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Asymptotic convergence of weighted random matrices: nonparametric cointegration analysis for I(2) processes

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  • Cerqueti, Roy
  • Costantini, Mauro

Abstract

The aim of this paper is to provide a new perspective on the nonparametric co-integration analysis for integrated processes of the second order. Our analysis focus on a pair of random matrices related to such integrated process. Such matrices are constructed by introducing some weight functions. Under asymptotic conditions on such weights, convergence results in distribution are obtained. Therefore, a generalized eigenvalue problem is solved. Differential equations and stochastic calculus theory are used.

Suggested Citation

  • Cerqueti, Roy & Costantini, Mauro, 2005. "Asymptotic convergence of weighted random matrices: nonparametric cointegration analysis for I(2) processes," Economics & Statistics Discussion Papers esdp05027, University of Molise, Department of Economics.
    • Handle: RePEc:mol:ecsdps:esdp05027
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    References listed on IDEAS

    as
    1. Paruolo, Paolo, 1996. "On the determination of integration indices in I(2) systems," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 313-356.
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    5. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    6. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    7. Cerqueti, Roy & Costantini, Mauro, 2005. "Generalization of a nonparametric co-integration analysis for multivariate integrated processes of an integer order," Economics & Statistics Discussion Papers esdp05026, University of Molise, Department of Economics.
    8. Rahbek, Anders & Christian Kongsted, Hans & Jorgensen, Clara, 1999. "Trend stationarity in the I(2) cointegration model," Journal of Econometrics, Elsevier, vol. 90(2), pages 265-289, June.
    9. Nielsen, Heino Bohn, 2002. "An I(2) Cointegration Analysis of Price and Quantity Formation in Danish Manufactured Exports," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 64(5), pages 449-472, December.
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    11. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    12. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April.
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    More about this item

    Keywords

    Co-integration; Nonparametric; Differential equations; Asymptotic properties.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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