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| Titel |
Local polynomial method for ensemble forecast of time series |
| VerfasserIn |
S. Regonda, B. Rajagopalan, U. Lall, M. Clark, Y.-I. Moon |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 12, no. 3 ; Nr. 12, no. 3 (2005-03-17), S.397-406 |
| Datensatznummer |
250010595
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| Publikation (Nr.) |
 copernicus.org/npg-12-397-2005.pdf |
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| Zusammenfassung |
| We present a nonparametric approach based on local polynomial regression for
ensemble forecast of time series. The state space is first reconstructed by
embedding the univariate time series of the response variable in a space of
dimension (D) with a delay time (τ). To obtain a forecast from a
given time point t, three steps are involved: (i) the current state of the
system is mapped on to the state space, known as the feature vector, (ii) a
small number (K=α*n, α=fraction (0,1] of the data,
n=data length) of neighbors (and their future evolution) to the feature
vector are identified in the state space, and (iii) a polynomial of order
p is fitted to the identified neighbors, which is then used for
prediction. A suite of parameter combinations (D, τ, α, p) is
selected based on an objective criterion, called the Generalized Cross
Validation (GCV). All of the selected parameter combinations are then used
to issue a T-step iterated forecast starting from the current time t, thus
generating an ensemble forecast which can be used to obtain the forecast
probability density function (PDF). The ensemble approach improves upon the
traditional method of providing a single mean forecast by providing the
forecast uncertainty. Further, for short noisy data it can provide better
forecasts. We demonstrate the utility of this approach on two synthetic
(Henon and Lorenz attractors) and two real data sets (Great Salt Lake
bi-weekly volume and NINO3 index). This framework can also be used to
forecast a vector of response variables based on a vector of predictors. |
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