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 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. © 2008 The American Physical Society.
Roman, H., Porto, M. (2008). Fractional derivatives of random walks: Time series with long-time memory. PHYSICAL REVIEW E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS, 78(3), 031127 [10.1103/PhysRevE.78.031127].
Fractional derivatives of random walks: Time series with long-time memory
Roman H. E.
;
2008
Abstract
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 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. © 2008 The American Physical Society.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.