Asymptotic distribution of the conditional-sum-of-squares estimator under moderate deviation from a unit root in MA(1)

We consider the conditional-sum-of-squares estimator (CSSE) for the moderate deviation moving average (MA(1)) process, which has a parameter belonging to a neighborhood of unity with a shrinking radius larger than O(T−1) of the near unit root. In this process, we prove consistency and asymptotic normality of the CSSE.