Analysis of Models with Complex Roots on the Unit Circle

Abstract

This paper deals with nonstationary autoregressive (AR) models with complex roots on the unit circle. We examine the asymptotic properties of the least squares estimators (LSEs) in the model. We also extend the model to the case where the error term follows a stationary linear process. We show that the limiting distribution of the LSE of the unit root parameter has a property comparable to that of the LSE in the standard nonstationary seasonal model with period two. Percent points and moments of the limiting distribution are computed by numerical integration.