A robust forward weighted Lagrange multiplier test for conditional heteroscedasticity

Statistical tests routinely adopted for detecting nonlinear components in time series rely on the auxiliary regression of ARMA lagged residuals, and the Lagrange multiplier test to detect ARCH components is an example. The size distortion of such test suggests adopting a weighted test, where the weights are computed through a forward search algorithm. Simulations show that the forward weighted robust test is preferable to the classical Lagrange test and to existing robust tests, which are based on backward weighted regression or on estimated autocorrelation function. The forward weighted robust test is applied to daily financial and quarterly macroeconomic time series, showing its usefulness in detecting ARCH effects, even when outliers are present.