dorsal/arxiv
View SchemaTime Series Forecasting: A Nonlinear Dynamics Approach
| Authors | Stefano Sello |
|---|---|
| Categories | |
| ArXiv ID | physics/9906035 |
| URL | https://arxiv.org/abs/physics/9906035 |
Abstract
The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the international monthly smoothed sunspot number. It is well known that the solar cycle is very difficult to predict due to the intrinsic complexity of the related time behaviour and to the lack of a succesful quantitative theoretical model of the Sun magnetic cycle. Starting from a previous recent work, we checked the reliability and accuracy of a forecasting model based on concepts of nonlinear dynamical systems applied to experimental time series, such as embedding phase space, Lyapunov spectrum, chaotic behaviour. The model is based on a local hypothesis of the behaviour on the embedding space, utilizing an optimal number k of neighbour vectors to predict the future evolution of the current point with the set of characteristic parameters determined by several previous parametric computations. The performances of this method suggest its valuable insertion in the set of the so-called statistical-numerical prediction techniques, like Fourier analyses, curve fitting, neural networks, climatological, etc. The main task is to set up and to compare a promising numerical nonlinear prediction technique, essentially based on an inverse problem, with the most accurate predictive methods like the so-called "precursor methods" which appear now reasonably accurate in predicting "long term" Sun activity, with particular reference to the "solar" precursor methods based on a solar dynamo theory.
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"abstract": "The problem of prediction of a given time series is examined on the basis of\nrecent nonlinear dynamics theories. Particular attention is devoted to forecast\nthe amplitude and phase of one of the most common solar indicator activity, the\ninternational monthly smoothed sunspot number. It is well known that the solar\ncycle is very difficult to predict due to the intrinsic complexity of the\nrelated time behaviour and to the lack of a succesful quantitative theoretical\nmodel of the Sun magnetic cycle. Starting from a previous recent work, we\nchecked the reliability and accuracy of a forecasting model based on concepts\nof nonlinear dynamical systems applied to experimental time series, such as\nembedding phase space, Lyapunov spectrum, chaotic behaviour. The model is based\non a local hypothesis of the behaviour on the embedding space, utilizing an\noptimal number k of neighbour vectors to predict the future evolution of the\ncurrent point with the set of characteristic parameters determined by several\nprevious parametric computations. The performances of this method suggest its\nvaluable insertion in the set of the so-called statistical-numerical prediction\ntechniques, like Fourier analyses, curve fitting, neural networks,\nclimatological, etc. The main task is to set up and to compare a promising\nnumerical nonlinear prediction technique, essentially based on an inverse\nproblem, with the most accurate predictive methods like the so-called\n\"precursor methods\" which appear now reasonably accurate in predicting \"long\nterm\" Sun activity, with particular reference to the \"solar\" precursor methods\nbased on a solar dynamo theory.",
"arxiv_id": "physics/9906035",
"authors": [
"Stefano Sello"
],
"categories": [
"physics.data-an",
"astro-ph",
"chao-dyn",
"nlin.CD"
],
"title": "Time Series Forecasting: A Nonlinear Dynamics Approach",
"url": "https://arxiv.org/abs/physics/9906035"
},
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