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>

An extensive literature in econometrics focuses on finding the exact and approximate first and second moments of the least-squares estimator in the stable first-order linear autoregressive model with normally distributed errors. Recently, Kiviet and Phillips (2005) developed approximate moments...

This paper introduces a novel way of differentiating a unit root from a stationary alternative. We write up the model consisting of zero and nonzero parameters. If the lagged dependent variable has a coefficient of zero, we know that the variable has a unit root. We exploit this property and...

In this paper I propose a novel optimal linear filter for smoothing, trend and signal extraction for time series with a unit root. The filter is based on the Singular Spectrum Analysis (SSA) methodology, takes the form of a particular moving average and is different from other linear filters...

This paper analyses the properties of jackknife estimators of the first-order autoregressive coefficient when the time series of interest contains a unit root. It is shown that, when the sub-samples do not overlap, the sub-sample estimators have different limiting distributions from the...

In this paper, we provide new evidence on the empirical usefulness of various simple seasonal models, and underscore the importance of carefully designing criteria by which one judges alternative models. In particular, we underscore the importance of both choice of forecast or simulation horizon...

This paper considers nonparametric additive models that have a deterministic time trend and both stationary and integrated variables as components. The diverse nature of the regressors caters for applications in a variety of settings. In addition, we extend the analysis to allow the stationary...

This paper focuses on two applications of time series methods. The first proposes a simple transformation of the unit root form of stationary testing to infer about the validity of smoothing by second-order running averages of a series, or of the variables in a linear model (here opposing...

This paper inspects a grid search algorithm to estimate the AR(1) process, based on the joint estimation of the canonical AR(1) equation along with its reverse form. The method relies on the GLS principle, accounting for the covariance error structure of the special estimable system....