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The Johansen-Granger Representation Theorem: An Explicit Expression for I(1) Processes

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  • Hansen, Peter Reinhard

Abstract

The Johansen-Granger representation theorem for the cointegrated vector autoregressive process is derived using the companion form. This approach yields an explicit representation of all coefficients and initial values. This result is useful for impulse response analysis, common feature analysis and asymptotic analysis of cointegrated processes.

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  • Hansen, Peter Reinhard, 2000. "The Johansen-Granger Representation Theorem: An Explicit Expression for I(1) Processes," University of California at San Diego, Economics Working Paper Series qt832256dg, Department of Economics, UC San Diego.
    • Handle: RePEc:cdl:ucsdec:qt832256dg
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    1. Johansen, Soren & Schaumburg, Ernst, 1998. "Likelihood analysis of seasonal cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 301-339, November.
    2. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 369-380, October.
    3. Engle, Robert F & Kozicki, Sharon, 1993. "Testing for Common Features: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(4), pages 393-395, October.
    4. Lutkepohl, Helmut & Saikkonen, Pentti, 1997. "Impulse response analysis in infinite order cointegrated vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 127-157, November.
    5. Lutkepohl, Helmut & Reimers, Hans-Eggert, 1992. "Impulse response analysis of cointegrated systems," Journal of Economic Dynamics and Control, Elsevier, vol. 16(1), pages 53-78, January.
    6. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
    7. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    8. Warne, A., 1993. "A Common Trends Model: Identification, Estimation and Inference," Papers 555, Stockholm - International Economic Studies.
    9. Hylleberg, S. & Engle, R. F. & Granger, C. W. J. & Yoo, B. S., 1990. "Seasonal integration and cointegration," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 215-238.
    10. 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.
    11. Hansen, Peter Reinhard & Johansen, Soren, 1998. "Workbook on Cointegration," OUP Catalogue, Oxford University Press, number 9780198776079.
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    1. Maciej Bukowski & Grzegorz Koloch & Piotr Lewandowski, 2013. "Shocks and rigidities as determinants of CEE labour markets’ performance," The Economics of Transition, The European Bank for Reconstruction and Development, vol. 21(3), pages 553-581, July.

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