Grassland ecosystems cover one-fourth of the global land area and harbor over 30% of the global carbon stored in soils. However, grasslands are subjected to extensive and intensive land degradation, which threatens biodiversity, the well-being and food-security of millions of people, and poses challenges for climate change mitigation. The question is where grasslands have degraded and where long-term greening is taking place. Time series of satellite data can be used for trend analyses, but when testing for statistical significance, it is important to account for temporal and spatial autocorrelation. Here we present our new statistical method to analyze long-term trends in grasslands based on physically-based Cumulative Endmember Fractions (annual sums of monthly ground cover fractions). Our trend analysis incorporates two steps: first we apply an autoregressive time series to each pixel to obtain a slope estimate while accounting for temporal autocorrelation. Second, we apply a general least-square regression to the slope estimates, in which we incorporate spatial covariance structure, as well as explanatory variables. We tested our approach mapping long-term trends in grasslands in Central Asia using MODSI 2001 2019 time series, which we regressed against meteorological measurements. Our results showed long term changes of both, positive (i.e., revegetation; e.g., east part of Central Asia) and negative trajectories (i.e., desiccation; e.g., north-west part of the Central Asia). Importantly, our method is scalable and transferable to other time series of satellite data and regions, and can be implemented in any computational environment, assuring accessibility and reproducibility.