Water Resources Management

, Volume 31, Issue 15, pp 4875–4890 | Cite as

Simulation of Nonstationary Spring Discharge Using Time Series Models

  • Y. Liu
  • B. Wang
  • H. Zhan
  • Y. Fan
  • Y. Zha
  • Y. Hao


We present a detailed analysis and comparison of two time series models, i.e., ARIMA and ARIMA-GARCH, to simulate the discharge of a karst spring (Niangziguan Springs (NS) complex) in the northern China. Statistical tests for the residuals are applied to examine the reasonability of the models. Statistically, both models are reasonably good to simulate the mean value of the discharge of the NS complex. The statistical test shows that the residual discharge data have conditional time-varying variance and volatility clustering, known as heteroscedasticity of the data. Calibration test shows that the ARIMA-GARCH model gives a varying confidence interval, which can more effectively capture the heteroscedasticity of the data, comparing with a constant confidence interval in the ARIMA model. In the validation and application process, we applied two approaches to simulate the discharge data: (1) fixed models, and (2) evolving models. The confidence interval width monotonically increases in both fixed models, and the fixed ARIMA-GARCH model has faster increasing confidence interval width than the fixed ARIMA model. This suggests that the fixed time series models are only suitable for short-term prediction. However, we found that this drawback can be compensated by updating the model once new data become available. Our evolving models show more reasonable confidence interval width for both models. In addition, the application shows that the ARIMA-GARCH model is very sensitive to the data fluctuation. We also found the evolving ARIMA-GARCH model was able to return to the narrow confidence interval width once the fluctuation diminished. Hence, we conclude that the ARIMA-GARCH model is more suitable for the sequences with strong heteroscedasticity.


ARIMA model ARIMA-GARCH model Heteroscedasticity Karst spring Niangziguan Springs 



This work is partially supported by the National Natural Science Foundation of China under the grant numbers 41402210, 41272245, 40972165, 40572150, 41471001 and 11601244 as well as the China Scholarship Council under the grant number 201508120014.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.College of Mathematical ScienceTianjin Normal UniversityTianjinChina
  2. 2.Geochemical and Environmental Research GroupTexas A&M UniversityCollege StationUSA
  3. 3.Department of Geology & GeophysicsTexas A&M UniversityCollege StationUSA
  4. 4.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanChina
  5. 5.Tianjin Key Laboratory of Water Resources and EnvironmentTianjin Normal UniversityTianjinPeople’s Republic of China

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