A Simple Mle of Cointegrating Vectors in Higher Order Integrated Systems

31 Pages Posted: 9 Mar 2004 Last revised: 26 Mar 2023

See all articles by James H. Stock

James H. Stock

Harvard University - Department of Economics; National Bureau of Economic Research (NBER); Harvard University - Harvard Kennedy School (HKS)

Mark W. Watson

Princeton University - Princeton School of Public and International Affairs; National Bureau of Economic Research (NBER)

Date Written: December 1989

Abstract

An MLE of the unknown parameters of co integrating vectors is presented for systems in which some variables exhibit higher orders of integration, in which there might be deterministic components, and in which the co integrating vector itself might involve variables of differing orders of integration. The estimator is simple to compute: it can be calculated by running GLS for standard regression equations with serially correlated errors. Alternatively, an asymptotically equivalent estimator can be computed using OLS. Usual Wald test statistics based on these MLE's (constructed using an autocorrelation robust covariance matrix in the case of the OLS estimator) have asymptotic x2 distributions.

Suggested Citation

Stock, James H. and Watson, Mark W., A Simple Mle of Cointegrating Vectors in Higher Order Integrated Systems (December 1989). NBER Working Paper No. t0083, Available at SSRN: https://ssrn.com/abstract=305522

James H. Stock (Contact Author)

Harvard University - Department of Economics ( email )

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Harvard University - Harvard Kennedy School (HKS) ( email )

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Mark W. Watson

Princeton University - Princeton School of Public and International Affairs ( email )

Princeton University
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United States

National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
United States

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