I am analyzing experimental time series ; I have input and output time series from a (blackbox) dynamical system, say X and Y. Time series Y should be fully determined by the history of X and I assume a linear relationship
Y(t) = integral (0<tau<infinity) X(t-tau) Chi(tau) dtau
Here Chi(tau) is the (unknown) linear response function of my dynamical system.
My question is: - What are good algorithms for determining Chi? - Where do I find literature? What are relevant key words?