I have a stateful black box with four real-valued inputs and one real-valued output. My problem is to predict the output at each moment in time, given the sequence of inputs seen up to that point. During a learning phase, I can vary the inputs however I want and observe the output. There's a little noise, of course, and the black box doesn't appear to be completely deterministic.
Specifically, I'm modeling a hard drive, and I want to predict the access time of the latest request given all previous requests. I want a more black-box approach, though, because of the complexity of explicit models, and because I want this to work for other similar devices such as SSDs.
A couple of people have suggested that signal processing might be appropriate to analyze the sequences of input and output values.
Are there any ideas from signal processing that could help me to predict the output, or to characterize the input?