How should I analyze a time series to predict a single continuous value?

I have many time series of brain responses, and I want to use them to predict their associated reaction times. I also want to know how much each time point in the time series contributed to the prediction. So, for example, I want to take 100 brain responses (each about 500ms worth of brain data, and one value for reaction time) and figure out what part of that brain response is the best predictor of reaction time. How would you go about doing this?