On an L2 norm for stationary ARMA processes

We propose an L2 norm for stationary Autoregressive Moving Average (ARMA) models. We look at ARMA models within the Hilbert space of the past with present of a true purely linearly non-deterministic stationary process Xt, and compute the L2 norm based on its Wold decomposition. As an application of this L2 norm, we derive bounds on the mean square prediction error for AR(1) models of MA(1) processes, and verify these bounds empirically for sample data.