Discrete-time inference for slow-fast systems driven by fractional Brownian motion

TL;DR

This paper develops and analyzes statistical estimators for multiscale systems driven by fractional Brownian motion, focusing on the slow component, and proves their consistency and asymptotic normality.

Contribution

It introduces new estimators for the Hurst index and parameters in fractional Brownian motion-driven systems, with theoretical guarantees and numerical validation.

Findings

Estimators are consistent as noise and scale separation vanish.

Estimators are asymptotically normal under the model.

Numerical simulations confirm theoretical properties.

Abstract

We study statistical inference for small-noise-perturbed multiscale dynamical systems where the slow motion is driven by fractional Brownian motion. We develop statistical estimators for both the Hurst index as well as a vector of unknown parameters in the model based on a single time series of observations from the slow process only. We prove that these estimators are both consistent and asymptotically normal as the amplitude of the perturbation and the time-scale separation parameter go to zero. Numerical simulations illustrate the theoretical results.