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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.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 17 (2001)
Issue (Month): 02 (April)
Pages: 327-356

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Handle: RePEc:cup:etheor:v:17:y:2001:i:02:p:327-356_17

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Cited by:
  1. Bruggemann, Ralf & Lutkepohl, Helmut & Saikkonen, Pentti, 2006. "Residual autocorrelation testing for vector error correction models," Journal of Econometrics, Elsevier, vol. 134(2), pages 579-604, October.
  2. Juhl, Ted & Xiao, Zhijie, 2005. "A nonparametric test for changing trends," Journal of Econometrics, Elsevier, vol. 127(2), pages 179-199, August.
  3. Marçal, Emerson Fernandes & Valls Pereira, Pedro L., 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, Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
  4. 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.
  5. 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.

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