Uncertainty bounds for long-term causal effects of perturbations in spatiotemporal systems
In time-dependent systems, autoregressive models are frequently employed to investigate the interactions between variables of interest in fields such as climate science, macroeconomics, and neuroscience. Typically, these variables are aggregated from smaller-scale variables into large-scale variable...
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Cambridge University Press
2025-01-01
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| Series: | Environmental Data Science |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2634460225100071/type/journal_article |
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| author | Kevin Debeire Andreas Gerhardus Renée Bichler Jakob Runge Veronika Eyring |
| author_facet | Kevin Debeire Andreas Gerhardus Renée Bichler Jakob Runge Veronika Eyring |
| author_sort | Kevin Debeire |
| collection | DOAJ |
| description | In time-dependent systems, autoregressive models are frequently employed to investigate the interactions between variables of interest in fields such as climate science, macroeconomics, and neuroscience. Typically, these variables are aggregated from smaller-scale variables into large-scale variables, for instance, representing modes of climate variability in climate science. A key aspect of these models is estimating the long-term effects of external perturbations, once the system stabilizes. Our primary contribution is an explicit formula for quantifying these long-term effects on small-scale variables, which is directly estimable from the model’s linear coefficients and aggregation weights. This improves traditional autoregressive models by providing a localized understanding of the system behavior. We conduct a series of numerical experiments to evaluate the performance of various methods to estimate perturbation effects from data. Our second contribution is the derivation of the asymptotic properties of these estimators under suitable assumptions. These asymptotic properties can be leveraged for uncertainty quantification. In a numerical experiment, we compare the uncertainty ranges of the proposed asymptotic-based approach with four bootstrap-based methods. Finally, we apply our methods to investigate the effects of economic activities on air pollution in Northern Italy, demonstrating their ability to reveal local effects. Our novel approach provides a comprehensive framework for analyzing the impacts of perturbations on both large- and small-scale variables, thereby enhancing our understanding of complex systems. Our research has implications for various disciplines where the study of perturbation effects is crucial for understanding and predicting systems’ behavior. |
| format | Article |
| id | doaj-art-09b3deec9c8247e18f27d7e17c61bcc6 |
| institution | Matheson Library |
| issn | 2634-4602 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Environmental Data Science |
| spelling | doaj-art-09b3deec9c8247e18f27d7e17c61bcc62025-07-03T09:30:54ZengCambridge University PressEnvironmental Data Science2634-46022025-01-01410.1017/eds.2025.10007Uncertainty bounds for long-term causal effects of perturbations in spatiotemporal systemsKevin Debeire0https://orcid.org/0000-0001-6006-8750Andreas Gerhardus1Renée Bichler2Jakob Runge3Veronika Eyring4Deutsches Zentrum für Luft- und Raumfahrt (DLR), https://ror.org/04bwf3e34Institut für Physik der Atmosphäre, Oberpfaffenhofen, GermanyDeutsches Zentrum für Luft- und Raumfahrt (DLR), Institut für Datenwissenschaften, Jena, GermanyDeutsches Zentrum für Luft- und Raumfahrt (DLR), German Remote Sensing Data Center, Oberpfaffenhofen, Germany Institute of Geography, https://ror.org/03p14d497 University of Augsburg , Augsburg, GermanyDeutsches Zentrum für Luft- und Raumfahrt (DLR), Institut für Datenwissenschaften, Jena, Germany Faculty of Electrical Engineering and Computer Science, https://ror.org/03v4gjf40 Technische Universität Berlin , Berlin, Germany now at: Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), Technische Universität Dresden, Dresden, GermanyDeutsches Zentrum für Luft- und Raumfahrt (DLR), https://ror.org/04bwf3e34Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany Institute of Environmental Physics (IUP), https://ror.org/04ers2y35 University of Bremen , Bremen, GermanyIn time-dependent systems, autoregressive models are frequently employed to investigate the interactions between variables of interest in fields such as climate science, macroeconomics, and neuroscience. Typically, these variables are aggregated from smaller-scale variables into large-scale variables, for instance, representing modes of climate variability in climate science. A key aspect of these models is estimating the long-term effects of external perturbations, once the system stabilizes. Our primary contribution is an explicit formula for quantifying these long-term effects on small-scale variables, which is directly estimable from the model’s linear coefficients and aggregation weights. This improves traditional autoregressive models by providing a localized understanding of the system behavior. We conduct a series of numerical experiments to evaluate the performance of various methods to estimate perturbation effects from data. Our second contribution is the derivation of the asymptotic properties of these estimators under suitable assumptions. These asymptotic properties can be leveraged for uncertainty quantification. In a numerical experiment, we compare the uncertainty ranges of the proposed asymptotic-based approach with four bootstrap-based methods. Finally, we apply our methods to investigate the effects of economic activities on air pollution in Northern Italy, demonstrating their ability to reveal local effects. Our novel approach provides a comprehensive framework for analyzing the impacts of perturbations on both large- and small-scale variables, thereby enhancing our understanding of complex systems. Our research has implications for various disciplines where the study of perturbation effects is crucial for understanding and predicting systems’ behavior.https://www.cambridge.org/core/product/identifier/S2634460225100071/type/journal_articleautoregressive spatiotemporal modelslong-term effectsuncertainty estimation |
| spellingShingle | Kevin Debeire Andreas Gerhardus Renée Bichler Jakob Runge Veronika Eyring Uncertainty bounds for long-term causal effects of perturbations in spatiotemporal systems Environmental Data Science autoregressive spatiotemporal models long-term effects uncertainty estimation |
| title | Uncertainty bounds for long-term causal effects of perturbations in spatiotemporal systems |
| title_full | Uncertainty bounds for long-term causal effects of perturbations in spatiotemporal systems |
| title_fullStr | Uncertainty bounds for long-term causal effects of perturbations in spatiotemporal systems |
| title_full_unstemmed | Uncertainty bounds for long-term causal effects of perturbations in spatiotemporal systems |
| title_short | Uncertainty bounds for long-term causal effects of perturbations in spatiotemporal systems |
| title_sort | uncertainty bounds for long term causal effects of perturbations in spatiotemporal systems |
| topic | autoregressive spatiotemporal models long-term effects uncertainty estimation |
| url | https://www.cambridge.org/core/product/identifier/S2634460225100071/type/journal_article |
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