Weak convergence of partial sums and multilinear forms in independent random variables and linear processes to stochastic integrals now plays a major role in nonstationary time series and has been central to the development of unit root econometrics. The present paper develops a new and...

An asymptotic theory is developed for the kernel density estimate of a random walk and the kernel regression estimator of a nonstationary first order autoregression. The kernel density estimator provides a consistent estimate of the local time spent by the random walk in the spatial vicinity of...

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...

An asymptotic theory for stochastic processes generated from nonlinear transformations of nonstationary integrated time series is developed. Various nonlinear functions of integrated series such as ARIMA time series are studied, and the asymptotic distributions of sample moments of such...

An asymptotic theory is developed for nonlinear regression with integrated processes. The models allow for nonlinear effects from unit root time series and therefore deal with the case of parametric nonlinear cointegration. The theory covers integrable, asymptotically homogeneous and explosive...

This paper develops an asymptotic theory for a first order autoregression with a root near unity. Deviations from the unit root theory are measured through a noncentrality parameter. When this parameter is negative we have a local alternative that is stationary; when it is positive, the local...

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 functional law for an I(1) sample data version of the continuous-path block bootstrap of Paparoditis and Politis (2001) is given. The results provide an alternative demonstration that continuous-path block bootstrap unit root tests are consistent under the null.

This paper provides a new unit root test based on an alternative parameterization which has previously been considered by Bhargava (1986). This parameterization allows for trend under both the null and the alternative, without introducing any parameters that are irrelevant under either. This is...

Under general conditions the sample covariance matrix of a vector martingale and its differences converges weakly to the matrix stochastic integral from zero to one of BdB; where B is vector Brownian motion. For strictly stationary and ergodic sequences, rather than martingale differences, a...