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Statistical mechanics and time-series analysis by L\'evy-parameters with the possibility of real-time application

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  • Alexander Jurisch

Abstract

We develop a method that relates the truncated cumulant-function of the fourth order with the L\'evian cumulant-function. This gives us explicit formulas for the L\'evy-parameters, which allow a real-time analysis of the state of a random-motion. Cumbersome procedures like maximum-likelihood or least-square methods are unnecessary. Furthermore, we treat the L\'evy-system in terms of statistical mechanics and work out it's thermodynamic properties. This also includes a discussion of the fractal nature of relativistic corrections. As examples for a time-series analysis, we apply our results on the time-series of the German DAX and the American S\&P-500\,.

Suggested Citation

  • Alexander Jurisch, 2019. "Statistical mechanics and time-series analysis by L\'evy-parameters with the possibility of real-time application," Papers 1902.09425, arXiv.org.
    • Handle: RePEc:arx:papers:1902.09425
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