Nonstationarity-extended local Whittle estimation

This paper extends the classical local Whittle estimation procedure of the memory parameter to fractionally integrated I(d) processes for d∈(-32,∞), covering stationary and nonstationary regions. We introduce the concepts of fully extended discrete Fourier transform and periodogram. We investigate the properties of our fully extended local Whittle (FELW) estimator, which is applicable not only for the traditional cases but also for nonlinear and non-Gaussian processes. For a wide class of processes, we show that the estimator is consistent and we derive its asymptotic expansion. In addition, when the generating process is linear, we show that the estimator satisfies the same normal CLT as in the stationary case. The performance of the estimator is illustrated by a simulation.