I'm in the process of starting to collect new time series data (monthly observations) which I would like to perform seasonal adjustment on. While I appreciate that there is no mathematically sound way to do so without a "critical mass" of previous observations, in this case an alternative might be conceivable:
The time series I am collecting is basically a reproduction of an existing time series and expected to behave very similar to the original one. So I was thinking to simply append my new observations to the unadjusted original series and adjust the combined series (using the same adjustment method as for the original time series). The idea is to jump start the adjustment process using the other time series and slowly move away from it when my own time series accumulates more observations.
One of my main concerns is that the new time series may e.g. be offset from the original one by a constant factor resulting in a break of the time series which may be smoothed away by the adjustment procedure or similar.
In general, do you think this approach is feasible? Is there any literature on this that I missed during my search?