On an L² norm for stationary ARMA processes

2024/08/20 by Anand Ganesh, Ganesh, Anand, Babhrubahan Bose +3
Engineering · #60G10 #FOS: Computer and information sciences #FOS: Mathematics #Fault Detection and Control Systems #G.3 #Machine Learning (cs.LG) #Methodology (stat.ME) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2408.10610

openalex publication_date 2024/08/20 · openalex created_date 2024/10/01 · openalex updated_date 2026/07/28

Abstract

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 X_t, 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.

Related

• Estimating invertible processes in Hilbert spaces, with applications to functional ARMA processes
• A unified theory for ARMA models with varying coefficients: One solution fits all
• Structure of continuous-time ARMA process driven by semi-Levy measure
• The Estimation of the Order of an ARMA Process
• Simulating Continuous-Time Autoregressive Moving Average Processes Driven By p-Tempered α-Stable Lévy Processes