Calibration of the subdiffusive arithmetic Brownian motion with tempered stable waiting-times
AbstractIn the classical analysis many models used to real data description are based on the standard Brownian diffusion-type processes. However, some real data exhibit characteristic periods of constant values. In such cases the popular systems seem not to be applicable. Therefore we propose an alternative approach, based on the combination of the popular arithmetic Brownian motion and tempered stable subordinator. The probability density function of the proposed model can be described by a Fokker-Planck type equation and therefore it has many similar properties as the popular arithmetic Brownian motion. In this paper we propose the estimation procedure for the considered tempered stable subdiffusive arithmetic Brownian motion and calibrate the analyzed process to the real financial data.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 28593.
Date of creation: 2010
Date of revision:
Subdiffusion; Tempered stable distribution; Calibration;
Find related papers by JEL classification:
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
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- Szymon Borak & Wolfgang Härdle & Rafal Weron, 2005. "Stable Distributions," SFB 649 Discussion Papers SFB649DP2005-008, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
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- Janczura, Joanna & Wyłomańska, Agnieszka, 2009. "Subdynamics of financial data from fractional Fokker-Planck equation," MPRA Paper 30649, University Library of Munich, Germany.
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- Rosinski, Jan, 2007. "Tempering stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 677-707, June.
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