This paper considers a SUTSE model embedded in a dynamic framework to estim
ate an energy cost share model for the Italian economy in an evolving envir
onmental. This is achieved by allowing stochastic seasonal and trend compon
ents in the long-run specification and constructing an error correction mec
hanism to model short-run dynamics. Modelling instability in the structural
time series approach is shown to be a very flexible approach to non conven
tional cointegration analysis. Tests for instability in the cointegrating r
egression support the evolving specification adopted.