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Statistical Inference In Cointegrated Vector Autoregressive Models With Nonlinear Time Trends In Cointegrating Relations

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  • Saikkonen, Pentti

Abstract

This paper continues the work of Saikkonen (2001, Econometric Theory 17, 296–326) and develops an asymptotic theory of statistical inference in cointegrated vector autoregressive models with nonlinear time trends in cointegrating relations and general nonlinear parameter restrictions. Inference on parameters in cointegrating relations and short-run dynamics is studied separately. It is shown that Gaussian maximum likelihood estimators of parameters in cointegrating relations have mixed normal limiting distributions and that related Wald, Lagrange multiplier, and likelihood ratio tests for general nonlinear hypotheses have usual asymptotic chi-square distributions. These results are shown to hold even if parameters in the short-run dynamics are not identified. In that case suitable estimators of the information matrix have to be used to justify the application of Wald and Lagrange multiplier tests, whereas the likelihood ratio test is free of this difficulty. Similar results are also obtained when inference on parameters in the short-run dynamics is studied, although then Gaussian maximum likelihood estimators have usual normal limiting distributions. All results of the paper are proved without assuming existence of second partial derivatives of the likelihood function, and in some cases even differentiability with respect to nuisance parameters is not required.

Suggested Citation

  • Saikkonen, Pentti, 2001. "Statistical Inference In Cointegrated Vector Autoregressive Models With Nonlinear Time Trends In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 17(2), pages 327-356, April.
  • Handle: RePEc:cup:etheor:v:17:y:2001:i:02:p:327-356_17
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    Cited by:

    1. 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.
    2. Hannu KOSKINEN, 2010. "Modelling of Structural Changes in Demand for Money Cointegration Relations," EcoMod2004 330600082, EcoMod.
    3. 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.
    4. Juhl, Ted & Xiao, Zhijie, 2005. "A nonparametric test for changing trends," Journal of Econometrics, Elsevier, vol. 127(2), pages 179-199, August.
    5. Hernández, Juan R., 2016. "Unit Root Testing in ARMA Models: A Likelihood Ratio Approach," MPRA Paper 100857, University Library of Munich, Germany.
    6. 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).
    7. 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.
    8. 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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