Goodness‐of‐fit tests of normality for the innovations in ARMA models

.  In this paper, we propose a goodness‐of‐fit test of normality for the innovations of an ARMA( p , q ) model with known mean or trend. The test is based on the data driven smooth test approach and is simple to perform. An extensive simulation study is conducted to study the behaviour of the test for moderate sample sizes. It is found that our approach is generally more powerful than existing tests while holding its level throughout most of the parameter space and, thus, can be recommended. This agrees with theoretical results showing the superiority of the data driven smooth test approach in related contexts.