Dealing with Collinearity in FIR models using Multiscale Estimation

In this paper, multiscale representation of data is utilized to reduce the collinearity problem often encountered in Finite Impulse Response (FIR) modeling. The idea is to decompose the input-output data at multiple scales, use the scaled signal approximations of the data to construct a FIR model at each scale, and then select among all scales the optimum estimated FIR model. The rationale behind this approach is that the number of significant cross correlation function (CCF) coefficients estimated using the scaled signal approximations of the input-output data decreases at coarser scales. This means that more parsimonious FIR models, with less collinearity and improved estimation accuracy, can be constructed at coarser scales. Of course, the estimation accuracy will deteriorate at very coarse scales. Therefore, it is very important to select the most appropriate scale for modeling purposes, which can be done by selecting the scale which results in the maximum prediction signal to noise ratio. The developed multiscale FIR modeling approach is shown to outperform existing methods, such as ordinary least squares (OLS) regression and ridge regression (RR).