We extend the classical local Whittle estimation procedure to fractionally integrated I(d) processes, where d-3/2, thus covering stationary and non-stationary regions. Asymptotic properties of the bias of the estimator are investigated. It is shown that in a wider region than previously...

We examine the estimation of the memory parameter d of I(d) series, by fitting an auto-regressive AR(k) representation where k approaches infinity simultaneously with the observed series length n. Under some conditions on the growth of k with respect to n, and on the short memory component of...

We deal with the important question of estimating the long-run variance of a stationary sequence. We derive the asymptotic properties of a generalized Newey-West type of estimator in the case of a linear I(d) process. The results show that the bias and asymptotic distribution of the generalized...

An asymptotic theory is developed for a quadratic form Q_{n,X} in linear random variables X1,…,X_{n} which can exhibit long, short, or negative dependence and whose kernel depends on n. It offers conditions under which Q_{n,X} can be approximated in the L1 and L2 norms by a form Q_{n,Z} in...

We suggest a rescaled variance type of test for the null hypothesis of stationarity against deterministic and stochastic trends (unit roots). The deterministic trend can be represented as a general function of time (e.g. non-parametric, linear or polynomial regression, abrupt changes in the...

This paper deals with estimation and hypothesis testing in stationary and nonstationary models with a linear trend. Using semiparametric estimators, we obtain asymptotic confidence intervals for mean, trend, and memory parameters. The confidence intervals are applicable for a wide class of...

First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient ?=?_{n}?[0,1) provided (1-?_{n})n??. This extends existing Gaussian limit theory by allowing for values of stationary ? that include neighbourhoods of unity...

For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogram and local Whittle estimators, has been exhaustively examined. However, except for some specific cases, little is known about the estimation of the memory parameter for nonlinear processes. The...