One of the things I've struggled with is the issue of effectively summarizing some sort of time series metric (i.e. independent variable) for use in a regression analysis. The most common solution that I've encountered (which may not be the best) is to compute a meaningful average. Although I can get a single number I still have the nagging feeling that it doesn't really capture what I need.
Let's assume that there are 3 data points which when plotted over time we can see different types of growth. What I wish to capture/model is that the "flattens" represents the possibility that item sale (or whatever it represents) is eventually going to take a downturn or just stop selling. The "growth" curve is something that won't immediately stop but for the time being (e.g. 1 month) it's a safe bet to assume item popularity.
Here are my questions:
- How can/should we capture the "shapes" of such time series based independent variables for regression? Does it even matter or is the average the best we can do?
- I thought of computing "slopes" (start, end) but as the graph shows (approximately) that there such a computation could lead to similar values for both flattens and growth curves. Is this even a thing?
- What could/should I use?
Note: These shapes are just examples and the actual time series could be rather fluctuating. What I think I'm interested in is a way to capture a notion of a general trend in some way (if at all). I understand trends could be captured via moving averages, but I don't know how to capture "up/down-ness" or summarize it in a meaningful way.
I'm hoping this doesn't become a two-step problem where we first train a model on "learning" these curves and what they represent and then feeding the output into the regression. That would be too complicated for now but I don't even know if that's a valid solution or should I just stick with averages.