Application of SARIMA model to forecasting monthly flows in Waterval River, South Africa

• Autorzy: Tadesse K. B. , Dinka M. O.

Identyfikatory

DOI

10.1515/jwld-2017-0088

Warianty tytułu

PL

Zastosowanie modelu SARIMA do prognozowania miesięcznych przepływów rzeki Waterval w Południowej Afryce

• Języki publikacji: EN

Abstrakty

EN

Knowledge of future river flow information is fundamental for development and management of a river system. In this study, Waterval River flow was forecasted by SARIMA model using GRETL statistical software. Mean monthly flows from 1960 to 2016 were used for modelling and forecasting. Different unit root and Mann–Kendall trend analysis proved the stationarity of the observed flow time series. Based on seasonally differenced correlogram characteristics, different SARIMA models were evaluated; their parameters were optimized, and diagnostic check up of forecasts was made using white noise and heteroscedasticity tests. Finally, based on minimum Akaike Information (AI) and Hannan–Quinn (HQ) criteria, SARIMA (3, 0, 2) x (3, 1, 3)12 model was selected for Waterval River flow forecasting. Comparison of forecast performance of SARIMA models with that of computational intelligent forecasting techniques was recommended for future study.

PL

Znajomość przyszłego przepływu wody w rzece jest istotna dla rozwoju i zarządzania w systemie rzecznym. W badaniach prezentowanych w niniejszym artykule prognozowano przepływ w rzece Waterval w Republice Południowej Afryki, używając modelu SARIMA i programu statystycznego GRETL. Do modelowania i budowania prognoz wykorzystano średnie miesięczne przepływy z lat 1960–2016. Różne pierwiastki jednostkowe i analiza trendu Manna–Kendalla dowiodły stacjonarności obserwowanych szeregów czasowych przepływu. Na podstawie sezonowo zróżnicowanych charakterystyk korelogramu oceniono różne modele SARIMA zoptymalizowano ich parametry i wykonano diagnostyczne sprawdzenie prognoz za pomocą białego szumu i testów heteroscedastyczności. Na podstawie minimum AI i kryteriów Hannana–Quinna (HQ), wybrano model SARIMA (3, 0, 2) x (3, 1, 3)12 do prognozowania przepływu w rzece Waterval. W dalszych badaniach proponuje się porównanie prognozowania za pomocą modeli SARIMA i technik komputerowych.

Słowa kluczowe

EN

heteroscedasticity; stationarity test; trend analysis; validation; white noise

PL

analiza trendu; biały szum; heteroscedastyczność; ocena; test stacjonarności

• Wydawca: Wydawnictwo ITP
• Czasopismo: Journal of Water and Land Development
• Rocznik: 2017
• Tom: no. 35
• Strony: 229--236
• Opis fizyczny: Bibliogr. 39 poz., rys., tab.

Twórcy

autor

Tadesse K. B.

• University of Johannesburg, Faculty of Engineering and the Built Environment, Department of Civil Engineering Science, Auckland Park Campus Kingsway, 524 Johannesburg, South Africa
• Debre Markos University, College of Agriculture and Natural Resources, Department of Natural Resources Management, 269 Debre Markos, Ethiopia

autor

Dinka M. O.

• University of Johannesburg, Faculty of Engineering and the Built Environment, Department of Civil Engineering Science, Johannesburg, South Africa

