Time-varying system identification using wavelets

An algorithm for identifying time-varying AR and ARMAX models is proposed. Each model coefficient is expanded onto a wavelet basis and the expansion parameters are estimated. An F-test and an AIC based procedure are developed to discard the insignificant terms of the expansion and provide a description for the system´s trajectory as well as its order. The choice of the optical wavelet basis for this problem is also discussed. The proposed method offers a parsimonious description of the system´s trajectory, while still being able to `zoom into´ the local variations where necessary