Nonparametric model reconstruction for stochastic differential equation from discretely observed time-series data

TL;DR

This paper introduces a nonparametric method combining maximum likelihood and kernel density estimation to reconstruct state-dependent drift and diffusion coefficients of stochastic differential equations from discretely observed data, enabling fast and flexible analysis.

Contribution

It presents a novel nonparametric estimation scheme that does not require predefined parametric forms, utilizing local linearization for efficient computation from discrete data.

Findings

Effective reconstruction of drift and diffusion coefficients from sparse data

No need for parametric assumptions about the coefficients

Fast estimation method suitable for discretely observed time-series

Abstract

A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion coefficients in advance. In order to perform the nonparametric estimation, a maximum likelihood method is combined with a concept based on a kernel density estimation. In order to deal with discrete observation or sparsity of the time-series data, a local linearization method is employed, which enables a fast estimation.