Local polynomial method for ensemble forecast of time series

Regonda, Satish Kumar; Rajagopalan, Balaji; Lall, U.; Clark, Michael P.; Moon, Young‐Il

doi:10.5194/npg-12-397-2005

Cited by 49 publications

(46 citation statements)

References 78 publications

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“…In addition they also indicated (for the Lorenz system) that the optimal parameters found, change accordingly with the initial conditions used. In line with previous results by Regonda et al (2005), that indicated that the forecasts initiated from several contiguous starting points show a change in the local predictability.…”

Section: Introductionsupporting

confidence: 93%

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Embedding reconstruction methodology for short time series – application to large El Niño events

Astudillo¹,

Borotto²,

Río

2010

Nonlin. Processes Geophys.

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Abstract.We propose an alternative approach for the embedding space reconstruction method for short time series. An m-dimensional embedding space is reconstructed with a set of time delays including the relevant time scales characterizing the dynamical properties of the system. By using a maximal predictability criterion a d-dimensional subspace is selected with its associated set of time delays, in which a local nonlinear blind forecasting prediction performs the best reconstruction of a particular event of a time series. An locally unfolded d-dimensional embedding space is then obtained. The efficiency of the methodology, which is mathematically consistent with the fundamental definitions of the local nonlinear long time-scale predictability, was tested with a chaotic time series of the Lorenz system. When applied to the Southern Oscillation Index (SOI) (observational data associated with the El Niño-Southern Oscillation phenomena (ENSO)) an optimal set of embedding parameters exists, that allows constructing the main characteristics of the El Niño 1982Niño -1983Niño and 1997Niño -1998 events, directly from measurements up to 3 to 4 years in advance.

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Section: Introductionsupporting

confidence: 93%

“…It's precisely by using the prediction power that Regonda et al (2005) developed an approach based on local polynomial regression for ensemble forecasting of time series. It was applied to two kinds of time series: chaotic (Hennon and Lorenz) and observational data (Great Salt Lake and NIÑO3 Index).…”

Section: Introductionmentioning

confidence: 99%

Embedding reconstruction methodology for short time series – application to large El Niño events

Astudillo¹,

Borotto²,

Río

2010

Nonlin. Processes Geophys.

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“…(9), one obtains the equation of a straight line, whose slope is two times the bias of the prediction, 1 n n i=1 (x i − x i ), and whose intercept with the ξ =0.5 vertical line is the MAE of the forecast, a measure of the spread of the prediction errors. As expected, both the (negative) bias and the spread of the errors increase when the prediction horizon passes from 1 to 6 h. The median prediction is better than the best deterministic prediction for ξ <0.5, which is mainly due to the beneficial effect of taking an ensemble of predictions rather than a single one (see Georgakakos et al, 2004;Tamea et al, 2005;Regonda et al, 2005).…”

Section: Median Predictionmentioning

confidence: 72%

“…The verification tools described in the previous sections are applied to the probabilistic forecasts of a discharge time series, obtained with a prediction method developed by Tamea et al (2005) and Laio et al (2007), and based on local polynomial regression techniques (Farmer and Sidorowich, 1987;Fan and Gijbels, 1996;Cleveland and Loader, 1996;Porporato and Ridolfi, 1997;Regonda et al, 2005). We use this prediction method as a mean to exemplify the described verification techniques; we therefore refer to Tamea et al (2005) and Laio et al (2007) for a detailed description of the prediction method, which is here briefly introduced.…”

Section: Application and Discussionmentioning

confidence: 99%

Verification tools for probabilistic forecasts of continuous hydrological variables

Laio

Tamea

2007

Hydrol. Earth Syst. Sci.

301

209

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Abstract. In the present paper we describe some methods for verifying and evaluating probabilistic forecasts of hydrological variables. We propose an extension to continuous-valued variables of a verification method originated in the meteorological literature for the analysis of binary variables, and based on the use of a suitable cost-loss function to evaluate the quality of the forecasts. We find that this procedure is useful and reliable when it is complemented with other verification tools, borrowed from the economic literature, which are addressed to verify the statistical correctness of the probabilistic forecast. We illustrate our findings with a detailed application to the evaluation of probabilistic and deterministic forecasts of hourly discharge values.

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“…Since ENSO phenomenon also exhibits chaotic behaviour (Tziperman et al, 1997;Samelson and Tziperman, 2001), the model is set to have D = 5. In fact, on their attempt to find the best state-space parameters for predicting geophysical time series including ENSO, Regonda et al (2005) found that D ranges from 2 to 5 and the number of delay time in each embedded space ranges from 11 to 21. Even though their model was apparently able to correctly predict the time evolution of the phenomenon around the peaks in the years 1982, 1984, 1997, and 1999, its skill still needs to be compared with the other models using appropriate skill measures.…”

Section: Datamentioning

confidence: 99%

Complicated ENSO models do not significantly outperform very simple ENSO models

Halide

Ridd

2007

Intl Journal of Climatology

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An extremely simple univariate statistical model called 'IndOzy' was developed to predict El Niño-Southern Oscillation (ENSO) events. The model uses five delayed-time inputs of the Niño 3.4 sea surface temperature anomaly (SSTA) index to predict up to 12 months in advance. The prediction skill of the model was assessed using both short-and long-term indices and compared with other operational dynamical and statistical models. Using ENSO-CLIPER(climatology and persistence) as benchmark, only a few statistical models including IndOzy are considered skillful for short-range prediction. All models, however, do not differ significantly from the benchmark model at seasonal Lead-3-6. None of the models show any skill, even against a no-skill random forecast, for seasonal Lead-7. When using the Niño 3.4 SSTA index from 1856 to 2005, the ultra simple IndOzy shows a useful prediction up to 4 months lead, and is slightly less skillful than the best dynamical model LDEO5. That such a simple model such as IndOzy, which can be run in a few seconds on a standard office computer, can perform comparably with respect to the far more complicated models raises some philosophical questions about modelling extremely complicated systems such as ENSO. It seems evident that much of the complexity of many models does little to improve the accuracy of prediction. If larger and more complex models do not perform significantly better than an almost trivially simple model, then perhaps future models that use even larger data sets, and much greater computer power may not lead to significant improvements in both dynamical and statistical models. Investigating why simple models perform so well may help to point the way to improved models. For example, analysing dynamical models by successively stripping away their complexity can focus in on the most important parameters for a good prediction.

show abstract

Local polynomial method for ensemble forecast of time series

Cited by 49 publications

References 78 publications

Embedding reconstruction methodology for short time series – application to large El Niño events

Embedding reconstruction methodology for short time series – application to large El Niño events

Verification tools for probabilistic forecasts of continuous hydrological variables

Complicated ENSO models do not significantly outperform very simple ENSO models

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