Estimation of the memory parameter (d) is considered for models of nonstationary fractionally integrated time series with d > (1/2). It is shown that the log periodogram regression estimator of d is inconsistent when 1 < d < 2 and is consistent when (1/2) < d = 1. For d > 1, the estimator is shown to converge in probability to unity.

Asymptotic properties of the local Whittle estimator in the nonstationary case (d > 1/2) are explored. For 1/2 < d < 1, the estimator is shown to be consistent, and its limit distribution and the rate of convergence depend on the value of d. For d = 1, the limit distribution is mixed normal. For d > 1 and when the process has a linear trend, the estimator is shown to be inconsistent and to converge in probability to unity.

Semiparametric estimation of the memory parameter is studied in models of fractional integration in the nonstationary case, and some new representation theory for the discrete Fourier transform of a fractional process is used to assist in the analysis. A limit theory is developed for an...

Discrete Fourier transforms (dft's) of fractional processes are studied and an exact representation of the dft is given in terms of the component data. The new representation gives the frequency domain form of the model for a fractional process, and is particularly useful in analyzing the...

Log periodogram (LP) regression is shown to be consistent and to have a mixed normal limit distribution when the memory parameter d = 1. Gaussian errors are not required. Tests of d = 1 based on LP regression are consistent against d < 1 alternatives but inconsistent against d > 1 alternatives. A test based on a modified LP regression that...</1>

Some limit properties for information based model selection criteria are given in the context of unit root evaluation and various assumptions about initial conditions. Allowing for a nonparametric short memory component, standard information criteria are shown to be weakly consistent for a unit...

An asymptotic theory is given for autoregressive time series with a root of the form rho_{n} = 1+c/n^{alpha}, which represents moderate deviations from unity when alpha in (0,1). The limit theory is obtained using a combination of a functional law to a diffusion on D[0,infinity) and a central...

It has been know since Phillips and Hansen (1990) that cointegrated systems can be consistently estimated using stochastic trend instruments that are independent of the system variables. A similar phenomenon occurs with deterministically trending instruments. The present work shows that such...

The maximum likelihood estimator (MLE) of the fractional difference parameter in the Gaussian ARFIMA(0,d,0) model is well known to be asymptotically N(0,6/pi2). This paper develops a second order asymptotic expansion to the distribution of this statistic. The correction term for the density is...

The asymptotic local powers of various panel unit root tests are investigated. The power envelope is obtained under homogeneous and heterogeneous alternatives. It is compared with asymptotic power functions of the pooled t-test, the Ploberger-Phillips (2002) test, and a point optimal test in...