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Iterative Maximum Likelihood Estimation of Cointegrating Vectors

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Author Info
Kim, In-Moo (Sungkyunkwan University)
Park, Joon Y. (Rice University and Sungkyunkwan University)
Abstract

This paper introduces an iterative method to estimate the cointegrating vectors in the error correction models. The method provides the asymptotically efficient estimators for the cointegrating vectors if iterated once or more. If it is iterated until convergence, we may obtain the maximum likelihood estimator by Johansen. For all values of 1 <= k <= infinity, the k-step iterative estimators are asymptotically equivalent, and as efficient as the maximum likelihood estimator. Their finite sample performances are, however, quite different for different values of k, most notably for the two extreme cases k = 1 and k = 1. The finite-step iterative estimators generally perform better in small samples than the infinite-step iterative estimator, i.e., the maximum likelihood estimator. In particular, the former are much more robust than the latter, which is known to occasionally yield some extreme outliers in samples of relatively small size. Our iterative procedure indeed can be very useful in detecting the occurrences of outliers for the maximum likelihood estimator, since its realized values tend to deviate largely from those of the finite-step iterative estimators when the extreme outliers are produced. The proposed method is very flexible and can be easily implemented for the cointegrated models that are specified in an arbitrary structural form.

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Paper provided by Rice University, Department of Economics in its series Working Papers with number 2005-02.

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Date of creation: Jan 2005
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Handle: RePEc:ecl:riceco:2005-02

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  1. Johansen, Søren & Juselius, Katarina, 1992. "Testing structural hypotheses in a multivariate cointegration analysis of the PPP and the UIP for UK," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 211-244. [Downloadable!] (restricted)
  2. Park, J.Y. & Ogaki, M., 1991. "Seemingly Unrelated Canonical Cointegrating Regressions," RCER Working Papers 280, University of Rochester - Center for Economic Research (RCER).
  3. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-43, January. [Downloadable!] (restricted)
  4. Park, J.Y. & Ogaki, M., 1991. "Inference in Cointegrated Models Using VAR Prewhitening to Estimate Shortrun Dynamics," RCER Working Papers 281, University of Rochester - Center for Economic Research (RCER).
  5. Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
  6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  7. 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. [Downloadable!] (restricted)
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  8. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March. [Downloadable!] (restricted)
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  9. Phillips, Peter C B, 1994. "Some Exact Distribution Theory for Maximum Likelihood Estimators of Cointegrating Coefficients in Error Correction Models," Econometrica, Econometric Society, vol. 62(1), pages 73-93, January. [Downloadable!] (restricted)
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  10. Nunzio Cappuccio & Diego Lubian, 2001. "Estimation And Inference On Long-Run Equilibria: A Simulation Study," Econometric Reviews, Taylor and Francis Journals, vol. 20(1), pages 61-84. [Downloadable!] (restricted)
  11. Cheng Hsiao, 1997. "Cointegration and Dynamic Simultaneous Equations Model," Econometrica, Econometric Society, vol. 65(3), pages 647-670, May.
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