Robust Lagrange multiplier test with forward search simulation envelopes

The Lagrange multiplier test, often adopted to detect heteroscedasticity, suffers from severe size distortion and has low power. An existing robust test based on a forward search algorithm has shown better performance than many existing robust methods. Nevertheless, such a forward robust test relies on con¯dence bands based on the Student's-t distribution which hold only approximately. The robust forward weighted Lagrange multiplier test can be improved through extensive simulation of forward search con¯dence bands, which are set up under the hypothesis of no outlier in the data.