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

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  • PEREAU Jean-Christophe
  • URSU Eugen

Abstract

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.

Suggested Citation

  • PEREAU Jean-Christophe & URSU Eugen, 2015. "Application of periodic autoregressive process to the modeling of the Garonne river flows," Cahiers du GREThA (2007-2019) 2015-14, Groupe de Recherche en Economie Théorique et Appliquée (GREThA).
  • Handle: RePEc:grt:wpegrt:2015-14
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    File URL: http://cahiersdugretha.u-bordeaux.fr/2015/2015-14.pdf
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    References listed on IDEAS

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    1. E. Ursu & Jean-Christophe Pereau, 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.
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    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. A. I. McLeod, 1994. "Diagnostic Checking Of Periodic Autoregression Models With Application," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(2), pages 221-233, March.
    8. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    9. 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.
    10. 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.
    11. Carlo Gaetan, 2000. "Subset ARMA Model Identification Using Genetic Algorithms," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(5), pages 559-570, September.
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    Cited by:

    1. Domenico Cucina & Manuel Rizzo & Eugen Ursu, 2018. "Identification of multiregime periodic autotregressive models by genetic algorithms," Post-Print hal-03187870, HAL.

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    More about this item

    Keywords

    River flows analysis; periodic time series; robust estimation; genetic algorithms; Garonne river;
    All these keywords.

    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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