An asymptotic theory is given for autoregressive time series with weakly dependent innovations and a root of the form rho_{n} = 1+c/n^{alpha}, involving moderate deviations from unity when alpha in (0,1) and c in R are constant parameters. The limit theory combines a functional law to a...

A limit theory is established for autoregressive time series that smooths the transition between local and moderate deviations from unity and provides a transitional form that links conventional unit root distributions and the standard normal. Edgeworth expansions of the limit theory are given....

This paper studies fractional processes that may be perturbed by weakly dependent time series. The model for a perturbed fractional process has a components framework in which there may be components of both long and short memory. All commonly used estimates of the long memory parameter (such as...

Recent work by the author on methods of spatial density analysis for time series data with stochastic trends is reviewed and extended. The methods are illustrated in some empirical applications and simulations. The empirical applications include macroeconomic data on inflation, financial data on...

This paper investigates a generalized method of moments (GMM) approach to the estimation of autoregressive roots near unity with panel data. The two moment conditions studied are obtained by constructing bias corrections to the score functions under OLS and GLS detrending, respectively. It is...

Stable autoregressive models of known finite order are considered with martingale differences errors scaled by an unknown nonparametric time-varying function generating heterogeneity. An important special case involves structural change in the error variance, but in most practical cases the...

The immense literature and diversity of unit root tests can at times be confusing even to the specialist and presents a truly daunting prospect to the uninitiated. In consequence, much empirical work still makes use of the simplest testing procedures because it is unclear from the literature and...

The bootstrap is shown to be inconsistent in spurious regression. The failure of the bootstrap is spectacular in that the bootstrap effectively turns a spurious regression into a cointegrating regression. In particular, the serial correlation coefficient of the residuals in the bootstrap...

A new approach to robust testing in cointegrated systems is proposed using nonparametric HAC estimators without truncation. While such HAC estimates are inconsistent, they still produce asymptotically pivotal tests and, as in conventional regression settings, can improve testing and inference....

A limit theory is developed for multivariate regression in an explosive cointegrated system. The asymptotic behavior of the least squares estimator of the cointegrating coefficients is found to depend upon the precise relationship between the explosive regressors. When the eigenvalues of the...