Robust model order selection for ARMA models based on the bounded innovation propagation τ-estimator

Abstract

A crucial task when fitting an ARMA model to real-world data is the selection of the autoregressive and moving-average orders. In real-world applications, the data may contain measurement artifacts or outliers (aberrant observations). Robust model order selection aims at finding a suitable statistical model to describe the majority of the data while preventing outliers or other contaminants from having overriding influence on the final conclusions. Three new approaches for robustly selecting the ARMA model orders based on the bounded innovation propagation (BIP) τ -estimator are presented. These are compared via Monte Carlo simulations to existing robust and non-robust criteria. A real-data application of ARMA modeling for artifact removal in intracranial pressure signals is provided.

Bounded Influence Propagation $\tau$ -Estimation: A New Robust Method for ARMA Model Estimation

“…Proof of Theorem 1: Take ξ > 0 arbitrarily small and let d be as in Lemma 3. The continuity of the M-scale functional σM (β) > 0 defined in (25) follows from Lebesgue's dominated convergence theorem. The continuity of στ (β) follows from (30) as long as ρ 2 satisfies A3.…”

“…8 (2nd from top). To determine the correct model order, i.e., to estimate p, robust model order selection criteria [25] were applied based on the final τ -estimate of the innovations scale, i.e.,…”

“…The results of the robust model order selection are provided in Table III. By choosing c pen = 2(p + 1) n, c pen = log(n)p n and c pen = 2 log(log(n))p n the criteria by Akaike, Schwarz and Hannan and Quinn, stated respectively in [25], [61] are obtained. The third plot of Fig.…”

“…BIP-τ BASED MODEL ORDER SELECTION[25] FOR THE R-R INTERVAL SERIES. THE CHOSEN ORDER IS HIGHLIGHTED WITH BOLD FONT.…”