Evaluation of structural approaches to state space compared to classical in predicting precipitation time series ( Dez catchment)

Document Type : Research Paper


1 Assistant Professor, Department of Hydrology and Water Resources, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

2 Ph.D. Student in Water Resources, Department of Hydrology and Water Resources, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

3 Associate Professor, Department of Hydrology and Water Resources, Faculty of Water and Environmental Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

4 Associate Professor, Department of Statistics, Faculty of Mathematics and Computer Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran.


In this paper, a study on the use of precipitation prediction techniques with time series data was presented. Time series are an effective tool for understanding the nature of hydrological phenomena that with sufficient knowledge of them, future changes can be modeled and predicted. Various statistical models have been considered with the aim of reducing error and increasing forecast accuracy. Due to its structural and flexibility, state space makes it possible to model each of the components of a variable, including surface, seasonal and random separately. Therefore, by identifying the system in the way of modeling the studied variable, it is possible to control and minimize the estimation error, more intelligently compared to classical models. In the present study, in order to evaluate the modeling capability of state space and compare it with classical models, monthly preciptation modeling was performed in three rain gauge stations in Dez catchment, with four structural models of state space including Kalman filter, ETS exponential smoothing model and Modified exponential smoothing models were BATS and TBATS and the classic model was ARIMA. The results showed that at Sepiddasht Sezar station based on RMSE and MAE criteria of TBATS model and in Tangpanj Bakhtiyari station based on RMSE and MAE criterion of Kalman filter model and in Telezang station according to RMSE and MAE criterion of TBATS model the best models were chosen.


Main Subjects

  1. Asemota, O. J., Bamanga, M. A. & Alaribe, O. J. (2016). Modelling seasonal behavior of rainfall in northeast Nigeria. A state space approach. International Journal of Statistics and Applications, 6 (4), 203-222.
  2. Brath, A., Montanari, A. & Toth, E. (2002). Neural networks and nonparametric methods for improving real-time flood forecasting through conceptual hydrological models. Hydrology and Earth System Sciences Discussions, 6 (4), 627-639.     
  3. Box, G. & Jenkins, G. (1970). Time Series Analysis: Forecasting and Control. Holden-Day, San Francisco.           
  4. Durbin, J. & Koopman, S. J. (2012). Time Series Analysis by State Space Methods. Oxford University 343.
  5. Gabriel, A.C. (2021). A SARIMA and Adjusted SARIMA Models in a Seasonal Nonstationary Time Series; Evidence of Enugu Monthly Rainfall. European Journal of Mathematics and Statistics, 2 (1), 13-18.
  6. Harting, C. (2010). Rainfall as an Energy Source. Available from: http://large.stanford.edu/courses/2010/ ph240/harting2/.
  7. Hyndman RJ, Khandakar Y. (2008). Automatic time series forecasting: the forecast package for R. Journal of Statistical Software, 27 (3), 1-22.
  8. Hyndman, R. J., Koehler, A. B., Ord, J. K. & Snyder, R. D. (2008). Forecasting with Exponential Smoothing: The State Space Approach. Springer-Verlag, Berlin.
  9. Little, R. J. A. & Rubin, D. B. (1987). Statistical Analysis with Missing Data. John Wiley & Sons, New York, NY.
  10. Livera, Alysha M., Rob J. Hyndman, and Ralph D. Snyder. (2011). Forecasting time series with complex seasonal patterns usi ng exponential smoothing. Journal of the American Statistical Association, 106(496), 1513-1527.
  11. Masazade, E., Bakır, A. K. & Kırcı, P. (2019). A Kalman filter application for rainfall estimation using radar reflectivity. Turkish Journal of Electrical Engineering and Computer Sciences, 27, 1198-1212.
  12. Neslihanoglu, S., Ünal, E., Yozgatlıgil, C. (2021). Performance comparison of filtering methods on modelling and forecasting the total precipitation amount: a case study for Muğla in Turkey. Journal of Water and Climate Change, 12.4, 1071-1085.
  13. Naim, I., Mahara, T., Idrisi, A.R. (2018). Effective Short-Term Forecasting for Daily Time Series with Complex Seasonal Patterns, Procedia Computer Science 132, 1832-1841.
  14. Ribeiro, M. I. (2000). Introduction to Kalman Filtering: A Set of Two Lectures.
  15. Ribeiro, M. I. (2004). Kalman and Extended Kalman Filters: Concept, Derivation and Properties. Lisboa: Institute for Systems and Robotics.
  16. Soltani, S., Modarres, R. & Eslamian, S. S. (2007). The use of time series modelling for the determination of rainfall climates of Iran. International Journal of Climatology, 27, 819-829.
  17. Sun, M., Li, X. & Kim, G. (2019). Precipitation analysis and forecasting using singular spectrum analysis with artificial neural networks. Cluster Computing, 22, 12633-12640.
  18. Sadeghi, M., Asanjan, A. A., Faridzad, M., Nguyen, P., Hsu, K., Sorooshian, S. & Braithwaite, D. (2019). PERSIANN-CNN: Precipitation estimation from remotely sensed information using artificial neural networks–convolutional neural networks. Journal of Hydrometeorology, 20 (12), 2273-2289.
  19. Shumway, R. H., & Stoffer, D. S. (2016). State Space Models. In Time Series Analysis and Its Applications with R Examples. 287-295. New York: Springer.
  20. Soumik, R., Soumitra, S. D., Pradeep, M., & Khatib, A. M. G. A. (2021). Time Series SARIMA Modelling and Forecasting of Monthly Rainfall and Temperature in the South Asian Countries. Earth Systems and Environment, 5, 531-546.
  21. Toth, E., Brath, A. & Montanari, A. (2000). Comparison of shortterm rainfall prediction models for real-time flood forecasting. Journal of Hydrology, 239, 132-147.
  22. Tamatta, R. K., (2018). Time series forecasting of hospital Inpatients and Day case waiting list using ARIMA, TBATS and Neural Network Models.
  23. Willmott, C.J., & Matsuura, K. (2005). Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. CLIMATE RESEARCH Clim Res, 30, 79-82.
  24. Yozgatligil, C., Aslan, S., Iyigun, C. & Batmaz, I. (2013). Comparison of missing value imputation methods for Turkish meteorological time series data. Theoretical and Applied Climatology, 112, 143-167.
  25. Yu, C., Xu, C., Li, Y., Yao, S., Bai, Y., Li, J, Wang, L., Wu, W., & Wang, Y., (2021). Time Series Analysis and Forecasting of the Hand-Foot-Mouth Disease Morbidity in China Using an Advanced Exponential Smoothing State Space TBATS Model. Infection and Drug Resistance, 14, 2809-2821.
  26. Zulfi, M., Hasan, M. & Purnomo, K. D. (2018). The development rainfall forecasting using Kalman filter. Journal of Physics: Conference Series, 1008 (1), 012006.
  27. Zeng, Q., Li, D., Huang, G., Xia, J., Wang, X., Zhang, Y., Tang, W., & Zhou, H. (2016). Time series analysis of temporal trends in the pertussis incidence in Mainland China from 2005 to 2016. Scientific RepoRts, 6, 32367.