Bibliografia

• ADHIKARY S.K, RAHMAN M.D.M., GUPTA A.D. 2012. A stochastic modelling technique for predicting groundwater table fluctuations with Time Series Analysis. International Journal of Applied Sciences and Engineering Research. Vol. 1. Iss. 2 p. 238–249.
• ADNAN R.M., YUAN X., KISI O., ANAM R. 2017. Improving accuracy of river flow forecasting using LSSVR with gravitational search algorithm. Advances in Meteorology. Vol. 2017. Art. ID 2391621 pp. 23. DOI 10.1155/2017/2391621.
• AKAIKE H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control. Vol. 19. Iss. 6 p. 716–723.
• ALI S.M. 2013. Time series analysis of Baghdad rainfall using ARIMA method. Iraqi Journal of Science. Vol. 54. Iss. 4 p. 1136–1142.
• BARZEGAR R., MOGHADDAM A.A., ADAMOWSKI J., OZGA-ZIELINSKI B. 2017. Multi-step water quality forecasting using a boosting ensemble multi-wavelet extreme learning machine model. Stochastic Environmental Research and Risk Assessment p. 1–15.
• BELAYNEH A., ADAMOWSKI J. 2013. Drought forecasting using new machine learning methods/Prognozowanie suszy z wykorzystaniem automatycznych samouczących się metod. Journal of Water and Land Development. No. 18 p. 3–12.
• BOX G.E.P, JENKINS G.M., REINSEL G.C. 2008. Time series analysis, forecasting and control. 4th ed. New Jersey. John Wiley and Sons, Inc. ISBN 978-0470272848 pp. 784.
• BROCKWELL P.J., DAVIS R.A. 2002. Introduction to time series and forecasting. 2nd ed. New York. Springer-Verlag. ISBN 978-1475777505 pp. 437.
• CHANG X., GAO M., WANG Y., HOU X. 2012. Seasonal autoregressive integrated moving average model for precipitation of time series. Journal of Mathematics and Statistics. Vol. 8. Iss. 4 p. 500–505.
• COTTRELL A., LUCCHETTI R.J. 2017. Gretl user’s guide. Gnu Regression, Econometrics and Time-series Library. [online]. [Access date 11.03.2017]. Available at: http://ricardo.ecn.wfu.edu/pub/gretl/manual/en/gretlguide-a4.pdf
• CRYER J.D., CHAN K.S. 2008. Time series analysis: With applications in R. New York. Springer-Verlag. ISBN 978-0-387-75958-6 pp. 491
• DICKEY D.A., FULLER W.A. 1979. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association. Vol. 74 Iss. 366 p. 427–431.
• DURBIN J., WATSON G.S. 1951. Testing for serial correlation in least squares regression, II. Biometrika. Vol. 38. Iss. 1–2 p. 159–179.
• GAUTAM R., SINHA A.K. 2016. Time series analysis of reference crop evapotranspiration for Bokaro District, Jharkhand, India. Journal of Water and Land Development. No. 30 p. 51–56. DOI 10.1515/jwld-2016-0021.
• GERRETSADIKAN A., SHARMA M.K. 2011. Modelling and forecasting of rainfall data of Mekele for Tigray region (Ethiopia). Statistics and Applications. Vol. 9. Iss. 1–2 p. 31–53.
• HAMILTON J.D. 1994. Time series analysis. Princeton. Princeton University Press. ISBN 978-0691042893 pp. 799.
• HANNAN E.J., QUINN B.G. 1979. The determination of the order of an autoregression. Journal of the Royal Statistical Society. Vol. 41 p. 190–195.
• JANHABI M., JHA R. 2013. Time-series analysis of monthly rainfall data for the Mahanadi River Basin, India. Sciences in Cold and Arid Regions. Vol. 5. Iss. 1 p. 73–84.
• KENDALL M. 1975. Multivariate analysis. London. Charles Griffin & Company. ISBN 978-0852642344 pp. 218.
• KOMORNÍKOVÁ M.A., SZOLGAY J., SVETLÍKOVÁ D.A., SZÖKEOVÁ D., JURČÁK S. 2008. A hybrid modelling framework for forecasting monthly reservoir inflows. Journal of Hydrology and Hydromechanics. Vol. 1. Iss. 3 p. 145–62.
• KWIATKOWSKI D., PHILLIPS P.C.B., SCHMIDT P., SHIN Y. 1992. Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics. Vol. 54 p. 159–178.
