SDS Colloquium Series

Abstract

The concept of the intrinsic processes proposed by Matheron (1973) provides an elegant mathematical framework for modeling nonstationary spatial phenomena. It can be viewed as a direct analogue of taking differences of nonstationary time series in order to achieve stationarity. But it is applicable to spatial data observed on both regular and irregular grids.

The goal of this paper is to establish the inference methods and the relevant theory for identifying the cointegration between two simple intrinsic processes. We apply the least squares estimation, similar to Engle and Granger (1987). However the asymptotic property of the estimation is much more complex, depending on the underlying processes as well as the manner in which the observations were taken. We propose some bootstrap approximations for the asymptotic distribution of the estimators. It turns out that under an additional condition, the wild bootstrap procedure is adaptive automatically to varying convergence rates and limiting distributions. Therefore it paves the way for constructing practically feasible confidence intervals for cointegration coefficients. A new and easy-to-use statistical test is constructed for testing the cointegration. The proposed methods, as well as the associated asymptotic results under various settings, are illustrated in simulation. The application to some real data examples is also reported.

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