Estimation of the Pointwise H\"older Exponent of Hidden Multifractional Brownian Motion Using Wavelet Coefficients

TL;DR

This paper introduces a wavelet-based method for accurately estimating the pointwise H"older exponent of a multifractional Brownian motion when the process is not directly observable, with applications to nonlinear models.

Contribution

It presents a novel wavelet-based estimator for the pointwise H"older exponent of hidden multifractional Brownian motion, addressing the challenge of indirect observation.

Findings

Estimator is consistent under certain conditions

Method effectively captures local regularity of the process

Application demonstrated in nonlinear model estimation

Abstract

We propose a wavelet-based approach to construct consistent estimators of the pointwise H\"older exponent of a multifractional Brownian motion, in the case where this underlying process is not directly observed. The relative merits of our estimator are discussed, and we introduce an application to the problem of estimating the functional parameter of a nonlinear model.