It is shown that the bias of estimated parameters in autoregressive models can increase as the sample size grows. This bias is also a nonmonotonic function of the largest autoregressive root, contrary to what asymptotic approximations had indicated so far in the literature. These unusual results...

and hence makes the test valid for any (T, N) combination. The asymptotic distributions of the tests are derived under the null and are shown to be normally distributed. Their moments for T fixed are derived analytically using Ghazal's (1994, Statistics and Probability letters 20, 313--319) ¹...