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Estimating the p-Variation Index of a Sample Function: An Application to Financial Data Set

Author

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  • Rimas Norvaiša

    (Institute of Mathematics and Informatics)

  • Donna Mary Salopek

    (York University)

Abstract

In this paper we apply a real analysis approach to test continuous time stochastic models of financial mathematics. Specifically, fractal dimension estimation methods are applied to statistical analysis of continuous time stochastic processes. To estimate a roughness of a sample function we modify a box-counting method typically used in estimating fractal dimension of a graph of a function. Here the roughness of a function f is defined as the infimum of numbers p > 0 such that f has bounded p-variation, which we call the p-variation index of f. The method is also tested on estimating the exponent α∈[1, 2] of a simulated symmetric α-stable process, and on estimating the Hurst exponent H ∈ (0, 1) of a simulated fractional Brownian motion.

Suggested Citation

  • Rimas Norvaiša & Donna Mary Salopek, 2002. "Estimating the p-Variation Index of a Sample Function: An Application to Financial Data Set," Methodology and Computing in Applied Probability, Springer, vol. 4(1), pages 27-53, March.
    • Handle: RePEc:spr:metcap:v:4:y:2002:i:1:d:10.1023_a:1015753313674
    DOI: 10.1023/A:1015753313674
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    References listed on IDEAS

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    1. Bick, Avi & Willinger, Walter, 1994. "Dynamic spanning without probabilities," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 349-374, April.
    2. Mark E. Crovella & Murad S. Taqqu, 1999. "Estimating the Heavy Tail Index from Scaling Properties," Methodology and Computing in Applied Probability, Springer, vol. 1(1), pages 55-79, July.
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    Cited by:

    1. Søren Asmussen, 2022. "On the role of skewness and kurtosis in tempered stable (CGMY) Lévy models in finance," Finance and Stochastics, Springer, vol. 26(3), pages 383-416, July.
    2. Jamison Wolf, 2010. "Random Fractals Determined by Lévy Processes," Journal of Theoretical Probability, Springer, vol. 23(4), pages 1182-1203, December.
    3. Xiaochuan Yang, 2018. "Hausdorff Dimension of the Range and the Graph of Stable-Like Processes," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2412-2431, December.

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