I have a series of numbers tracking the performance of an entity on any given day. It's nothing but a simple integer for each date. For example, here's a series for Entity "X"
11/1/2012 - 11/30/2012 - 3000 (one month summary) 12/1/2012 - 123 12/2/2012 - 129 12/3/2012 - 131 12/4/2012 - 112 ... 12/31/2012 - 147
Ultimately I'm trying to output some form of momentum indicator for this entity for a day, week, and month. My initial attempts were as follows:
I could simply calculate the slope between two points. For daily, I would compare day 1 versus day 2 and take the slope. For weekly, the average count for week 1 and compare to average count for week 2, etc.
Use a theoretical formula for detecting whether or not the count is "breaking out" of a local or global maxima (up) or minima (down) and assign a value based on the distance from the local or global maxima/minima. Unfortunately I'm not sure how one would approach calculating this.
An additional formula that determines whether or not the trend created in #2 is actually sustained.
My question is this: in a very simple time series, is there a relatively straight-forward approach to coming up with a momentum indicator? Obviously there are flaws with a simple equation but the more simple the better. I can improve the equation over time.
One assumption: There are no other variables to be taken into consideration aside from this number. All other things are constant.