Multiscale representation of data has shown great shrinkage abilities when used in data filtering. This paper shows that multiscale representation has similar advantages when used in empirical process modeling. One advantage is that it helps separate noise from important features, which helps improve the accuracy of estimated models. Another advantage is the fact that the number of significant cross-correlation function (CCF) coefficients relating the scaled signal approximations of the input and output data shrinks in half (i.e., decreases dyadically) at every subsequent coarser scale. This advantage is very important in FIR modeling because it means that smaller FIR models are needed at coarse scales. This advantage is exploited to develop a Multiscale Finite Impulse Response (MSFIR) modeling algorithm that helps deal with the collinearity problem often encountered in FIR models. The idea is to decompose the input-output data at multiple scales, and using the scaled signals at each scale, construct smaller FIR models with less collinearity, and then select among all scales the optimum estimated model. The developed MSFIR modeling algorithm is finally shown to outperform some of the existing FIR model estimation methods, such as Ordinary Least Squares (OLS) regression, Ridge Regression (RR), and Principal Component Regression (PCR). A key reason for the advantage of MSFIR over RR is that MSFIR shrinks the statistically insignificant CCF coefficients and noise wavelet coefficients (which are statistically zero) towards zero, while RR shrinks the FIR coefficients towards zero, while they are not. 2005 Elsevier Ltd. All rights reserved.
