Although it may not be in the format type you want, check out the Combine tool http://resources.arcgis.com/en/help/main/10.2/index.html#//009z0000007r000000 but it only works with integer values...floating point inputs will be truncated
This is something that is doable with your rasters. The best way to accomplish is to load the rasters into aRaster Catalog or Mosaic Dataset within a file geodatabase. In a Raster Catalog, you have an attribute table that can be used to store year information for each raster within the catalog. This attribute can then be used to create the time series maps.
Sample Workflow for Raster Catalog:
1. Rename your raster datasets with a year suffix (i.e. "Rainfall_2014.tif")
2. Load those rasters into a Raster Catalog
3. Add a field called to the Raster Catalog to represent your time field
4. Start an edit session in ArcMap to edit the time field to match your Rasters
5. Save your edits