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Goodness of fit assessment for a fractal model of stock markets

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  • Frezza, Massimiliano

Abstract

An assessment of the goodness of fit of a new stochastic model of stock dynamics is investigated. The model is the multifractional Brownian motion (mBm), introduced independently by Péltier and Lévy Véhel (1995) [2] and Benassi (1997) [3]. The analysis concerns the (un)conditional distributions of log-variations of the Dow Jones Industrial Average (DJIA). By comparing the performance of mBm with respect to a Garch (1,1), we argue that the former captures the distributional features as well as the pathwise empirical ones displayed by the U.S. Dow Jones index, while the Garch (1,1) works better in global terms.

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  • Frezza, Massimiliano, 2014. "Goodness of fit assessment for a fractal model of stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 41-50.
    • Handle: RePEc:eee:chsofr:v:66:y:2014:i:c:p:41-50
    DOI: 10.1016/j.chaos.2014.05.005
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    1. Tapia Cortez, Carlos A. & Hitch, Michael & Sammut, Claude & Coulton, Jeff & Shishko, Robert & Saydam, Serkan, 2018. "Determining the embedding parameters governing long-term dynamics of copper prices," Chaos, Solitons & Fractals, Elsevier, vol. 111(C), pages 186-197.
    2. Adil Yilmaz & Gazanfer Unal, 2016. "Chaos in Fractionally Integrated Generalized Autoregressive Conditional Heteroskedastic Processes," Papers 1601.08099, arXiv.org, revised Feb 2016.
    3. Sixian Jin & Qidi Peng & Henry Schellhorn, 2018. "Estimation of the pointwise Hölder exponent of hidden multifractional Brownian motion using wavelet coefficients," Statistical Inference for Stochastic Processes, Springer, vol. 21(1), pages 113-140, April.
    4. Tapia, Carlos & Coulton, Jeff & Saydam, Serkan, 2020. "Using entropy to assess dynamic behaviour of long-term copper price," Resources Policy, Elsevier, vol. 66(C).
    5. Bianchi, Sergio & Pianese, Augusto, 2018. "Time-varying Hurst–Hölder exponents and the dynamics of (in)efficiency in stock markets," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 64-75.

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