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arXiv · 2408.10610

On an $L^2$ norm for stationary ARMA processes

Anand Ganesh·Babhrubahan Bose·Anand Rajagopalan
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Abstract

We propose an $L^2$ 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 $X_t$, and compute the $L^2$ norm based on its Wold decomposition. As an application of this $L^2$ 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.

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Anand Ganesh, Babhrubahan Bose, Anand Rajagopalan. 2024-08-20. On an $L^2$ norm for stationary ARMA processes. https://arxiv.org/abs/2408.10610

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