Comparison of prediction performances between Box–Jenkins and Kalman filter models––Case of annual and monthly sreamflows in Algeria

Abstract

The present study aims to investigate and to compare Box–Jenkins (BJ) and Kalman filter (KF) models to predict stream flows in northern Algeria. For this purpose, annual and monthly data of 10 hydrometric stations have been considered for application. The results with BJ models led to five Autoregressive and integrated moving average (ARIMA) models for the annual streamflows, with an overall mean explained variance at 63% level, whereas for the monthly flows they led to 10 Seasonal Autoregressive and integrated moving average (SARIMA) models, with an overall mean explained variance around 75%. On the other hand, KF methodology led to two on-line operations, where multisite optimal annual and monthly predictions are obtained. The KF and BJ predictive performances are then compared via some statistical parameters of their prediction error. For both of annual and monthly scales, it is found that KF model performs better in predictions. For example, the mean prediction error for KF is 16 times smaller than the BJ models, the corresponding standard deviation, minimum and maximum values are respectively, 5, 6, and 3 times smaller than the BJ alternatives. This denotes the superiority of KF for the prediction of stream flows in northern Algeria. In addition, an eventual tendency of KF to the underestimation has also been noticed from the prediction error standard deviation illustration.

Keywords:

• Stream flows
• ARIMA
• SARIMA
• Kalman filter
• Prediction error

Notes

Presented at the 7th International Conference on Water Resources in the Mediterranean Basin (WATMED7) 8–11 October 2014, Marrakesh, Morocco