The paper considers a SUTSE model embedded in a dynamic framework to estimate an energy cost share model for the Italian economy in an evolutionary environment. This is achieved by allowing stochastic seasonal and trend components in the long-run specification and constructing an error correction mechanism to model short-run dynamics. Modelling instability in the structural time series approach has provided some improvement in the estimates of the elasticities of substitutions and of the price elasticities with respect to those obtained using deterministic trend and seasonal components. Tests for instability in the cointegrating regression support the evolutionary specification adopted.