We present a sequential Bayesian method for dynamic estimation and prediction of local mean (shadow) powers from instantaneous signal powers in composite fading-shadowing wireless communication channels. We adopt a Nakagami-m fading model for the instantaneous signal powers and a first-order autoregressive [AR(1)] model for the shadow process in decibels. The proposed dynamic method approximates predictive shadow-power densities using a Gaussian distribution. We also derive Crame/spl acute/r-Rao bounds (CRBs) for stationary lognormal shadow powers and develop methods for estimating the AR model parameters. Numerical simulations demonstrate the performance of the proposed methods.