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On the choice of GARCH parameters for efficient modelling of real stock price dynamics

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  • Pokhilchuk, K.A.
  • Savel’ev, S.E.

Abstract

We propose two different methods for optimal choice of GARCH(1,1) parameters for the efficient modelling of stock prices by using a particular return series. Using (as an example) stock return data for Intel Corporation, we vary parameters to fit the average volatility as well as fourth (linked to kurtosis of data) and eighth statistical moments and observe pure convergence of our simulated eighth moment to the stock data. Results indicate that fitting higher-order moments of a return series might not be an optimal approach for choosing GARCH parameters. In contrast, the simulated exponent of the Fourier spectrum decay is much less noisy and can easily fit the corresponding decay of the empirical Fourier spectrum of the used return series of Intel stock, allowing us to efficiently define all GARCH parameters. We compare the estimates of GARCH parameters obtained by fitting price data Fourier spectra with the ones obtained from standard software packages and conclude that the obtained estimates here are deeper in the stability region of parameters. Thus, the proposed method of using Fourier spectra of stock data to estimate GARCH parameters results in a more robust and stable stochastic process but with a shorter characteristic autocovariance time.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:448:y:2016:i:c:p:248-253
    DOI: 10.1016/j.physa.2015.12.046
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    References listed on IDEAS

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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
    2. Constantinides, A. & Savel’ev, S.E., 2013. "Modelling price dynamics: A hybrid truncated Lévy Flight–GARCH approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2072-2078.
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    5. 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.
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    Cited by:

    1. Luke De Clerk & Sergey Savel'ev, 2021. "Non-stationary GARCH modelling for fitting higher order moments of financial series within moving time windows," Papers 2102.11627, arXiv.org, revised Mar 2021.
    2. De Clerk, Luke & Savel’ev, Sergey, 2022. "AI algorithms for fitting GARCH parameters to empirical financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).

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