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Consistent Estimation In Cointegrated Vector Autoregressive Models With Nonlinear Time Trends In Cointegrating Relations

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  • Saikkonen, Pentti

Abstract

This paper studies the consistency of the Gaussian maximum likelihood estimator in a cointegrated vector autoregressive model with nonlinear time trends in cointegrating relations. The results are proved in a coordinate free framework that readily allows for general nonlinear parameter restrictions and makes it possible to show the consistency of reduced form parameter estimators without assuming identifiability of underlying structural parameters. Various consistency results for structural parameter estimators can then be obtained by imposing suitable identification conditions for the parameters of interest but not necessarily for nuisance parameters. Orders of consistency are also obtained because they are needed to develop a related asymptotic theory of statistical inference.

Suggested Citation

  • Saikkonen, Pentti, 2001. "Consistent Estimation In Cointegrated Vector Autoregressive Models With Nonlinear Time Trends In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 17(2), pages 296-326, April.
    • Handle: RePEc:cup:etheor:v:17:y:2001:i:02:p:296-326_17
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    Cited by:

    1. Sébastien Morin, 2004. "Ruptures structurelles sur les marchés action et obligataire américains : preuve empirique à partir de la méthode de Saikkönen," Economie & Prévision, La Documentation Française, vol. 166(5), pages 87-98.
    2. Lütkepohl, Helmut, 2008. "Problems related to over-identifying restrictions for structural vector error correction models," Economics Letters, Elsevier, vol. 99(3), pages 512-515, June.
    3. Changli He & Timo Terasvirta & Andres Gonzalez, 2009. "Testing Parameter Constancy in Stationary Vector Autoregressive Models Against Continuous Change," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 225-245.
    4. Holt, Matthew T. & Teräsvirta, Timo, 2020. "Global hemispheric temperatures and co-shifting: A vector shifting-mean autoregressive analysis," Journal of Econometrics, Elsevier, vol. 214(1), pages 198-215.
    5. Hannu KOSKINEN, 2010. "Modelling of Structural Changes in Demand for Money Cointegration Relations," EcoMod2004 330600082, EcoMod.
    6. Antonio N. Bojanic, 2009. "The impact of tin on the economic growth of Bolivia," Coyuntura Económica, Fedesarrollo, December.
    7. Chambers, M.J. & McCrorie, J.R., 2004. "Frequency Domain Gaussian Estimation of Temporally Aggregated Cointegrated Systems," Discussion Paper 2004-40, Tilburg University, Center for Economic Research.
    8. Hannu Koskinen, 2004. "Modelling of Structural Changes in Demand for Money Cointegration Relations," Finnish Economic Papers, Finnish Economic Association, vol. 17(2), pages 63-72, Autumn.
    9. Juhl, Ted & Xiao, Zhijie, 2005. "A nonparametric test for changing trends," Journal of Econometrics, Elsevier, vol. 127(2), pages 179-199, August.
    10. Hernández, Juan R., 2016. "Unit Root Testing in ARMA Models: A Likelihood Ratio Approach," MPRA Paper 100857, University Library of Munich, Germany.
    11. Marçal, Emerson Fernandes & Pereira, Pedro L. Valls, 2012. "Evaluating the existence of structural change in the brazilian term structure of interest: evidence based on cointegration models with structural break," Textos para discussão 314, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    12. Takamitsu Kurita & Mototsugu Shintani, 2023. "Johansen Test with Fourier-Type Smooth Nonlinear Trends in Cointegrating Relations," CIRJE F-Series CIRJE-F-1216, CIRJE, Faculty of Economics, University of Tokyo.
    13. He, Changli & Sandberg, Rickard, 2005. "Inference for Unit Roots in a Panel Smooth Transition Autoregressive Model where the Time Dimension is Fixed," SSE/EFI Working Paper Series in Economics and Finance 581, Stockholm School of Economics, revised 18 Feb 2005.
    14. Chambers, Marcus J. & Roderick McCrorie, J., 2007. "Frequency domain estimation of temporally aggregated Gaussian cointegrated systems," Journal of Econometrics, Elsevier, vol. 136(1), pages 1-29, January.

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