In the framework of integer-valued autoregressive processes of order 1
[INAR(1)], two new tests for the null hypothesis of Poisson-distributed innovations are
developed. The tests focus on time reversibility, as this feature is shown to be satisfied
exclusively by Poisson INAR(1) processes. The necessary asymptotic variances are
explicitly calculated using the joint cumulants of these processes. The finite-sample
behavior of the test statistics and the power of the tests are investigated in a simulation
study. The results show that the newly developed tests perform better than existing
ones in certain situations.

EB00000004423K

Available

• Testing for Poisson arrivals in INAR(1) processes