Impact of complexity on daily and multi-step forecasting of streamflow with chaotic, stochastic, and black-box models

Research output: Contribution to journalArticle


Despite significant research advances achieved during the last decades, seemingly inconsistent forecasting results related to stochastic, chaotic, and black-box approaches have been reported. Herein, we attempt to address the entropy/complexity resulting from hydrological and climatological conditions. Accordingly, mutual information function, correlation dimension, averaged false nearest neighbor with E1 and E2 quantities, and complexity analysis that uses sample entropy coupled with iterative amplitude adjusted Fourier transform were employed as nonlinear deterministic identification tools. We investigated forecasting of daily streamflow for three climatologically different Swedish rivers, Helge, Ljusnan, and Kalix Rivers using self-exciting threshold autoregressive (SETAR), k-nearest neighbor (k-nn), and artificial neural networks (ANN). The results suggest that the streamflow in these rivers during the 1957–2012 period exhibited dynamics from low to high complexity. Specifically, (1) lower complexity lead to higher predictability at all lead-times and the models’ worst performances were obtained for the most complex streamflow (Ljusnan River), (2) ANN was the best model for 1-day ahead forecasting independent of complexity, (3) SETAR was the best model for 7-day ahead forecasting by means of performance indices, especially for less complexity, (4) the largest error propagation was obtained with the k-nn and ANN and thus these models should be carefully used beyond 2-day forecasting, and (5) higher number input variables except for the dominant variables made insignificant impact on forecasting performances for ANN and k-nn models.


External organisations
  • Süleyman Demirel University
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Water Engineering
  • Probability Theory and Statistics


  • Artificial neural networks, Averaged false nearest neighbor (AFN), Correlation dimension, k-Nearest neighbor, Sample entropy, Self-exciting threshold autoregressive
Original languageEnglish
Pages (from-to)661-682
JournalStochastic Environmental Research and Risk Assessment
Issue number3
Early online date2016 Mar 15
Publication statusPublished - 2017 Mar
Publication categoryResearch