-Li statistic, stochastic volatility.