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Testing for Autocorrelation and Unit Roots in the Presence of Conditional Heteroskedasticity of Unknown Form

The presence of conditional heteroskedasticity invalidates standard autocorrelation tests such as the Durbin-Watson statistic and its many variants, and reduces the power of standard unit root tests like the Dickey-Fuller test. This paper addresses the problem of testing for AR(1) and AR(p) alternatives in the presence of conditional heteroskedasticity, constructs new autocorrelation tests (called g- and gl- tests), and derives an asymptotic theory for the new statistics. The g test is shown to be robust to any form of conditional heteroskedasticity, while the gl test is robust to the joint presence of conditional heteroskedasticity and lagged dependent variables. The paper also develops a GLS-type unit root test that allows for conditional heteroskedasticity. Its limit distribution turns out to be a convex mixture of the Dickey-Fuller distribution and the standard normal distribution. It is shown that the GLS statistic improves the power of the Dickey-Fuller test under condictional heteroskedasticity. Some Monte Carlo simulations with the new tests are reported.