# detect gradual change in time series data

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:

• It would help immensely to have a model--preferably quantitative, but even a conceptual one will do--of the phenomenon you are studying. In addition, can you supply some information about the consequences of underestimating or overestimating the correct inflection point? Without such information you can only hope for generic answers that implicitly rely on models that might not be applicable in any particular instance. – whuber Feb 8 at 13:00
• Ok I added a description and a graph, may be that makes it clear? – rookie Feb 8 at 14:58
• The additional information about monotonicity is useful, but the graph doesn't add anything to your original post: it doesn't suggest a model and doesn't tell us any more about whatever it is you might be measuring. – whuber Feb 8 at 15:43