A local limit theorem is proved for sample covariances of nonstationary time series and integrable functions of such time series that involve a bandwidth sequence. The resulting theory enables an asymptotic development of nonparametric regression with integrated or fractionally integrated...

This paper proposes some new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The...

We correct the limit theory presented in an earlier paper by Hu and Phillips (Journal of Econometrics, 2004) for nonstationary time series discrete choice models with multiple choices and thresholds. The new limit theory shows that, in contrast to the binary choice model with nonstationary...

This paper studies regressions for partially identified equations in simultaneous equations models (SEMs) where all the variables are I(l) and cointegrating relations are present. Asymptotic properties of OLS and 2SLS estimators under partial identification are derived. The results show that the...

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.

This paper reexamines the permanent income hypothesis (PIH) in the frequency domain. Using a simple model, we demonstrate that the PIH implies the marginal propensity to consume (MPC) out of zero frequency income is unity. The PIH also implies that the MPC out of transitory (or high frequency)...

An asymptotic expansion is given for the autocovariance matrix of a vector of stationary long-memory processes with memory parameters d satisfying 0 < d < 1/2. The theory is then applied to deliver formulae for the long run covariance matrices of multivariate time series with long memory.

This paper implements a new statistical approach to robust regression with nonstationary time series. The methods are presently under theoretical development in other work, and are briefly exposited here. They allow us to perform regressions in levels with nonstationary time series data, they...

Employing power kernels suggested in earlier work by the authors (2003), this paper shows how to re.ne methods of robust inference on the mean in a time series that rely on families of untruncated kernel estimates of the long-run parameters. The new methods improve the size properties of...