Asymptotic Distribution of the Conditional Sum of Squares Estimator Under Moderate Deviation From a Unit Root in MA(1)

This paper considers the conditional sum of squares estimator (CSSE) for the moderate deviation MA(1) process that has the parameter of the MA(1) with the distance between the parameter and unity being larger than O(T -1). We show that the asymptotic distribution of the CSSE is normal, even though the process belongs to the local-to-unity class. The convergence rate continuously changes from an invertible order to a noninvertible one. In this sense, the moderate deviation process in MA(1) has a continuous bridge property like the AR process.