I have a stream of real continuous numbers (Figure. 1). The stream flows from left to right. At $t_1$ the first number entered the stream. Every time a new number enters the stream I check if there is a sudden change or high variation.
How can I compute the
sudden change or
high variation without using any threshold. The following picture is just and example.
What I was doing is simply compute a quantity $Q_x = |t_4 - t_5|$ and if $Q_x > \delta$ then there is a sudden change and a high variation. Using a threshold is wrong in my situation because there is no bound for the real numbers in the stream. Another idea came to my mind which is the following:
$if\;|t_5-t_4| >|t_4-t_3| + \delta $ where $\delta = [0,1]$ then there is a sudden change.
What do you think? Thank you.