A time-series model has no inputs. However, you can use many response computation commands on such models. The software treats (implicitly) the noise source e(t) as a measured input. Thus, step(sys) plots the step response assuming that the step input was applied to the noise channel e(t).
To avoid ambiguity in how the software treats a time-series model, you can transform it explicitly into an input-output model using noise2meas. This command causes the noise input e(t) to be treated as a measured input and transforms the linear time series model with Ny outputs into an input-output model with Ny outputs and Ny inputs. You can use the resulting model with commands, such as, bode, nyquist, and iopzmap to study the characteristics of the H transfer function. For example:
iosys = noise2meas(sys); % step response of H if the step command was applied % to the noise source e(t) step(iosys) % poles and zeros of H iopzmap(iosys)
You can calculate and plot the time-series spectrum directly (without conversion using noise2meas) using spectrum. For example:
plots the time-series spectrum amplitude: