Intrinsic predictability is imperative to quantify inherent information contained in a time series and assists in evaluating the performance of different forecasting methods to get the best possible prediction. Model forecasting performance is the measure of the probability of success. Nevertheless, model performance or the model does not provide understanding for improvement in prediction. Intuitively, intrinsic predictability delivers the highest level of predictability for a time series and informative in unfolding whether the system is unpredictable or the chosen model is a poor choice. We introduce a novel measure, the Wavelet Entropy Energy Measure (WEEM), based on wavelet transformation and information entropy for quantification of intrinsic predictability of time series. To investigate the efficiency and reliability of the proposed measure, model forecast performance was evaluated via a wavelet networks approach. The proposed measure uses the wavelet energy distribution of a time series at different scales and compares it with the wavelet energy distribution of white noise to quantify a time series as deterministic or random. We test the WEEM using a wide variety of time series ranging from deterministic, non-stationary, and ones contaminated with white noise with different noise-signal ratios. Furthermore, a relationship is developed between the WEEM and Nash–Sutcliffe Efficiency, one of the widely known measures of forecast performance. The reliability of WEEM is demonstrated by exploring the relationship to logistic map and real-world data.
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March 2020
Research Article|
March 09 2020
Wavelet entropy-based evaluation of intrinsic predictability of time series
Special Collection:
Rare Events in Complex Systems: Understanding and Prediction
Ravi Kumar Guntu
;
Ravi Kumar Guntu
1
Department of Hydrology, Indian Institute of Technology Roorkee
, Roorkee 247667, India
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Pavan Kumar Yeditha
;
Pavan Kumar Yeditha
2
Department of Civil Engineering, MVGR College of Engineering
, Vizianagaram 535005, India
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Maheswaran Rathinasamy
;
Maheswaran Rathinasamy
2
Department of Civil Engineering, MVGR College of Engineering
, Vizianagaram 535005, India
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Matjaž Perc
;
Matjaž Perc
3
Faculty of Natural Sciences and Mathematics, University of Maribor
, 2000 Maribor, Slovenia
4
Center for Applied Mathematics and Theoretical Physics, University of Maribor
, 2000 Maribor, Slovenia
5
Department of Medical Research, China Medical University Hospital, China Medical University
, Taichung 40402, Taiwan
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Norbert Marwan
;
Norbert Marwan
6
Potsdam Institute for Climate Impact Research
, Telegrafenberg, 14412 Potsdam, Germany
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Jürgen Kurths;
Jürgen Kurths
6
Potsdam Institute for Climate Impact Research
, Telegrafenberg, 14412 Potsdam, Germany
7
Institute of Physics, Humboldt University
, 12489 Berlin, Germany
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Ankit Agarwal
Ankit Agarwal
a)
1
Department of Hydrology, Indian Institute of Technology Roorkee
, Roorkee 247667, India
a)Author to whom correspondence should be addressed: agarwal.10891.ankit@gmail.com
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a)Author to whom correspondence should be addressed: agarwal.10891.ankit@gmail.com
Note: This article is part of the Focus Issue, Rare Events in Complex Systems: Understanding and Prediciton.
Chaos 30, 033117 (2020)
Article history
Received:
January 13 2020
Accepted:
February 17 2020
Citation
Ravi Kumar Guntu, Pavan Kumar Yeditha, Maheswaran Rathinasamy, Matjaž Perc, Norbert Marwan, Jürgen Kurths, Ankit Agarwal; Wavelet entropy-based evaluation of intrinsic predictability of time series. Chaos 1 March 2020; 30 (3): 033117. https://doi.org/10.1063/1.5145005
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