Identification of finite impulse response models with continuum regression

Abstract

AbstractThe use of continuum regression (CR) for the identification of finite impulse response (FIR) dynamic models is investigated. CR encompasses the methods of principal component regression (PCR), partial least squares (PLS) and multiple linear regression (MLR). PCR and MLR are at the two extremes of the continuum. In PCR and PLS, cross‐validation is used to determine the optimum number of factors or ‘latent variables’ to retain in the regression model. CR allows one to vary the method in addition. Cross‐validation then determines both the optimum method and the number of latent variables. The CR ‘prediction error surface’—a function of the method and number of latent variables—is elucidated. The optimal model is defined as the minimum of this surface. Among the cases studied, the optimal model usually comes from the region of the continuum between PCR and PLS. Few derive from the region between PLS and MLR. It is also demonstrated that FIR models identified by CR have frequency domain properties similar to those identified by PCR.