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

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.