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Varianza condicional de medias móviles no-lineales


  • Daniel Ventosa-Santaulària

    () (Escuela de Economía Universidad de Guanajuato.)

  • Alfonso Mendoza Velázquez

    () (Departamento de Economía y Centro de Investigación e Inteligencia Económica (CIIE), Universidad Popular Autónoma del Estado de Puebla.)

  • Manuel Gómez-Zaldívar

    () (Escuela de Economía Universidad de Guanajuato.)


We present a new heteroskedastic conditional variance model using NonLinear Moving Average as the basis for this specification [NLMACH(q)]. The typical problem of this class of models-i.e., noninvertibility—is solved by means of an intuitive parametric restriction; this allows us to use Maximum Likelihood as the estimation procedure. The statistical properties of the new model are both simple and attractive for empirical purposes in finance: a natural fat-tailed distribution stands out. The Autocorrelation Function of the squared process allows us for identification of the number of lags to be included in the new specification. In addition, we present several Monte Carlo experiments where the properties of the model using finite samples are exhibited. Finally, an empirical application using exchange rates and capital market bonds is shown.

Suggested Citation

  • Daniel Ventosa-Santaulària & Alfonso Mendoza Velázquez & Manuel Gómez-Zaldívar, 2008. "Varianza condicional de medias móviles no-lineales," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 29-48, November.
  • Handle: RePEc:ere:journl:v:xxvii:y:2008:i:2:p:29-48

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    References listed on IDEAS

    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Robinson, P. M., 1977. "The estimation of a nonlinear moving average model," Stochastic Processes and their Applications, Elsevier, vol. 5(1), pages 81-90, February.
    3. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, December.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    6. 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, vol. 55(2), pages 391-407, March.
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    More about this item


    Conditionally Heteroskedastic Models; NLMACH(q); Volatility; Fat-tailed Distributions;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes


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