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Nonlinear error correction models

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  • Mira, Santiago

Abstract

The relationship between co integration an error correction models (EC) is well characterized in a linear context, see Engle and Granger (1987) and Johansen (1991), but the extension to the nonlinear context is still a challenge. Few extensions of the linear framework were done in the context of nonlinear error correction (NEC), see Escribano (1986 and 1987), or asymmetric and time varying error correction models, see Granger and Lee (1989) and Burguess (1992). In this paper we propose a theoretical framework based on the concept of near epoch dependece (NED) that allow us to formally address those issues. In particular, we partially extend Granger Representation Theorem to the nonlinear case and we study the estimation and -inference properties of least squares when the co integrating relation is linear but the dynamic model is a NEC. The two-step estimation approach of Engle and Granger (1987) is extended when the co integrating errors are NED and the dynamic model is a NEC. Some potentially useful NEC models are proposed and Monte Carlo simulations are provided.

Suggested Citation

  • Mira, Santiago, 1997. "Nonlinear error correction models," DES - Working Papers. Statistics and Econometrics. WS 6206, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:6206
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    1. 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.
    2. Burgess, S M, 1992. "Nonlinear Dynamics in a Structural Model of Employment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 101-118, Suppl. De.
    3. Granger, C W J & Lee, T H, 1989. "Investigation of Production, Sales and Inventory Relationships Using Multicointegration and Non-symmetric Error Correction Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages 145-159, Supplemen.
    4. 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).
    5. 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.
    6. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    7. Stock, James H, 1987. "Asymptotic Properties of Least Squares Estimators of Cointegrating Vectors," Econometrica, Econometric Society, vol. 55(5), pages 1035-1056, September.
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