Revisiting inference for ARMA models: Improved fits and superior confidence intervals.
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| Titel: | Revisiting inference for ARMA models: Improved fits and superior confidence intervals. |
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| Autoren: | Wheeler J; Department of Statistics, University of Michigan, Ann Arbor, Michigan, United States of America.; Department of Mathematics and Statistics, Idaho State University, Pocatello, Idaho, United States of America., Ionides EL; Department of Statistics, University of Michigan, Ann Arbor, Michigan, United States of America. |
| Quelle: | PloS one [PLoS One] 2025 Oct 24; Vol. 20 (10), pp. e0333993. Date of Electronic Publication: 2025 Oct 24 (Print Publication: 2025). |
| Publikationsart: | Journal Article |
| Sprache: | English |
| Info zur Zeitschrift: | Publisher: Public Library of Science Country of Publication: United States NLM ID: 101285081 Publication Model: eCollection Cited Medium: Internet ISSN: 1932-6203 (Electronic) Linking ISSN: 19326203 NLM ISO Abbreviation: PLoS One Subsets: MEDLINE |
| Imprint Name(s): | Original Publication: San Francisco, CA : Public Library of Science |
| MeSH-Schlagworte: | Models, Statistical*, Algorithms ; Confidence Intervals ; Likelihood Functions ; Computer Simulation |
| Abstract: | Competing Interests: The authors have declared that no competing interests exist. Autoregressive moving average (ARMA) models are widely used for analyzing time series data. However, standard likelihood-based inference methodology for ARMA models has avoidable limitations. We show that currently accepted standards for ARMA likelihood maximization frequently lead to sub-optimal parameter estimates. Existing algorithms have theoretical support, but can result in parameter estimates that correspond to a local optimum. While this possibility has been previously identified, it remains unknown to most users, and no routinely applicable algorithm has been developed to resolve the issue. We introduce a novel random initialization algorithm, designed to take advantage of the structure of the ARMA likelihood function, which overcomes these optimization problems. Additionally, we show that profile likelihoods provide superior confidence intervals to those based on the Fisher information matrix. The efficacy of the proposed methodology is demonstrated through a data analysis example and a series of simulation studies. This work makes a significant contribution to statistical practice by identifying and resolving under-recognized shortcomings of existing procedures that frequently arise in scientific and industrial applications. (Copyright: © 2025 Wheeler, Ionides. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.) |
| References: | IEEE Trans Biomed Eng. 1997 Mar;44(3):168-74. (PMID: 9216130) |
| Entry Date(s): | Date Created: 20251024 Date Completed: 20251024 Latest Revision: 20251027 |
| Update Code: | 20251027 |
| PubMed Central ID: | PMC12551883 |
| DOI: | 10.1371/journal.pone.0333993 |
| PMID: | 41134851 |
| Datenbank: | MEDLINE |
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Nájsť tento článok vo Web of Science | Abstract: | Competing Interests: The authors have declared that no competing interests exist.<br />Autoregressive moving average (ARMA) models are widely used for analyzing time series data. However, standard likelihood-based inference methodology for ARMA models has avoidable limitations. We show that currently accepted standards for ARMA likelihood maximization frequently lead to sub-optimal parameter estimates. Existing algorithms have theoretical support, but can result in parameter estimates that correspond to a local optimum. While this possibility has been previously identified, it remains unknown to most users, and no routinely applicable algorithm has been developed to resolve the issue. We introduce a novel random initialization algorithm, designed to take advantage of the structure of the ARMA likelihood function, which overcomes these optimization problems. Additionally, we show that profile likelihoods provide superior confidence intervals to those based on the Fisher information matrix. The efficacy of the proposed methodology is demonstrated through a data analysis example and a series of simulation studies. This work makes a significant contribution to statistical practice by identifying and resolving under-recognized shortcomings of existing procedures that frequently arise in scientific and industrial applications.<br /> (Copyright: © 2025 Wheeler, Ionides. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.) |
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| ISSN: | 1932-6203 |
| DOI: | 10.1371/journal.pone.0333993 |