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The influence of rainfall time series fractality on forecasting models’ efficiency

Abstract

Forecasting rainfall time series is of great significance for hydrologists and geoscientists. Thus, this study represents a contribution to understanding the impact of the fractal time series variety on forecasting model performance. Multiple fractal series were generated via p-model and used for modeling. Subsequently, the forecasting was delivered based on existing observed monthly rainfall data (three stations in the UK, from 1865 to 2002) through five forecasting models. Finally, the association between series fractality and models’ performance was examined. The results indicated that the forecasting based on the mono-fractal series resulted in the most reliable results (R2 = 1 and RMSE less than 0.02). In the case of multifractal series, modeling based on series with the right side of the asymmetric curve of the multifractal spectrum presented series with the lowest RMSE (0.96) and highest R2 (0.99) (desirable performance). In contrast, the forecasting based on series with the left side of the asymmetric curve of the multifractal spectrum suggested the most unreliable outcomes (R2 range [− 0.0007 ~ 0.988] and RMSE range [0.8526 ~ 39.3]). The forecasting based on the symmetric curve of the multifractal spectrum series delivered regular performance. Accordingly, high and low errors are expected from forecasting based on the time series with a left-skewed multifractal spectrum and right-skewed multifractal spectrum (and mono-fractal time series), respectively. Hybrid models were the best options for forecasting mono-fractal and multifractal time series with right side asymmetric and symmetric multifractal spectrum curves. The ARIMA model was suitable to predict multifractal time series with left side asymmetric multifractal spectrum curves.

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Data availability

Some or all data and models that support the findings of this study are available from the corresponding author upon reasonable request. The corresponding author is ready to share data with other researchers who send their requests to this Email address: farhang.rahmani@miau.ac.ir.

Code availability

Codes that support the findings of this study are available from the corresponding author upon reasonable request. The corresponding author is ready to share data with other researchers who send their requests to this Email address: farhang.rahmani@miau.ac.ir.

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Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

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Contributions

Conceptualization: FR and MHF; Methodology: FR; Formal analysis and investigation: FR; Writing-original draft preparation: FR; Writing-review and editing: FR and MHF; Supervision: MHF.

Corresponding author

Correspondence to Farhang Rahmani.

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Authors have no conflict of interest to declare.

Additional information

Edited by Prof. Jarosław Napiórkowski (ASSOCIATE EDITOR) / Dr. Michael Nones (CO-EDITOR-IN-CHIEF).

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Rahmani, F., Fattahi, M.H. The influence of rainfall time series fractality on forecasting models’ efficiency. Acta Geophys. 70, 1349–1361 (2022). https://doi.org/10.1007/s11600-022-00776-w

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  • DOI: https://doi.org/10.1007/s11600-022-00776-w

Keywords

  • ANFIS
  • Autoregressive integrated moving average (ARIMA)
  • Radial basis function (RBF)
  • Multifractal detrended fluctuation analysis (MF-DFA)
  • Hurst exponent
  • Multifractal spectrum