A simple additivity test for conditionally heteroscedastic nonlinear autoregression

In this article, we propose a test for the additivity of a nonlinear conditionally heteroscedastic autoregressive model. The test is based on the unequal variance unbalanced design ANOVA scheme. An asymptotic distribution of the test statistic is derived and the test performance in finite samples is studied using simulation. To the best of our knowledge, this is the first additivity test for a conditionally heteroscedastic time series model.