Local statistical moments to capture Kramers-Moyal coefficients

TL;DR

This paper presents a new local statistical moment method for estimating Kramers-Moyal coefficients, enhancing stochastic process analysis by combining nonparametric flexibility with parametric interpretability, applicable to various real-world systems.

Contribution

It introduces a versatile local estimation framework for Kramers-Moyal coefficients, bridging nonparametric and parametric methods for stationary and non-stationary data.

Findings

Effective in analyzing stationary and non-stationary time series

Applicable to real-world complex systems like wind turbines

Improves coefficient estimation accuracy

Abstract

This study introduces an innovative local statistical moment approach for estimating Kramers-Moyal coefficients, effectively bridging the gap between nonparametric and parametric methodologies. These coefficients play a crucial role in characterizing stochastic processes. Our proposed approach provides a versatile framework for localized coefficient estimation, combining the flexibility of nonparametric methods with the interpretability of global parametric approaches. We showcase the efficacy of our approach through use cases involving both stationary and non-stationary time series analysis. Additionally, we demonstrate its applicability to real-world complex systems, specifically in the energy conversion process analysis of a wind turbine.