A UNIFIED THEORY FOR ARMA MODELS WITH VARYING COEFFICIENTS: ONE SOLUTION FITS ALL
Abstract
A preprint version of the article is available at: arXiv:2110.06168v1 [math.ST], https://arxiv.org/abs/2110.06168 under a CC BY licence. It has not been certified by peer review.A new explicit solution representation is provided for ARMA recursions with drift and either deterministically or stochastically varying coefficients.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.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)Similar works
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Last time updated on 12/09/2024
This paper was published in Brunel University Research Archive.
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