A LIMIT THEOREM FOR MILDLY EXPLOSIVE AUTOREGRESSION WITH STABLE ERRORS

We discuss the limiting behavior of the serial correlation coefficient in mildly explosive autoregression, where the error sequence is in the domain of attraction of an a-stable law, a ~0,2# + Therein, the autoregressive coefficient r rn 1 is assumed to satisfy the condition rn r 1 such that n~rn 1! r ` as n r `+ In contrast to the vast majority of existing literature in the area, no specific form of r is required+ We show that the serial correlation coefficient converges in distribution to a ratio of two independent stable random variables+