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I currently have quarterly time series data that I would like to have weighted and annualized. I would like the weights to be as follows: Q1=.1, Q2=.2, Q3=.3 and Q4=.4. How would I go about assigning these weights to each quarter and thus finding the average?

You'll probably have to create a new series that is the weighted series, then find the average of it.

In your case, you could create the weighted series as: where X is the name of your base series.