A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances.

This paper considers testing for autoregressive conditional heteroskedasticity and generalized autoregressive conditional heteroskedasticity disturbances in the linear regression model. These testing problems are one-sided in nature; a fact ignored by the Lagrange multiplier test. A test that exploits this one-sided aspect is constructed based on the sum of the scores. The size and power properties of two versions of this test under normal and leptokurtic disturbances are investigated via a Monte Carlo experiment. The results indicate that both version s of the new test typically have superior power to two versions of the Lagrange multiplier test and possibly also more accurate asymptotic critical values.