Assume a single-input single-output model $y = f(x)$ where time series $x = (x_0, .., x_{n})$ is the input, time series $y = (y_0, .., y_n)$ is the output and $f$ a function mapping $x$ to $y$.
If the system $f$ is linear and time-invariant, it is completely determined by its impulse/frequency response.
However, if this is not the case, how to find $f$?