Testing for Serial Correlation in the Presence of Dynamic Heteroscedasticity

A test for the presence of serial correlation is routinely carried out as a test for efficiency in financial markets. The problems inherent in such testing in the presence of dynamic heteroscedasticity are addressed in this paper. The accuracy of using standard critical values of serial correlation tests in the presence of autoregressive conditional heteroscedasticity (ARCH), generalized ARCH (GARCH), normal and non-normal disturbances is investigated. Tests examined include the conventional Durbin-Watson, Box-Pierce, Ljung-Box, Lagrange multiplier tests, proposed ARCH-corrected versions of these tests, and the robust tests of Diebold (1986) and Wooldridge (1992). Standard serial correlation tests are derived assuming that the disturbances are homoscedastic, but this study shows that asymptotic critical values are not accurate when this assumption is violated. Asymptotic critical values for the ARCH(2)-corrected LM, BP and BL tests are valid only when the underlying ARCH process is strictly stationary, whereas Wooldridge's robust LM test has good size and power properties overall. These tests exhibit similar behaviour even when the underlying process is GARCH (1, 1). When the regressors include lagged dependent variables, the sizes and powers of the corrected tests depend on the coefficient of the lagged dependent variables, and the ratio of signal to noise. They appear to be robust across various disturbance distributions.