Regression Theory for Near-Integrated Time Series
The concept of a near-integrated vector random process is introduced. Such processes help us to work towards a general asymptotic theory of regression for multiple time series in which some series may be integrated processes of the ARIMA type, others may be stable ARMA processes with near unit roots, and yet others may be mildly explosive. A limit theory for the sample moments of such time series is developed using weak convergence and is shown to involve a simple functionals of a vector diffusion. The results suggest finite sample approximations which in the stationary case correspond to conventional central limit theory. The theory is applied to the study of vector autoregressions and cointegrating regressions of the type recently advanced by Granger and Engle (1987). A noncentral limiting distribution theory is derived for some recently proposed multivariate unit root tests. This yields some interesting insights into the asymptotic power properties of the various tests. Models with drift and near integration are also studied. The asymptotic theory in this case helps to bridge the gap between the nonnormal asymptotics obtained by Phillips and Durlauf (1986) for regressions with integrated regressors and the normal asymptotics that usually apply in regressions with deterministic regressors.
|Date of creation:||Jan 1986|
|Date of revision:||Jan 1987|
|Publication status:||Published in Econometrica (September 1988), 56(5): 1021-1043|
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Cowles Foundation Discussion Papers
795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
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"Statistical Inference in Regressions with Integrated Processes: Part 1,"
Cambridge University Press, vol. 4(03), pages 468-497, December.
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- Peter C.B. Phillips, 1986. "Weak Convergence to the Matrix Stochastic Integral BdB," Cowles Foundation Discussion Papers 796, Cowles Foundation for Research in Economics, Yale University.
- Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
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