Wavelet Variance Based Robust Estimation of Composite Stochastic Models

Estimation and inference for complex parametric models related to signal and time-series analysis is still an extremely relevant area of research for many domains of application. In particular, with increasing data being collected and stored in different settings, there is a need for methods that provide these inferential solutions and that scale adequately with the large sample sizes. The availability of such methods is scarce and these can breakdown in particularly challenging circumstances also linked to the complexity of the models of interest. Another challenge that additionally constrains the availability of usable methods is the presence of contamination (outliers) in the signals which require even more tailored approaches to analyse them. In this context, the Robust Generalized Method of Wavelet Moments (RGMWM) was put forward to provide one of the few scalable and robust solution to perform inference for these complex stochastic models. Being based on a new bounded estimator of the Wavelet Variance and the previously proposed Generalized Method of Wavelet Moments, the RGMWM provides important solutions to model signals and time-series recorded in various domains going from engineering to finance, for the latter of which we also discuss an applied example.