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Cointegration Analysis with State Space Models

  • Wagner, Martin

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria and Frisch Centre for Economic Research, Oslo, Norway)

This paper presents and exemplifies results developed for cointegration analysis with state space models by Bauer and Wagner in a series of papers. Unit root processes, cointegration and polynomial cointegration are defined. Based upon these definitions the major part of the paper discusses how state space models, which are equivalent to VARMA models, can be fruitfully employed for cointegration analysis. By means of detailing the cases most relevant for empirical applications, the I(1), MFI(1) and I(2) cases, a canonical representation is developed and thereafter some available statistical results are briefly mentioned.

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File URL: http://www.ihs.ac.at/publications/eco/es-248.pdf
File Function: First version, 2010
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Paper provided by Institute for Advanced Studies in its series Economics Series with number 248.

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Length: 30 pages
Date of creation: Feb 2010
Date of revision:
Handle: RePEc:ihs:ihsesp:248
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  1. Bauer, Dietmar & Wagner, Martin, 2009. "Using subspace algorithm cointegration analysis: Simulation performance and application to the term structure," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1954-1973, April.
  2. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  3. 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.
  4. Dietmar Bauer & Martin Wagner, 2000. "Estimating Cointegrated Systems Using Subspace Algorithms," Econometric Society World Congress 2000 Contributed Papers 0293, Econometric Society.
  5. Martin Wagner, 2002. "A Comparison of Johansen's, Bierens and the Subspace Algorithm Method for Cointegration Analysis," Diskussionsschriften dp0210, Universitaet Bern, Departement Volkswirtschaft.
  6. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
  7. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-44, January.
  8. Gregoir, Stephane & Laroque, Guy, 1994. "Polynomial cointegration estimation and test," Journal of Econometrics, Elsevier, vol. 63(1), pages 183-214, July.
  9. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
  10. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543, March.
  11. Lee, Hahn Shik, 1992. "Maximum likelihood inference on cointegration and seasonal cointegration," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 1-47.
  12. Gregoir, St phane, 1999. "Multivariate Time Series With Various Hidden Unit Roots, Part Ii," Econometric Theory, Cambridge University Press, vol. 15(04), pages 469-518, August.
  13. Lutkepohl, Helmut & Claessen, Holger, 1997. "Analysis of cointegrated VARMA processes," Journal of Econometrics, Elsevier, vol. 80(2), pages 223-239, October.
  14. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : II. New directions," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 309-341.
  15. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
  16. Ahn, Sung K. & Reinsel, Gregory C., 1994. "Estimation of partially nonstationary vector autoregressive models with seasonal behavior," Journal of Econometrics, Elsevier, vol. 62(2), pages 317-350, June.
  17. Aoki, Masanao & Havenner, Arthur, 1989. "A method for approximate representation of vector-valued time series and its relation to two alternatives," Journal of Econometrics, Elsevier, vol. 42(2), pages 181-199, October.
  18. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
  19. 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.
  20. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  21. Saikkonen, Pentti, 1992. "Estimation and Testing of Cointegrated Systems by an Autoregressive Approximation," Econometric Theory, Cambridge University Press, vol. 8(01), pages 1-27, March.
  22. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April.
  23. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  24. John Y. Campbell, 1992. "Inspecting the Mechanism: An Analytical Approach to the Stochastic Growth Model," NBER Working Papers 4188, National Bureau of Economic Research, Inc.
  25. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
  26. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  27. Hall, Anthony D & Anderson, Heather M & Granger, Clive W J, 1992. "A Cointegration Analysis of Treasury Bill Yields," The Review of Economics and Statistics, MIT Press, vol. 74(1), pages 116-26, February.
  28. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  29. King, Robert G. & Plosser, Charles I. & Rebelo, Sergio T., 1988. "Production, growth and business cycles : I. The basic neoclassical model," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 195-232.
  30. Granger, C W J & Lee, T H, 1989. "Investigation of Production, Sales and Inventory Relationships Using Multicointegration and Non-symmetric Error Correction Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages S145-59, Supplemen.
  31. Zellner, Arnold & Palm, Franz, 1974. "Time series analysis and simultaneous equation econometric models," Journal of Econometrics, Elsevier, vol. 2(1), pages 17-54, May.
  32. Dietmar Bauer & Martin Wagner, 2002. "Asymptotic Properties of Pseudo Maximum Likelihood Estimates for Multiple Frequency I(1) Processes," Diskussionsschriften dp0205, Universitaet Bern, Departement Volkswirtschaft.
  33. Neusser, Klaus, 2000. "An algebraic interpretation of cointegration," Economics Letters, Elsevier, vol. 67(3), pages 273-281, June.
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