Fractional derivatives of random walks: Time series with long-time memory

Details Fractional derivatives of random walks: Time series with long-time memory Fractional derivatives of random walks: Time series with long-time memory

2008-06-19

arxiv.org/abs/0806.3171v1

Phys. Rev. E. 78, 031127 (2008)

Physics

Condensed Matter

Statistical Mechanics

10 pages, 14 figures

Scientific paper

10.1103/PhysRevE.78.031127

We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly-decaying autocorrelation functions. The relation between these correlated walks and the well-known fractionally integrated autoregressive (FIGARCH) models, commonly used in econometric studies, is discussed. The application of correlated random walks to simulate empirical financial times series is considered and compared with the predictions from FIGARCH and the simpler FIARCH processes. A comparison with empirical data is performed.

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