# Analyze Time-Series Models

This example shows how to analyze time-series models.

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.

Estimate a time-series model.

sys = ar(z9,4);

Convert the time-series model to an input-output model.

iosys = noise2meas(sys);

Plot the step response of H.

step(iosys);

Plot the poles and zeros of H.

iopzmap(iosys);

Calculate and plot the time-series spectrum directly without converting to an input-output model.

spectrum(sys);

The command plots the time-series spectrum amplitude $\Phi \left(\omega \right)={‖H\left(\omega \right)‖}^{2}$.

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