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The Performance of Subspace Algorithm Cointegration Analysis: A Simulation Study

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  • Dietmar Bauer
  • Martin Wagner

Abstract

This paper presents a simulation study that assesses the finite sample performance of the subspace algorithm cointegration analysis developed in Bauer und Wagner (2002b). The method is formulated in the state space framework, which is equivalent to the VARMA framework, in a sense made precise in the paper. This implies applicability to VARMA processes. The paper proposes and compares six different tests for the cointegrating rank. The simulations investigate four issues: the order estimation, the size performance of the proposed tests, the accuracy of the estimation of the cointegrating space and the forecasting performance. of the state space models estimated by the proposed method. The simulations are performed on a set of trivariate processes with cointegrating ranks ranging from zero to three as well as on processes of output dimension four and cointegrating rank two. We analyze the influence of the sample size on the results as well as the sensitivity of the results with respect to stable poles approaching the unit circle. All results are compared to benchmark results obtained by applying the Johansen procedure on VAR models fitted to the data. The simulations show advantages of subspace algorithm cointegration analysis for the small sample performance of the tests for the cointegrating rank in many cases. However, we find that the accuracy of the subspace algorithm based estimation of the cointegrating space is unsatisfactory for the four-dimensional simulated systems. The forecasting performance is grosso modo comparable to the results obtained by applying the Johansen methodology on VAR approximations, although for very small sample sizes the forecasts based on VAR approximations outperform the subspace forecasts. The appendix provides critical values for the test statistics

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Bibliographic Info

Paper provided by Universitaet Bern, Departement Volkswirtschaft in its series Diskussionsschriften with number dp0308.

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Date of creation: May 2003
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Handle: RePEc:ube:dpvwib:dp0308

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Keywords: State space representation; cointegration; subspace algorithms; simulation study;

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References

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  1. Peter C.B. Phillips, 1993. "Fully Modified Least Squares and Vector Autoregression," Cowles Foundation Discussion Papers 1047, Cowles Foundation for Research in Economics, Yale University.
  2. 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.
  3. Dietmar Bauer & Martin Wagner, 2002. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0204, Universitaet Bern, Departement Volkswirtschaft.
  4. repec:cup:etheor:v:8:y:1992:i:1:p:1-27 is not listed on IDEAS
  5. 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.
  6. Dietmar Bauer & Martin Wagner, 2000. "Estimating Cointegrated Systems Using Subspace Algorithms," Econometric Society World Congress 2000 Contributed Papers 0293, Econometric Society.
  7. 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.
  8. Dietmar Bauer & Martin Wagner, 2002. "Asymptotic Properties of Pseudo Maximum Likelihood Estimates for Multiple Frequency I(1) Processes," Diskussionsschriften dp0205, Universitaet Bern, Departement Volkswirtschaft.
  9. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
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Cited by:
  1. Martin Wagner & Jaroslava Hlouskova, 2010. "The Performance of Panel Cointegration Methods: Results from a Large Scale Simulation Study," Econometric Reviews, Taylor & Francis Journals, vol. 29(2), pages 182-223.
  2. Martin Wagner, 2002. "A Comparison of Johansen's, Bierens and the Subspace Algorithm Method for Cointegration Analysis," Diskussionsschriften dp0210, Universitaet Bern, Departement Volkswirtschaft.
  3. Segismundo Izquierdo & Ces�reo Hern�ndez & Javier Pajares, 2005. "State Space Modelling of Cointegrated Systems using Subspace Algorithms," Econometrics 0509010, EconWPA, revised 07 Feb 2006.

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