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The Performance of Subspace Algorithm Cointegration Analysis: A Simulation Study

  • Dietmar Bauer
  • Martin Wagner

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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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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  1. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
  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. 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.
  4. repec:cup:etheor:v:8:y:1992:i:1:p:1-27 is not listed on IDEAS
  5. Bauer, Dietmar & Wagner, Martin, 2002. "Estimating cointegrated systems using subspace algorithms," Journal of Econometrics, Elsevier, vol. 111(1), pages 47-84, November.
  6. Dietmar Bauer & Martin Wagner, 2003. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0312, Universitaet Bern, Departement Volkswirtschaft.
  7. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-78, September.
  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. 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.
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