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On Asymptotic Inference in Linear Cointegrated Time Series Systems

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  • Jeganathan, P.

Abstract

This paper considers vector-valued nonstationary time series models, in particular, autoregressive models, whose nonstationarity is driven by a few nonstationary (induced by “unit roots”) trends, in such a way that some of the linear combinations of the components of the vector model will be stationary. Models of this form are called cointegrated models. These stationary linear combinations are called cointegrating relationships. Asymptotic inference problems associated with the parameters of the cointegrating relationships when the remaining parameters are treated as unknown nuisance parameters are considered. Similarly, inference problems associated with the unit roots are considered. All possible unit roots, including complex ones, together with their possible multiplicities, are allowed. The framework under which the asymptotic inference problems are dealt with is the one described in LeCam (1986, Asymptotic Methods in Statistical Decision Theory ) and LeCam and Yang (1990, Asymptotics in Statistics: Some Basic Concepts ), though it will be seen that the usual normal or mixed normal situations do not apply in the present context.

Suggested Citation

  • Jeganathan, P., 1997. "On Asymptotic Inference in Linear Cointegrated Time Series Systems," Econometric Theory, Cambridge University Press, vol. 13(05), pages 692-745, October.
  • Handle: RePEc:cup:etheor:v:13:y:1997:i:05:p:692-745_00
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    Cited by:

    1. Hallin, M. & van den Akker, R. & Werker, B.J.M., 2012. "Rank-based Tests of the Cointegrating Rank in Semiparametric Error Correction Models," Discussion Paper 2012-089, Tilburg University, Center for Economic Research.
    2. Michael Jansson, 2008. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 76(5), pages 1103-1142, September.
    3. W. K. Li & Shiqing Ling & Michael McAleer, 2001. "A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors," ISER Discussion Paper 0545, Institute of Social and Economic Research, Osaka University.
    4. Müller, Ulrich K. & Watson, Mark W., 2013. "Low-frequency robust cointegration testing," Journal of Econometrics, Elsevier, vol. 174(2), pages 66-81.
    5. Andreou, E. & Werker, B.J.M., 2004. "An Alternative Asymptotic Analysis of Residual-Based Statistics," Discussion Paper 2004-56, Tilburg University, Center for Economic Research.
    6. Hualde Javier & Iacone Fabrizio, 2012. "First Stage Estimation of Fractional Cointegration," Journal of Time Series Econometrics, De Gruyter, vol. 4(1), pages 1-32, May.
    7. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    8. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
    9. Hallin, M. & Werker, B.J.M. & van den Akker, R., 2015. "Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models," Discussion Paper 2015-001, Tilburg University, Center for Economic Research.
    10. Moreira, Marcelo J. & Mourão, Rafael & Moreira, Humberto Ataíde, 2016. "A critical value function approach, with an application to persistent time-series," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 778, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    11. Hallin, Marc & van den Akker, Ramon & Werker, Bas J.M., 2016. "Semiparametric error-correction models for cointegration with trends: Pseudo-Gaussian and optimal rank-based tests of the cointegration rank," Journal of Econometrics, Elsevier, vol. 190(1), pages 46-61.
    12. Andreou, E. & Werker, B.J.M., 2003. "A Simple Asymptotic Analysis of Residual-Based Statistics," Discussion Paper 2003-118, Tilburg University, Center for Economic Research.

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