Estimation of Kramers-Moyal coefficients at low sampling rates

TL;DR

This paper introduces a novel optimization method for accurately estimating Kramers-Moyal coefficients from sparse, stationary Markovian time series by leveraging exact finite sampling effects via the adjoint Fokker-Planck equation.

Contribution

It presents a new optimization procedure that improves estimation accuracy for Kramers-Moyal coefficients at low sampling rates, applicable with or without parametric assumptions.

Findings

Effective in synthetic data experiments

Handles sparse sampling effectively

Flexible with parametric or non-parametric approaches

Abstract

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.