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I am looking to perform principal component analysis (PCA), based on daily gridded raster datasets (7 different climate variables) between 1985 and 2015. I was hoping to take each daily dataset (a single raster) and create an average for, say, an entire year, or even for a season of time. However, it would take a lot of work and time, using the Raster Calculator tool, to come up with an average raster for that length of time.

Would it be possible to automate a task like this, using ModelBuilder within ArcMap?

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Yes, you can do that with the model builder, or even better, you can create a Python script that would help you automatizing the task. You're right, it would be incredibly tedious to do it by hand.

Take you have 365, one for every day of a year. You would need to do two things: First, add all the rasters with the raster calculator so you get an added raster AND a second step in which you divide the result raster by 365 so you get the average.

Have a look here and here about how to automatize it.

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