The paper considers different versions of the Lagrange
multiplier (LM) tests for autocorrelation and/or for conditional
heteroskedasticity. These versions differ in terms of the
residuals, and of the functions of the residuals, used
to build the tests. In particular, we compare ordinary
least squares versus least absolute deviation (LAD) residuals,
and we compare squared residuals versus their absolute
value. We show that the LM tests based on LAD residuals
are asymptotically distributed as a χ2
and that these tests are robust to nonnormality. The Monte
Carlo study provides evidence in favor of the LAD residuals,
and of the absolute value of the LAD residuals, to build
the LM tests here discussed.