On reconstruction of the Ito-like equation from persistent time series

The Langevin equation with finite-range persistence was introduced as a macroscopic model of various geophysical phenomena. The modified histogram procedure (MHP) of reconstruction of the equation from time series was proposed. An efficiency of MHP was tested on artificial persistent time series (with short and long-tail distributions) generated by different Ito-like equations. For an exemplary geophysical time series, the appropriate Ito-like equation was reconstructed.