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 |
| _version_ | 1797210784461225984 |
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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 |