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A new estimator method for GARCH models

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  • R. N. Onody
  • G. M. Favaro
  • E. R. Cazaroto

Abstract

The GARCH (p, q) model is a very interesting stochastic process with widespread applications and a central role in empirical finance. The Markovian GARCH (1, 1) model has only 3 control parameters and a much discussed question is how to estimate them when a series of some financial asset is given. Besides the maximum likelihood estimator technique, there is another method which uses the variance, the kurtosis and the autocorrelation time to determine them. We propose here to use the standardized 6th moment. The set of parameters obtained in this way produces a very good probability density function and a much better time autocorrelation function. This is true for both studied indexes: NYSE Composite and FTSE 100. The probability of return to the origin is investigated at different time horizons for both Gaussian and Laplacian GARCH models. In spite of the fact that these models show almost identical performances with respect to the final probability density function and to the time autocorrelation function, their scaling properties are, however, very different. The Laplacian GARCH model gives a better scaling exponent for the NYSE time series, whereas the Gaussian dynamics fits better the FTSE scaling exponent. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • R. N. Onody & G. M. Favaro & E. R. Cazaroto, 2007. "A new estimator method for GARCH models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(4), pages 487-493, June.
    • Handle: RePEc:spr:eurphb:v:57:y:2007:i:4:p:487-493
    DOI: 10.1140/epjb/e2007-00191-6
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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
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    1. Pokhilchuk, K.A. & Savel’ev, S.E., 2016. "On the choice of GARCH parameters for efficient modelling of real stock price dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 248-253.

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