Robustness of the arch tests in the presence of serial correlation

This paper investigates the accuracy of the autoregressive conditional heteroscedasticity (ARCH) tests' asymptotic distributions in the presence of autoregressive moving average (ARMA) errors. These tests include the Lagrange multiplier (LM) and locally best score (LBS) tests, and their ARMA-corrected versions that are proposed in this paper. A simulation study finds that the LM and LBS tests erroneously reject the null of no ARCH far more frequently if serial correlation is unwittingly omitted. The corrected versions have sizes that are generally close to the nominal level and have good powers. An encouraging finding is that the augmented LM and LBS tests' sizes and powers are not sensitive to the slight over-specification of the dynamics, particularly in large samples. These tests do not appear to be sensitive to non-normal errors. The results in this study suggest that the LM and LBS procedures can be used to test independent against ARMA-ARCH disturbances.