Should I be trying to replicate the NEAS results?

[NEAS: This is an independent student project. The NEAS postings are suggestions to get you started. You can construct an ARIMA model, compare two or more models for a given era, compare two or three eras by type of model of by model parameters, examine seasonality, test out-of-sample forecasts, and many other items.]

My previous question on seasonality was probably not clear. I'm asking lets say I have temperature data, and I know there is seasonality. If I have data for every month, the seasonality is easy to get rid of, was can subtract Yt-12 from Yt. However, let's say you have data for 4 years. Year, you are missing data on February and March. Year 2 you are missing data from May, Year 3 you are missing data from December, year 4 you are missing the last half of the year. So I have a total of 38 data points. Or 48 data points with 10 data points of 0. Now lag 13, which is 12 lags after lag 1, is not January, it is March. How do I unseasonalize these temperatures?

Are you saying that I should just get an average of every month and an average of the year and then just subtract from each month the difference? Because that would make some sense.

[NEAS: With missing data points, time series analysis is more difficult. Your proposed method is fine; other methods can also be used. Alternatively, instead of the 0's, you can use the monthly averages for the missing values.]