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This Applet demonstates the properties of an ARMA(2,2) time series.

The triangular region for the AR parameters is the region that ensures the time series is stationary.
The triangular region for the MA parameters is the region that ensures the time series is invertible.

Displayed for the ARMA(2,2) model is:

The auto correlation function.
The partial autocorrelation function.
The spectral density function.
A realization of the time series.

You can control the values of the parameters by moving the red points around in each triangle. To regenerate a realization press the generate a realization button. The maximum value for n is 600.