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A UNIFIED THEORY FOR ARMA MODELS WITH VARYING COEFFICIENTS: ONE SOLUTION FITS ALL

Published online by Cambridge University Press:  27 February 2025

Menelaos Karanasos,
Alexandros G. Paraskevopoulos,
Tassos Magdalinos and
Alessandra Canepa
Menelaos Karanasos
Affiliation:
Department of Economics and Finance, Brunel University London
Alexandros G. Paraskevopoulos
Affiliation:
University of Piraeus
Tassos Magdalinos*
Affiliation:
University of Southampton
Alessandra Canepa
Affiliation:
University of Turin
*
Address correspondence to Tassos Magdalinos, University of Southampton, Southampton, UK; e-mail: a.magdalinos@soton.ac.uk
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Abstract

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A new explicit solution representation is provided for ARMA recursions with drift and either deterministically or stochastically varying coefficients. It is expressed in terms of the determinants of banded Hessenberg matrices and, as such, is an explicit function of the coefficients. In addition to computational efficiency, the proposed solution provides a more explicit analysis of the fundamental properties of such processes, including their Wold–Cramér decomposition, their covariance structure, and their asymptotic stability and efficiency. Explicit formulae for optimal linear forecasts based either on finite or infinite sequences of past observations are provided. The practical significance of the theoretical results in this work is illustrated with an application to U.S. inflation data. The main finding is that inflation persistence increased after 1976, whereas from 1986 onward, the persistence declines and stabilizes to even lower levels than the pre-1976 period.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 42 , Issue 1 , February 2026, pp. 192 - 245
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2025. Published by Cambridge University Press

Footnotes

The first two author names are in alphabetical order. We thank the Editor, the Co-Editor, and two anonymous referees for their thoughtful comments and constructive suggestions. We gratefully acknowledge the helpful conversations we had with L. Giraitis, and G. Kapetanios in the preparation of the paper. We have also benefited from the comments given by participants (R. Baillie, M. Brennan, L. Bauwens, A. Demos, W. Distaso, D. van Dijk, C. Francq, P. Fryzlewicz, E. Guerre, C. Gourieroux, M. Guidolin, A. Harvey, C. Hommes, E. Kyriazidou, S. Leybourne, P. Marsh, P. Minford, C. Robotti, W. Semmler, R. Smith, T. Teräsvirta, E. Tzavalis, P. Zaffaroni, and J.-M. Zakoian) at various seminars and conferences. We would like to thank S. Dafnos, who contributed to the interpretation and synthesis in the initial version of the paper, and P. Koutroumpis, who provided the empirical section in an earlier version. Magdalinos gratefully acknowledges financial support by the British Academy: grant SRG2324\241667. Alessandra Canepa acknowledges financial support under the National Recovery and Resilience Plan (NRRP), Mission 4, Component 2, Investment 1.1, Call for tender No. 104 published on February 2, 2022 by the Italian Ministry of University and Research (MUR), funded by the European Union—NextGenerationEU—Project Title 20223725WE—Methodological and computational issues in large-scale time series models for economics and finance – CUP J53D23003960006—Grant Assignment Decree No. 967 adopted on June 30, 2023 by the Italian Ministry of Ministry of University and Research (MUR).

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