Ahoy, As an example, I have multiple time series of temperature. These times series are of different lengths (1-8 days), and generally from non-overlapping date:time, but the interval between data points are consistent (30 minutes). Each time series is associated with a single numeric outcome, let's in this example call it total mls of rainfall over the associated time series. This outcome is obviously not the same variable as the time series, so I'm not after forecasting temperature. There's also no time series available for the rainfall variable, just a single measurement at the end of each time series. So no rainfall data matched with each temperature measurement. What I'm after is a way of using the temperature data, specifically as a time series, to predict a point estimate of the total rainfall over the period of the time series. Let's assume that the signal I'm trying to model, is that a higher mean temperature is associated with lower total rainfall.
I have been able to turn the time series data into a simple regression problem, by making variables out of key features of each time series, e.g. max temp, mean temp, min temp, cumulative temp, etc, but I'm specifically interested in a way to use the multiple time series to train one model.
I'm hoping someone can direct me to a model, literature, methodology or other posts with a possible solution.
I haven't worked with these personally, but I believe what you are looking for is known (at least in some circles) as scalar on function regression. It is also sometimes referred to as signal regression. It may be worth looking into the
refundpackage in R to get some ideas and further guidance. Sorry I can't be more helpful with examples though