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Global change analyses are facilitated by the growing number of remote-sensing datasets that have both broad spatial extent and repeated observations over decades. These datasets provide unprecedented power to detect patterns of time trends involving information from all pixels on a map. However, rigorously testing for time trends requires a solid statistical foundation to identify underlying patterns and test hypotheses. Appropriate statistical analyses are challenging because environmental data often have temporal and spatial autocorrelation, which can either obscure underlying patterns in the data or suggest false associations between patterns in the data and independent values used to explain them. Existing statistical methods that account for temporal and spatial autocorrelation are not practical for remote-sensing datasets that often contain millions of pixels. Here, we first analyze simulated data to show the need to account for both spatial and temporal autocorrelation in time-trend analyses. Second, we present a new statistical approach, PARTS (Partitioned Autoregressive Time Series), to identify underlying patterns and test hypotheses about time trends using all pixels in large remote-sensing datasets. PARTS is flexible and can include, for example, the effects of multiple independent variables, such as land-cover or latitude, on time trends. Third, we use PARTS to analyze global trends in NDVI, focusing on trends in pixels that have not experienced land-cover change. We found that despite the appearance of overall increases in NDVI in all continents, there is little statistical support for these trends except for Asia and Europe, and only in some land-cover classes. Furthermore, we found no overall latitudinal trend in greening for any continent, but some latitude by land-cover class interactions, implying that latitudinal patterns differed among land-cover classes. PARTS makes it possible to identify patterns and test hypotheses that involve the aggregate information from many pixels on a map, thereby increasing the value of existing remote-sensing datasets. • Analyses of global change using satellite data must be statistically valid. • Our new PARTS analysis can analyze map-scale patterns in large datasets. • PARTS flexibly formulates regression models to address global-scale problems. [ABSTRACT FROM AUTHOR]