Generalization of a nonparametric co-integration analysis for multivariate integrated processes of an integer order
This paper provides a further generalization of co-integration tests in a nonparametric setting. We adopt Bierens' approach in order to give an extension for processes I(d), with a fixed integer d. A generalized eigenvalue problem is solved, and the test statistics involved are obtained starting from two matrices that are independent on the data generating process. The mathematical tools we adopt are related to the asymptotic theory of the stochastic processes. The key point of our work is linked to the distinguishing between the stationary and non-stationary part of an integrated process.
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- Bierens, H.J., 1995.
"Nonparametric cointegration analysis,"
1995-123, Tilburg University, Center for Economic Research.
- Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
- Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
- Engle, Robert F & Granger, Clive W J, 1987.
"Co-integration and Error Correction: Representation, Estimation, and Testing,"
Econometric Society, vol. 55(2), pages 251-276, March.
- Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
- James H. Stock & Mark W. Watson, 1991.
"A simple estimator of cointegrating vectors in higher order integrated systems,"
Working Paper Series, Macroeconomic Issues
91-3, Federal Reserve Bank of Chicago.
- Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
- Peter C.B. Phillips, 1988.
"Optimal Inference in Cointegrated Systems,"
Cowles Foundation Discussion Papers
866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
- Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
- Engle, Robert F. & Yoo, Byung Sam, 1987. "Forecasting and testing in co-integrated systems," Journal of Econometrics, Elsevier, vol. 35(1), pages 143-159, May.
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