Tracking rapidly changing dynamical systems using a non-parametric statistical method based on wavelets

A non-parametric statistical method of tracking rapidly changing dynamical systems is introduced. The method implements the non-linear wavelet thresholding estimator to estimate the evolutionary transfer function of the system. The consistency and optimality of the resulting estimate of our method on rapidly changing systems are stated, while no linear estimator can achieve the same optimality. Two examples of real data are studied using this non-parametric method, including two vertical seismic array case studies and a series of seismic slope experiments. The analysis results are consistent with previous research for the vertical seismic array data. Moreover, our estimate is superior to those from previous research in the sense that our estimate is neither over-smoothed nor under-smoothed. The analysis results are also consistent with the experimental observations for the seismic slope experimental data. Copyright ? 2003 John Wiley & Sons, Ltd.