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Modelos autorregresivos para la varianza condicionada heteroscedastica (ARCH)

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Author Info

  • Marc Saez Zafra

    (Departamento de economía. Universidad Pompeu Fabra)

  • Jorge V. Pérez Rodríguez

    (Departamento de Econometría. Universidad de Barcelona.)

Abstract

En el presente trabajo se introduce al lector en los modelos autorregresivos para la varianza condicionada heterocedástica, incidiendo en los problemas que plantean los esquemas más sencillo y sugiriendo diversas soluciones. Se describe el concepto, las hipótesis y los modelos que explican la varianza condicionada en el tiempo desde diversas perspectivas del análisis estadístico: relación lineal o no lineal entre las variables y métodos de estimación de los parámetros. Finalmente, se discuten diversos contrastes que permiten escoger entre diversas especificaciones alternativas. In this paper the Autoregressive Conditional Heteroskedasticity (ARCH) models are introduced to the reader. The problems implied by their different parameterizations are pointed out and the corresponding solutions are suggested. Several statistical perspectives are used to explain the concept, the assumptions and the models that explain the temporal behaviour of the conditional variances. The paper exposed lineal and non-lineal relationships and several methods of estimation of the parameters of the models. Finally, some tests that allow to choose between alternative specifications are described.

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Bibliographic Info

Article provided by Estudios de Economía Aplicada in its journal Estudios de Economía Aplicada.

Volume (Year): 2 (1994)
Issue (Month): (Diciembre)
Pages: 71-106

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Handle: RePEc:lrk:eeaart:2_3_4

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Related research

Keywords: ARCH Models; Conditional and unconditional variances; time-varying factors;

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References

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  1. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 6(03), pages 318-334, September.
  2. Pagan, A.R. & Schwert, G.W., 1989. "Alternative Models For Conditional Stock Volatility," Papers, Rochester, Business - General 89-02, Rochester, Business - General.
  3. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
  4. Nelson, Daniel B., 1992. "Filtering and forecasting with misspecified ARCH models I : Getting the right variance with the wrong model," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 61-90.
  5. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  6. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  8. Ray Chou & Robert F. Engle & Alex Kane, 1991. "Measuring Risk Aversion From Excess Returns on a Stock Index," NBER Working Papers 3643, National Bureau of Economic Research, Inc.
  9. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-58, February.
  10. E.K. Berndt & B.H. Hall & R.E. Hall, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 103-116 National Bureau of Economic Research, Inc.
  11. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 2(01), pages 107-131, April.
  12. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, Econometric Society, vol. 55(2), pages 391-407, March.
  13. Mark, Nelson C., 1988. "Time-varying betas and risk premia in the pricing of forward foreign exchange contracts," Journal of Financial Economics, Elsevier, Elsevier, vol. 22(2), pages 335-354, December.
  14. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 7-38.
  15. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 5-59.
  16. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 129-157.
  17. Ng, Victor & Engle, Robert F. & Rothschild, Michael, 1992. "A multi-dynamic-factor model for stock returns," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 245-266.
  18. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 96(1), pages 116-31, February.
  19. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 8(2), pages 225-34, April.
  20. Engle, Robert F. & Granger, C. W. J. & Kraft, Dennis, 1984. "Combining competing forecasts of inflation using a bivariate arch model," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 8(2), pages 151-165, November.
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