ARCH and bilinearity as competing models for nonlinear dependence

In this article we consider whether the wide acceptance of autoregressive conditional heteroscedasticity (ARCH) models may be at the expense of other nonlinear processes, such as bilinear models. We first propose a joint test for ARCH and bilinearity. A nonnested test is then suggested to determine whether nonlinear dependence should be attributed to ARCH or bilinearity. The tests are then applied to three series. When generalized ARCH (GARCH) models are taken as the null hypothesis, we fail to reject it for all the data series. When bilinearity is taken as the null, however, it is rejected in two cases. Moreover, an out-of-sample forecasting exercise shows that the GARCH model is superior. The results, therefore, indicate a strong preference for the GARCH model.