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Pathwise Identification Of The Memory Function Of Multifractional Brownian Motion With Application To Finance


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    (University of Cassino, Faculty of Economics, Via S. Angelo, 03043 Cassino, Italy)


We extend and adapt a class of estimators of the parameter H of the fractional Brownian motion in order to estimate the (time-dependent) memory function of a multifractional process. We provide: (a) the estimator's distribution when H ∈ (0,3/4); (b) the confidence interval under the null hypothesis H = 1/2; (c) a scaling law, independent on the value of H, discriminating between fractional and multifractional processes. Furthermore, assuming as a model for the price process the multifractional Brownian motion, empirical evidence is offered which is able to conciliate the inconsistent results achieved in estimating the intensity of dependence in financial time series.

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Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 08 (2005)
Issue (Month): 02 ()
Pages: 255-281

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Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:02:p:255-281

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Keywords: (Multi)fractional Brownian motion; LRD estimators; financial markets;


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Cited by:
  1. M. Cadoni & R. Melis & A. Trudda, 2012. "Financial crisis: a new measure for risk of pension funds assets," Working Paper CRENoS 201231, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
  2. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2007. "Queueing Theoretic Approaches to Financial Price Fluctuations," Science & Finance (CFM) working paper archive math/0703832, Science & Finance, Capital Fund Management.
  3. Erhan Bayraktar & Ulrich Horst & Ronnie Sircar, 2007. "A Limit Theorem for Financial Markets with Inert Investors," Science & Finance (CFM) working paper archive math/0703831, Science & Finance, Capital Fund Management.
  4. Sergio, Bianchi & Alessandro, Trudda, 2008. "Global Asset Return in Pension Funds: a dynamical risk analysis," MPRA Paper 12011, University Library of Munich, Germany, revised 14 Jun 2008.


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