A consistent test for conditional symmetry in time series models

The assumption of conditional symmetry is often invoked to validate adaptive estimation and consistent estimation of ARCH/GARCH models by quasi-maximum likelihood. Imposing conditional symmetry can increase the efficiency of bootstraps if the symmetry assumption is valid. This paper proposes a procedure for testing conditional symmetry. The proposed test does not require the data to be stationary or i.i.d., and the dimension of the conditional variables can be infinite. The proposed test is consistent and is asymptotically distribution free. In addition, the test is shown to have nontrivial power against root-T local alternatives. The size and power of the test are satisfactory even for small samples. Applying the test to various time series, we reject conditional symmetry in inflation, exchange rate and stock returns. Among the nonfinancial time series considered, we find that investment, the consumption of durables, and manufacturing employment also reject conditional symmetry.