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Discussion Paper

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.