• LJUNG G.M., BOX G.E.P. 1978. On a measure of a lack of fit in time series models. Biometrika. Vol. 65. Iss. 2 p. 297–303.
• MOEENI H., HOSSIEN B., FATEMI S.E. 2017. Stochastic model stationarization by eliminating the periodic term and its effect on time series prediction. Journal of Hydrology. Vol. 547 p. 348–364.
• NAILL P.E., MOMANI M. 2009. Time series analysis model for rainfall data in Jordan: A case study for using time series analysis. American Journal of Environmental Sciences. Vol. 5 p. 599–600.
• OSARUMWENSE O.I. 2013. Applicability of Box Jenkins SARIMA model in rainfall forecasting: A case study of Port-Harcourt south Nigeria. Canadian Journal on Computing in Mathematics, Natural Sciences, Engineering and Medicine. Vol. 4. Iss. 1 p. 1–4.
• PAPALASKARIS T., THEOLOGOS P., PANTRAKIS A. 2016. Stochastic monthly rainfall time series analysis, modeling and forecasting in Kavala City, Greece, North-Eastern Mediterranean Basin. International Conference on Efficient and Sustainable Water Systems Management toward worth Living Development, 2nd EWaS 2016. Proceedia Engineering. Vol. 162 p. 254–263.
• PEKÁROVÁ P., ONDERKA M., PEKÁR J., RONČÁK P., MIKLÁNEK P. 2009. Prediction of water quality in the Danube River under extreme hydrological and temperature conditions. Journal of Hydrology and Hydromechanics. Vol. 1. Iss. 57 p. 3–15.
• PHILLIPS P.C.B., PERRON P. 1988. Testing for a unit root in time series regression. Biometrika. Vol. 75. Iss. 2 p. 335–346.
• SALAS J.D., DELLEUR J.W., YEVJEVICH V., LANE W.L. 1980. Applied modelling of hydrologic time series. Littleton, Colorado. Water Resource Publications pp. 484.
• SCHWARZ G.E. 1978. Estimating the dimension of a model. Annals of Statistics. Vol. 6. Iss. 2 p. 461–464.
• SINGH M., SINGH R., SHINDE V. 2012. Application of software packages for monthly stream flow forecasting of Kangsabati River in India. International Journal of Computer Applications. Vol. 20. Iss. 3 p. 7–14.
• TARIQ M.M., ABBASABD A.I. 2016. Time series analysis of Nyala rainfall using ARIMA method. SUST Journal of Engineering and Computer Science. Vol. 17. Iss. 1 p. 5–11.
• TEYMOURI M., FATHZADEH A. 2015. Stochastic modeling of monthly river flow forecasting (Case study: Atrak River Basin, Iran). Journal of Selçuk University Natural and Applied Science. Vol. 4. Iss. 2 p. 38–48.
• TIWARI M., ADAMOWSKI J., ADAMOWSKI K. 2016. Water demand forecasting using extreme learning machines. Journal of Water and Land Development. No. 28 p. 37–52. DOI 10.1515/jwld-2016-0004.
• VAHDAT S.F., SARRAF A., SHAMSNIA A., SHAHIDI N. 2011. Prediction of monthly mean Inflow to Dez Dam reservoir using time series models (Box-Jenkins). International Conference on Environment and Industrial Innovation IPCBEE. 12 (2001). Singapore. IACSIT Press p. 162–166.
• VALIPOUR M. 2015. Long-term runoff study using SARIMA and ARIMA models in the United States. Meteorological Applications. Vol. 22. Iss. 3 p. 592–598.
• WANG J., DU Y.H., ZHANG X.T. 2008. Theory and application with seasonal time series. 1st ed. Nankai. Nankai University Press.
• YADAV B., CH S., MATHUR S., ADAMOWSKI J. 2017. Assessing the suitability of extreme learning machines (ELM) for groundwater level prediction. Journal of Water and Land Development. No. 32 p. 103–112. DOI 10.1515/jwld-2017-0012.
• YANG T., ASANJAN A.A., WELLES E., GAO X., SOROOSHIAN S., LIU X. 2017. Developing reservoir monthly inflow forecasts using artificial intelligence and climate phenomenon information. Water Resources Research. Vol. 53. Iss. 4 p. 2786–2812.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).