Sales Predictions Over Time I'd like to model the evolution of the sales of a store.

Here are the data I have :




Customers are aggregated into monthly cohort depending on the date of the first purchase
eg : customers who did their 1st purchase in Jan 2015 are in the cohort 1, customers who did their 1st purchase in Fev 2015 are in the cohort 2.
Sales : aggregated for each Month * Cohort (cohort 4 is not visible because there is no line for only 1 record)




if we put all the cohorts at the same origin:


Question: How to predict the spending of the next 2 months, ie :


the spending of the cohort 1 in its aging 5 and 6
the spending of the cohort 2 in its aging 4 and 5
the spending of the cohort 3 in its aging 3 and 4
the spending of the cohort 4 in its aging 2 and 3


But also for the cohort who don't exist yet :


the spending of the cohort 5 in its aging 1 and 2
the spending of the cohort 6 in its aging 1 


I have 2 methodologies in mind, but don't know if they're good:


Polynomial regression by using 2 parameters:


aging: because there is a clear evolution over the time, up then down.
cohort number: because more recent cohort seems to spend less.

Time series : I didn't perform time series recently I'm a bit rust so I would prefer to use something else but I think it could fit with this problem.


Indeed it seems obvious that yt-1 t in yt-2... are good predictors of yt but how to predict spending of future cohort with no history ?
It sounds like you are making this more complicated than it is with trying to predict spend at the cohort level. It is best to use cohorts for understanding "why" something occurred and time series analysis for understanding "what" will occur. 

The Forecast package in R seems to be solution to your problem. Just forecast Monthly spend and be done with it!