Nonstationary signal processing and model validation

A model validation procedure based on Theil's inequality coefficient (TIC) is extended for handling nonstationary signal responses from actual systems and simulated models. Initially, the parent coefficient for TIC and its estimate, as defined by Theil, are presented. Thereafter, trend removal concepts are applied to the nonstationary data to produce weakly stationary difference data from which desired statistics may be computed by time series analysis. A least-squares curve fit is proposed for removing time-varying means. For certain applications more elaborate procedures involving nonlinear operations are required to handle time-varying variances. Some cases require segmenting the data and using trend removal procedures on a piece-wise basis. After time series analysis has been utilized on the resulting weakly stationary data, the removed trends are reinserted to yield a time-varying estimate of TIC. Examples are provided to illustrate two types of nonstationary cases.