I am looking for an algorithm to detect when a stream of data is showing an usual trend.
For example: You are logging your bookings, and over the last couple of weeks they have been stable with the usual ups and downs. But suddenly your payment provider stops working, and within hours your bookings decline drastically. The catch is to minimise false alerts, and the solution should adapt to a long term decline.
What is the statistical approach to this problem?
What is the name of such an algorithm?