Statistical inference of one-dimensional persistent nonlinear time series and application to predictions
We introduce a method for reconstructing macroscopic models of one-dimensional stochastic processes with long-range correlations from sparsely sampled time series by combining fractional calculus and discrete-time Langevin equations. The method is illustrated for the ARFIMA(1,d,0) process and a nonl...
Main Authors: | , |
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Format: | Article |
Language: | English |
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American Physical Society
2022-03-01
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Series: | Physical Review Research |
Online Access: | http://doi.org/10.1103/PhysRevResearch.4.013206 |
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author | Johannes A. Kassel Holger Kantz |
author_facet | Johannes A. Kassel Holger Kantz |
author_sort | Johannes A. Kassel |
collection | DOAJ |
description | We introduce a method for reconstructing macroscopic models of one-dimensional stochastic processes with long-range correlations from sparsely sampled time series by combining fractional calculus and discrete-time Langevin equations. The method is illustrated for the ARFIMA(1,d,0) process and a nonlinear autoregressive toy model with multiplicative noise. We reconstruct a model for daily mean temperature data recorded at Potsdam, Germany and use it to predict the first-frost date by computing the mean first passage time of the reconstructed process and the 0^{∘}C temperature line, illustrating the potential of long-memory models for predictions in the subseasonal-to-seasonal range. |
first_indexed | 2024-04-24T10:16:06Z |
format | Article |
id | doaj.art-495169f254bc48deabea90827d4405ac |
institution | Directory Open Access Journal |
issn | 2643-1564 |
language | English |
last_indexed | 2024-04-24T10:16:06Z |
publishDate | 2022-03-01 |
publisher | American Physical Society |
record_format | Article |
series | Physical Review Research |
spelling | doaj.art-495169f254bc48deabea90827d4405ac2024-04-12T17:18:59ZengAmerican Physical SocietyPhysical Review Research2643-15642022-03-014101320610.1103/PhysRevResearch.4.013206Statistical inference of one-dimensional persistent nonlinear time series and application to predictionsJohannes A. KasselHolger KantzWe introduce a method for reconstructing macroscopic models of one-dimensional stochastic processes with long-range correlations from sparsely sampled time series by combining fractional calculus and discrete-time Langevin equations. The method is illustrated for the ARFIMA(1,d,0) process and a nonlinear autoregressive toy model with multiplicative noise. We reconstruct a model for daily mean temperature data recorded at Potsdam, Germany and use it to predict the first-frost date by computing the mean first passage time of the reconstructed process and the 0^{∘}C temperature line, illustrating the potential of long-memory models for predictions in the subseasonal-to-seasonal range.http://doi.org/10.1103/PhysRevResearch.4.013206 |
spellingShingle | Johannes A. Kassel Holger Kantz Statistical inference of one-dimensional persistent nonlinear time series and application to predictions Physical Review Research |
title | Statistical inference of one-dimensional persistent nonlinear time series and application to predictions |
title_full | Statistical inference of one-dimensional persistent nonlinear time series and application to predictions |
title_fullStr | Statistical inference of one-dimensional persistent nonlinear time series and application to predictions |
title_full_unstemmed | Statistical inference of one-dimensional persistent nonlinear time series and application to predictions |
title_short | Statistical inference of one-dimensional persistent nonlinear time series and application to predictions |
title_sort | statistical inference of one dimensional persistent nonlinear time series and application to predictions |
url | http://doi.org/10.1103/PhysRevResearch.4.013206 |
work_keys_str_mv | AT johannesakassel statisticalinferenceofonedimensionalpersistentnonlineartimeseriesandapplicationtopredictions AT holgerkantz statisticalinferenceofonedimensionalpersistentnonlineartimeseriesandapplicationtopredictions |