The Role of Initial Values in Nonstationary Fractional Time Series Models

Abstract

We consider the nonstationary fractional model Delta^d Xt = epsilon t with epsilon t i.i.d.(0;sigma^2) and d > 1/2. We derive an analytical expression for the main term of the asymptotic bias of the maximum likelihood estimator of d conditional on initial values, and we discuss the role of the initial values for the bias. The results are partially extended to other fractional models, and three different applications of the theoretical results are given.

Keywords: Asymptotic expansion, bias, conditional inference, fractional integration, initial values, likelihood inference

JEL Classification: C22