Comparison of stochastic and machine learning methods for multi-step ahead forecasting of hydrological processes

  • Georgia PapacharalampousEmail author
  • Hristos Tyralis
  • Demetris Koutsoyiannis
Original Paper


Research within the field of hydrology often focuses on the statistical problem of comparing stochastic to machine learning (ML) forecasting methods. The performed comparisons are based on case studies, while a study providing large-scale results on the subject is missing. Herein, we compare 11 stochastic and 9 ML methods regarding their multi-step ahead forecasting properties by conducting 12 extensive computational experiments based on simulations. Each of these experiments uses 2000 time series generated by linear stationary stochastic processes. We conduct each simulation experiment twice; the first time using time series of 100 values and the second time using time series of 300 values. Additionally, we conduct a real-world experiment using 405 mean annual river discharge time series of 100 values. We quantify the forecasting performance of the methods using 18 metrics. The results indicate that stochastic and ML methods may produce equally useful forecasts.


No free lunch theorem Random forests River discharge Stochastic hydrology Support vector machines Time series 



We thank the Associate Editor and two reviewers for their useful suggestions. Part of the Discussion section, in particular the comments on the no free lunch theorem and the use of exogenous variables, has been inspired by the “Energy Forecasting” blog (

Author contributions

HT conceived the idea of comparing stochastic and machine learning methods in hydrological univariate time series forecasting using large datasets. GP designed the experiments, performed the computations and wrote the manuscript under the supervision of HT and DK during her MSc thesis. All authors have discussed the results and edited the manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Water Resources and Environmental Engineering, School of Civil EngineeringNational Technical University of AthensZografouGreece
  2. 2.Air Force Support Command, Hellenic Air ForceElefsina Air BaseElefsinaGreece

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