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Abstract

In this paper the properties of so called subspace methods in the context of cointegrated processes of order one are investigated. It is shown that the algorithms deliver consistent estimates of the transfer function in the case of general VARMA models and under mild conditions on the underlying noise process. A procedure for the estimation of the dimension of the cointegrating space is presented and consistency for this procedure is proven. Also the estimation of the order of the system is discussed. Simulation examples demon- strate the usefulness of the subspace algorithms for the estimation of cointegrated systems.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 111 (2002)
Issue (Month): 1 (November)
Pages: 47-84

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Handle: RePEc:eee:econom:v:111:y:2002:i:1:p:47-84

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Web page: http://www.elsevier.com/locate/jeconom

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1. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
2. Saikkonen, Pentti & Luukkonen, Ritva, 1997. "Testing cointegration in infinite order vector autoregressive processes," Journal of Econometrics, Elsevier, vol. 81(1), pages 93-126, November.
3. Wagner, Martin, 1999. "Bierens' and Johansen's Method - Complements or Substitutes?," Economics Series 74, Institute for Advanced Studies.
4. H. Lütkepohl & P. Saikkonen, 1995. "Impulse Response Analysis in Infinite Order Cointegrated Vector Autoregressive Processes," SFB 373 Discussion Papers 1995,11, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
   
   • 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. Peter C.B. Phillips, 1988. "Optimal Inference in Cointegrated Systems," Cowles Foundation Discussion Papers 866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
   
   • Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
6. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
7. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-78, September.
   
   • 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.
8. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April.
   
   • Bierens, H.J., 1995. "Nonparametric cointegration analysis," Discussion Paper 1995-123, Tilburg University, Center for Economic Research.
9. Poskitt, Don S, 2000. "Strongly Consistent Determination of Cointegrating Rank via Canonical Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(1), pages 77-90, January.
10. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
11. 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.
12. Lai, T. L. & Wei, C. Z., 1982. "Asymptotic properties of projections with applications to stochastic regression problems," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 346-370, September.
13. repec:cup:etheor:v:8:y:1992:i:1:p:1-27 is not listed on IDEAS
14. Wagner, Martin, 1999. "VAR Cointegration in VARMA Models," Economics Series 65, Institute for Advanced Studies.

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Citations

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Cited by:

1. Dietmar Bauer & Martin Wagner, 2003. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0312, Universitaet Bern, Departement Volkswirtschaft.
   
   • Dietmar Bauer & Martin Wagner, 2002. "A Canonical Form for Unit Root Processes in the State Space Framework," Diskussionsschriften dp0204, Universitaet Bern, Departement Volkswirtschaft.
2. Dietmar Bauer & Martin Wagner, 2002. "Asymptotic Properties of Pseudo Maximum Likelihood Estimates for Multiple Frequency I(1) Processes," Diskussionsschriften dp0205, Universitaet Bern, Departement Volkswirtschaft.
3. Martin Wagner, 2004. "A Comparison of Johansen's, Bierens' and the Subspace Algorithm Method for Cointegration Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(3), pages 399-424, 07.
   
   • Martin Wagner, 2002. "A Comparison of Johansen's, Bierens and the Subspace Algorithm Method for Cointegration Analysis," Diskussionsschriften dp0210, Universitaet Bern, Departement Volkswirtschaft.
4. Wagner, Martin, 2010. "Cointegration Analysis with State Space Models," Economics Series 248, Institute for Advanced Studies.
   
   • Martin Wagner, 2010. "Cointegration analysis with state space models," AStA Advances in Statistical Analysis, Springer, vol. 94(3), pages 273-305, September.
5. Christian Kascha & Karel Mertens, 2006. "Business Cycle Analysis and VARMA models," Economics Working Papers ECO2006/37, European University Institute.
   
   • Kascha, Christian & Mertens, Karel, 2009. "Business cycle analysis and VARMA models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 267-282, February.
   • Christian Kascha & Karel Mertens, 2008. "Business cycle analysis and VARMA models," Working Paper 2008/05, Norges Bank.
6. Izquierdo, Segismundo S. & Hernández, Cesáreo & del Hoyo, Juan, 2006. "Forecasting VARMA processes using VAR models and subspace-based state space models," MPRA Paper 4235, University Library of Munich, Germany.
7. Dietmar Bauer & Martin Wagner, 2003. "The Performance of Subspace Algorithm Cointegration Analysis: A Simulation Study," Diskussionsschriften dp0308, Universitaet Bern, Departement Volkswirtschaft.
8. Mauricio, Jose Alberto, 2006. "Exact maximum likelihood estimation of partially nonstationary vector ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3644-3662, August.
9. Phillips, Peter C.B., 2005. "Automated Discovery In Econometrics," Econometric Theory, Cambridge University Press, vol. 21(01), pages 3-20, February.
   
   • Peter C.B. Phillips, 2004. "Automated Discovery in Econometrics," Cowles Foundation Discussion Papers 1469, Cowles Foundation for Research in Economics, Yale University.
10. Martin Wagner, 2008. "On PPP, unit roots and panels," Empirical Economics, Springer, vol. 35(2), pages 229-249, September.
    
    • Wagner, Martin, 2005. "On PPP, Unit Roots and Panels," Economics Series 176, Institute for Advanced Studies.
11. 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.
12. Dietmar Bauer & Martin Wagner, 2005. "Autoregressive Approximations of Multiple Frequency I(1) Processes," Economics Working Papers ECO2005/09, European University Institute.
    
    • Bauer, Dietmar & Wagner, Martin, 2005. "Autoregressive Approximations of Multiple Frequency I(1) Processes," Economics Series 174, Institute for Advanced Studies.
13. 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.
14. Manfred GILLI & Peter WINKER, . "A review of heuristic optimization methods in econometrics," Swiss Finance Institute Research Paper Series 08-12, Swiss Finance Institute.
    
    • Manfred Gilli & Peter Winker, 2008. "Review of Heuristic Optimization Methods in Econometrics," Working Papers 001, COMISEF.
15. Alfredo García Hiernaux & Miguel Jerez & José Casals, 2005. "Deteccióon de Raíces Unitarias y Cointegración mediante Métodos de Subespacios," Documentos del Instituto Complutense de Análisis Económico 0503, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.

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