Robust Tests for Heteroskedasticity and Autocorrelation Using Score Function

The standard Lagrange multiplier test for heteroskedasticity was originally developed assuming normality of the disturbance term see Godfrey (1978b), and Breush and Pagan (1979)]. Therefore, the resulting test depends heavily on the normality assumption. Koenker (1981) suggests a studentized form which is robust to nonnormality. This approach seems to be limited because of the unavailability of a general procedure that transforms a test to a robust one. Following Bickel (1978), we use a diierent approach to take account of nonnormality. Our tests will be based on the score function which is deened as the negative derivative of the log-density function with respect to the underlying random variable. To implement the test we use a nonparametric estimate of the score function. Our robust test for heteroskedasticity is obtained by running a regression of the product of the score function and ordinary least squares residuals on some exogenous variables which are thought to be causing the heteroskedasticity. We also use our procedure to develop a robust test for autocorrelation which can be computed by regressing the score function on the lagged ordinary least squares residuals and the independent variables. Finally, we carry out an extensive Monte Carlo study which demonstrates that our proposed tests have superior nite sample properties compared to the standard tests.