March 2024 Moment conditions for random coefficient AR() under non-negativity assumptions
Pascal Maillard, Olivier Wintenberger
Author Affiliations +
Braz. J. Probab. Stat. 38(1): 88-107 (March 2024). DOI: 10.1214/23-BJPS594

Abstract

We consider random coefficient autoregressive models of infinite order (AR()) under the assumption of non-negativity of the coefficients. We develop novel methods yielding sufficient or necessary conditions for finiteness of moments, based on combinatorial expressions of first and second moments. The methods based on first moments recover previous sufficient conditions by (Stoch. Process. Their Appl. 118 (2008) 1997–2013) in our setting. The second moment method provides in particular a necessary and sufficient condition for finiteness of second moments which is different, but shown to be equivalent to the classical criterion of (Random Coefficient Autoregressive Models: An Introduction (1982) Springer) in the case of AR(p) models with finite order p<. We further illustrate our results through two examples.

Funding Statement

PM acknowledges support of the French Agence Nationale de la Recherche (ANR) under reference ANR-20-CE92-0010-01 (REMECO project) and ANR-11-LABX-0040 (ANR program “Investissements d’Avenir”).
OW acknowledges support of the French Agence Nationale de la Recherche (ANR) under reference ANR20-CE40-0025-01 (T-REX project).

Citation

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Pascal Maillard. Olivier Wintenberger. "Moment conditions for random coefficient AR() under non-negativity assumptions." Braz. J. Probab. Stat. 38 (1) 88 - 107, March 2024. https://doi.org/10.1214/23-BJPS594

Information

Received: 1 July 2022; Accepted: 1 December 2023; Published: March 2024
First available in Project Euclid: 4 March 2024

MathSciNet: MR4718427
Digital Object Identifier: 10.1214/23-BJPS594

Keywords: heavy tails , power-law tails , Random coefficient autoregressive model , Second moment method , stochastic recurrence equations

Rights: Copyright © 2024 Brazilian Statistical Association

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Vol.38 • No. 1 • March 2024
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