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  Wavelet entropy-based evaluation of intrinsic predictability of time series

Guntu, R. K., Yeditha, P. K., Rathinasamy, M., Perc, M., Marwan, N., Kurths, J., Agarwal, A. (2020): Wavelet entropy-based evaluation of intrinsic predictability of time series. - Chaos, 30, 3, 033117.
https://doi.org/10.1063/1.5145005

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 Creators:
Guntu, R. K.1, Author
Yeditha, P. K.1, Author
Rathinasamy, M.1, Author
Perc, M.1, Author
Marwan, Norbert2, Author              
Kurths, Jürgen2, Author              
Agarwal, Ankit1, Author
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1External Organizations, ou_persistent22              
2Potsdam Institute for Climate Impact Research, ou_persistent13              

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 Abstract: 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. This study explores the application of wavelet energy function and entropy for possible quantification of intrinsic predictability of a time series in terms of the Wavelet Energy Entropy Measure. One of the advantages of the proposed measure is that it considers the dynamics of the process spread across different time scales, which other similarity measures of predictability have not considered explicitly. Furthermore, the proposed measure is linked to forecasting performances. The proposed measure can be used for estimating the intrinsic predictability of a time series, understanding the capability of models in capturing the underlying system, and among others

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 Dates: 2020
 Publication Status: Finally published
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1063/1.5145005
PIKDOMAIN: RD4 - Complexity Science
eDoc: 8985
MDB-ID: No data to archive
Research topic keyword: Nonlinear Dynamics
Research topic keyword: Extremes
Research topic keyword: Weather
Model / method: Nonlinear Data Analysis
Regional keyword: Asia
Organisational keyword: RD4 - Complexity Science
Working Group: Development of advanced time series analysis techniques
 Degree: -

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Title: Chaos
Source Genre: Journal, SCI, Scopus, p3
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Pages: - Volume / Issue: 30 (3) Sequence Number: 033117 Start / End Page: - Identifier: CoNE: https://publications.pik-potsdam.de/cone/journals/resource/180808
Publisher: American Institute of Physics (AIP)