On the robustness of nonlinearity tests to moment condition failure

This paper investigates the consequences of testing nonlinearities in data that suffer from moment condition failure. Simulation experiments indicate that tests designed to have maximal power against misspecification of the conditional variance seem to be especially sensitive to the nonexistence of moments. The relationship between findings of nonlinearity and moment condition failure is further investigated in a sample of daily stock returns. The empirical study shows that evidence of nonlinearity in stock returns cannot all be attributed to the nonrobustness of nonlinearity tests to moment condition failure. However, it is shown that most tests of nonlinearity are not reliable in testing situations involving heavy-tailed data.