I have two RasterBrick objects in R! Both RasterBrick objects describes the same area and the same time periods. Each raster in RasterBrick stores values for one specific month.

I would like to test whether distributions of their values are similar, if they're showing the same trend, whether they're describing the same process/phenomena.

Obviously I can calculate Pearson/Spearman correlation coefficients (Spearman correlation between two rasters in R), but I would like to use some sort of spatial statistical test.

I've found some information about autocorrelation testing for spatial data in R!, but very little about checking relation between two spatial data sets (many mentions mainly correlation coefficients: https://www.researchgate.net/post/How_to_statistically_compare_two_maps).

Is there any package which allows me to apply spatial/geostatistical tests directly on Raster objects (for example Mantel test - I mentioning this test, because I've found and example http://www.ats.ucla.edu/stat/r/faq/mantel_test.htm although not for raster objects)?

Could you suggest any statistical/geostatical tests/package, please?

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