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Nonlinear cointegration with mixing errors

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  • Mira, Santiago

Abstract

In this paper we consider an extension of the linear concept of co integration to a nonlinear context. We discuss the advantages and disadvantages of alternatives concepts of 1(0) and 1(1) based on the concept of a-mixing and study their relationship with the concept of short memory in distribution. Our concept of nonlinear co integration can be introduced without having to formally characterize the time series properties of the nonlinear transformations of 1(1) variables. The nonlinear least squares (NLS) estimator of the co integrating relationship is studied under alternative assumptions provided that the nonlinear function is Hadamard differentiable. With some Monte Carlo simulation we found that the bias of NLS estimator can either be large or small depending on the type of nonlinearity allowed in the individual series or in the co integrating function. We conclude that the proposed framework allows interesting extensions of the classical approach, but is not flexible enough to include several interesting nonlinearities.

Suggested Citation

  • Mira, Santiago, 1997. "Nonlinear cointegration with mixing errors," DES - Working Papers. Statistics and Econometrics. WS 6204, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:6204
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    1. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    2. Granger, Clive W J & Hallman, Jeffrey J, 1991. "Long Memory Series with Attractors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 53(1), pages 11-26, February.
    3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    4. Stock, James H., 1994. "Deciding between I(1) and I(0)," Journal of Econometrics, Elsevier, vol. 63(1), pages 105-131, July.
    5. Escribano, A., 1987. "Error-correction systems: nonlinear adjustments to linear long-run relationships," LIDAM Discussion Papers CORE 1987030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    7. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-279, March.
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    Cited by:

    1. Valerie Mignon & Gilles Dufrenot & Slim Chaouachi, 2004. "Modelling the misalignments of the Dollar-Sterling real exchange rate: A nonlinear cointegration perspective," Economics Bulletin, AccessEcon, vol. 3(19), pages 1-11.
    2. repec:ebl:ecbull:v:3:y:2004:i:19:p:1-11 is not listed on IDEAS
    3. Mármol, Francesc & Aparicio, Felipe M., 1999. "A new instrumental variable approach for estimation and testing in fractional cointegrating regressions," DES - Working Papers. Statistics and Econometrics. WS 6298, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Gilles Dufrenot & Elisabeth Grimaud & Eugénie Latil & Valerie Mignon, 2008. "Modelling The Slow Mean‐Reversion Of The Central And Eastern European Countries' Real Exchange Rates," Manchester School, University of Manchester, vol. 76(1), pages 21-43, January.
    5. Aparicio, Felipe M., 1997. "Searching for linear and nonlinear cointegration: a new approach," DES - Working Papers. Statistics and Econometrics. WS 6219, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Aparicio, Felipe M. & Escribano, Álvaro & Mármol, Francesc, 1999. "A new instrumental variable approach for estimation and testing in fractional cointegrating regressions," DES - Working Papers. Statistics and Econometrics. WS 6298, Universidad Carlos III de Madrid. Departamento de Estadística.

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    Keywords

    Nonlinear cointegration;

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