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

@article{Roman2008FractionalDO,
  title={Fractional derivatives of random walks: time series with long-time memory.},
  author={H. Eduardo Roman and Markus Porto},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2008},
  volume={78 3 Pt 1},
  pages={
          031127
        }
}
  • H. Roman, M. Porto
  • Published 19 June 2008
  • Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
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 models with conditional heteroskedasticity (FIGARCH), commonly used in econometric studies, is discussed. The application of correlated… 
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