Estimation of Kramers-Moyal coefficients at low sampling rates

Details Estimation of Kramers-Moyal coefficients at low sampling rates Estimation of Kramers-Moyal coefficients at low sampling rates

2011-02-25

arxiv.org/abs/1102.5264v1

Phys. Rev. E 83, 066701 (2011)

Physics

Data Analysis, Statistics and Probability

6 pages, 5 figures

Scientific paper

10.1103/PhysRevE.83.066701

A new optimization procedure for the estimation of Kramers-Moyal coefficients from stationary, one-dimensional, Markovian time series data is presented. The method takes advantage of a recently reported approach that allows to calculate exact finite sampling interval effects by solving the adjoint Fokker-Planck equation. Therefore it is well suited for the analysis of sparsely sampled time series. The optimization can be performed either making a parametric ansatz for drift and diffusion functions or also parameter free. We demonstrate the power of the method in several numerical examples with synthetic time series.

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