Parametric identification of time-varying (TV) systems is possible if each TV coefficient can be expanded onto a finite set of basis sequences. The problem then becomes time invariant with respect to the parameters of the expansion. In this paper, we address the question of selecting This set of basis sequences. We advocate the use of a wavelet basis because of its flexibility in capturing the signal's characteristics at differerent scales, and discuss how to choose the optimal wavelet basis for a given system trajectory. We also develop statistical tests to keep only the basis sequences that significantly contribute to the description of the system's time-variation. By formulating the problem as a regressor selection problem, we apply an F-test and an AIC based approach for multiresolution analysis of TV systems. The resulting algorithm can estimate TV AR or ARMAX models and determine their orders. We apply this algorithm to both synthetic and real speech data and compare it with the Kalman filtering TV parameter estimator.