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Application of periodic autoregressive process to the modeling of the Garonne river flows


  • PEREAU Jean-Christophe
  • URSU Eugen


Accurate forecasting of river flows is one of the most important applications in hydrology, especially for the management of reservoir systems. To capture the seasonal variations in river flow statistics, this paper develops a robust modeling approach to identify and estimate periodic autoregressive (PAR) model in the presence of additive outliers. Since the least squares estimators are not robust in the presence of outliers, we suggest a robust estimation based on residual autocovariances. A genetic algorithm with Bayes information criterion is used to identify the optimal PAR model. The method is applied to average monthly and quarter-monthly flow data (1959-2010) for the Garonne river in the southwest of France. Results show that forecasts are better off in the robust model rather than the unrobust model. The accuracy of the forecasts is also improved when the model is specified in quarter-monthly flows, especially for the dry seasons.

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  • PEREAU Jean-Christophe & URSU Eugen, 2015. "Application of periodic autoregressive process to the modeling of the Garonne river flows," Cahiers du GREThA 2015-14, Groupe de Recherche en Economie Théorique et Appliquée(GREThA).
  • Handle: RePEc:grt:wpegrt:2015-14

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    References listed on IDEAS

    1. Jean-Christophe Pereau & E. Ursu, 2014. "Robust modelling of periodic vector autoregressive time series," Post-Print hal-01135627, HAL.
    2. Eugen Ursu & Pierre Duchesne, 2009. "On modelling and diagnostic checking of vector periodic autoregressive time series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 70-96, January.
    3. Paul L. Anderson & Mark M. Meerschaert & Kai Zhang, 2013. "Forecasting with prediction intervals for periodic autoregressive moving average models," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 187-193, March.
    4. Franses, Philip Hans & Paap, Richard, 2004. "Periodic Time Series Models," OUP Catalogue, Oxford University Press, number 9780199242030.
    5. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    6. Eugen Ursu & Kamil Feridun Turkman, 2012. "Periodic autoregressive model identification using genetic algorithms," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(3), pages 398-405, May.
    7. Bénédicte Vidaillet & V. D'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    8. Sarnaglia, A.J.Q. & Reisen, V.A. & Lévy-Leduc, C., 2010. "Robust estimation of periodic autoregressive processes in the presence of additive outliers," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2168-2183, October.
    9. Noakes, Donald J. & McLeod, A. Ian & Hipel, Keith W., 1985. "Forecasting monthly riverflow time series," International Journal of Forecasting, Elsevier, vol. 1(2), pages 179-190.
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    More about this item


    River flows analysis; periodic time series; robust estimation; genetic algorithms; Garonne river;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • Q25 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Water

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