Draft:Generalized method of wavelet moments

The Generalized Method of Wavelet Moments (GMWM) is a statistical estimation technique that combines wavelet-based analysis with the generalized method of moments framework. It is primarily used in time series modeling and parameter estimation for stochastic processes, particularly in signal processing applications.

Overview

The Generalized Method of Wavelet Moments (GMWM), introduced by Guerrier et al. (2013), leverages the Wavelet Variance (WV)—the variance of wavelet coefficients obtained from the wavelet decomposition of a time series (see, for example, Percival, 1995). The WV is widely used in time series analysis across various fields, including geophysics and aerospace engineering, as it helps decompose and interpret the variance of a time series across different scales. It also serves as an effective statistic for summarizing the key characteristics of time series that exhibit certain properties, such as intrinsic stationarity. In the GMWM framework, the WV is employed as an auxiliary parameter within a minimum distance estimation setting, enabling the estimation of a broad class of intrinsically second-order stationary models in a numerically stable and computationally efficient manner.

See also

• Allan variance