Robustness of Some Portmanteau Correlation Tests in Financial Time Series

Abstract

SYNOPTIC ABSTRACTThe Box–Pierce and Ljung–Box tests are portmanteau tests generally used to test the independence in time series data. These tests can also be applied to the squares of the observations to detect independence. Because most financial time series data show heavy-tailed behavior, these tests may incorrectly reject the null hypothesis of no correlation when there is volatility clustering in the data. A modified version of the Box–Pierce test is introduced to capture this heavy-tailed behavior and showed that the modified test performs better when there is an autoregressive conditional heteroscedasticity (ARCH) effect. In this article, we introduce a correction factor for the Ljung–Box test. In addition, we conduct a series of simulations to study the robustness of the Box–Pierce and Ljung–Box tests and their modified versions in situations where the data exhibit ARCH, generalized ARCH (GARCH), and stochastic volatility (SV) effects. Our simulation studies indicate that the modified versions of the Box–Pierce and Ljung–Box tests are more robust when the data exhibit ARCH, GARCH, and SV effects.