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Nonlinear GARCH model and 1/f noise

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  • Aleksejus Kononovicius
  • Julius Ruseckas

Abstract

Auto-regressive conditionally heteroskedastic (ARCH) family models are still used, by practitioners in business and economic policy making, as a conditional volatility forecasting models. Furthermore ARCH models still are attracting an interest of the researchers. In this contribution we consider the well known GARCH(1,1) process and its nonlinear modifications, reminiscent of NGARCH model. We investigate the possibility to reproduce power law statistics, probability density function and power spectral density, using ARCH family models. For this purpose we derive stochastic differential equations from the GARCH processes in consideration. We find the obtained equations to be similar to a general class of stochastic differential equations known to reproduce power law statistics. We show that linear GARCH(1,1) process has power law distribution, but its power spectral density is Brownian noise-like. However, the nonlinear modifications exhibit both power law distribution and power spectral density of the power law form, including 1/f noise.

Suggested Citation

  • Aleksejus Kononovicius & Julius Ruseckas, 2014. "Nonlinear GARCH model and 1/f noise," Papers 1412.6244, arXiv.org, revised Feb 2015.
    • Handle: RePEc:arx:papers:1412.6244
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    Cited by:

    1. Gontis, V. & Havlin, S. & Kononovicius, A. & Podobnik, B. & Stanley, H.E., 2016. "Stochastic model of financial markets reproducing scaling and memory in volatility return intervals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1091-1102.
    2. Gontis, V. & Kononovicius, A., 2017. "Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 266-272.
    3. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.
    4. Ngozi G. Emenogu & Monday Osagie Adenomon & Nwaze Obini Nweze, 2020. "On the volatility of daily stock returns of Total Nigeria Plc: evidence from GARCH models, value-at-risk and backtesting," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-25, December.
    5. Vygintas Gontis & Shlomo Havlin & Aleksejus Kononovicius & Boris Podobnik & H. Eugene Stanley, 2015. "Stochastic model of financial markets reproducing scaling and memory in volatility return intervals," Papers 1507.05203, arXiv.org, revised Oct 2016.

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