Hello,
Determining (running) the profile day-by-day does not give you a definite answer on a possible population drift. You would still have to compare the distributions for variable i to get alerted on a SIGNIFICANT change.
In Credit Scoring (finance) there exists sthg. called the stability report and the stability index.
It measures possible population drift that can be due to :
• Seasonality
• Changing economic climate
• Customer drop-out
• Changing sales and marketing strategies, marketing campaign, niche competition
• Customer profile changed independently e.g. demographic change
• Mistakes in data capture, systematic error (coding), non-random sample, exclusions
I don't know about the technical underpinnings of this index, but I believe it's close to the Kullback-Leibler Distance / divergence.
It would require you to bin the range of your variables (10 or 15 buckets will do).
Let me know if you need more info on this. If needed I can make and upload some code, but if you can sort it out yourself, that's even better of course ;-).
Cheers,
Koen