I have a time series data where I need to detect the movement of the data-point by a certain threshold. The data can gradually move up instead of a one step increase, for example - I want to detect a threshold change of approx 500, and my data is
[10, 10, 10, 10, 100, 250, 500, 600, 600, 600]. A simple derivative between successive samples will not detect a change, since the required change (500) happens over a period of a few samples. I can filter the data with a low pass filter like moving average, but that wouldn't help either. How can I detect this change in level?
EDIT : This data is generated by a simple algorithm that only increases in steps - they may be small or large, but will only increase or remain constant. An example graph would be something like this: