Nowadays, the process of change detection is regarded as an outstanding way for urban planning and design. The major concern of this paper is to investigate the nonstationary character of multi-temporal time series. To overcome this problem, we propose an adaptive multiplicative decomposition of non-stationary multi-temporal satellite image, which allows to decompose the series into three components: trend, seasonal and random, to properly model the evolution of land cover. We carried several experiments to validate our approach based on Landsat images covering the region of "Tres Cantos-Madrid" in Spain. The obtained results show the effectiveness of our proposed method comparing to some conventional methods.