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...

Employing recent results of Robinson (2005) we consider the asymptotic properties of conditional-sum-of-squares (CSS) estimates of parametric models for stationary time series with long memory. CSS estimation has been considered as a rival to Gaussian maximum likelihood and Whittle estimation of...