Abstract
This study applied the time series analysis approach to model and predict univariate dissolved oxygen and temperature time series for four water quality assessment stations at Stillaguamish River located in the state of Washington. The order series method was applied to fulfill the normality assumption for modeling the univariate time series. Then, the AR(I)MA models were applied to study the stationary and nonstationary time series, the Auto-Regressive Fractionally Integrated Moving Average model was applied to study the time series with long memory. The results showed there existed three different structures for the univariate water quality time series at Stillaguamish River watershed. The identified time series model for each univariate water quality time series was found to be capable of predicting future values with reasonable accuracy. Overall, the time series modeling approach may be an efficient tool in assessment of the water quality in the river system.
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References
Abudu S, King JP, Bawazir AS (2011) Forecasting monthly streamflow of spring–summer runoff season in Rio Grande headwaters basin using stochastic hybrid modeling approach. J Hydrol Eng 16(4):384–390. doi:10.1061/(Asce)He.1943-5584.0000322
Ahmad S, Khan IH, Parida BP (2001) Performance of stochastic approaches for forecasting river water quality. Water Res 35(18):4261–4266. doi:10.1016/S0043-1354(01)00167-1
Akaike H (1974) New look at statistical model identification. IEEE Trans Autom Control 19:716–723. doi:10.1109/TAC.1974.1100705
Bhangu I, Whitfield PH (1997) Seasonal and long-term variations in water quality of the Skeena River at Usk, British Columbia. Water Res 31(9):2187–2194. doi:10.1016/S0043-1354(97)00063-8
Box GEP, Jenkins GM, Reinsel GC (2008) Time series analysis: forecasting and control. Wiley series in probability and statistics, 4th edn. Wiley, Hoboken
Chuang MD, Yu GH (2007) Order series method for forecasting non-Gaussian time series. J Forecast 26(4):239–250. doi:10.1002/For.1024
Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time-series with a unit root. J Am Stat Assoc 74(366):427–431. doi:10.2307/2286348
Durdu OF (2010) Stochastic approaches for time series forecasting of boron: a case study of Western Turkey. Environ Monit Assess 169(1–4):687–701. doi:10.1007/s10661-009-1208-y
Granger CWJ, Joyeux R (1980) An Introduction to long-memory time series models and fractional differencing. J Time Ser Anal 1(1):15–29. doi:10.1111/j.1467-9892.1980.tb00297.x
Granger CWJ, Newbold P (1976) Forecasting transformed series. J R Stat Soc B Methodol 38(2):189–203
Guo H, Qi M, Liu C, Wei J (2012) Stochastic simulation of daily river flows based on FARIMA model. Shuili Fadian Xuebao/J Hydroelectr Eng 31(6):22–27
Hipel KW, McLeod AI (1994) Time series modelling of water resources and environmental systems. Developments in water science, vol 45. Elsevier, Amsterdam
Hosking JRM (1981) Fractional differencing. Biometrika 68(1):165–176. doi:10.1093/biomet/68.1.165
Hurst HE (1951) Long term storage capacity of reservoirs. Trans Am Soc Civ Eng 116:770–779
Janacek GJ, Swift AL (1990) A class of models for non-normal time series. J Time Ser Anal 11(1):19–31. doi:10.1111/j.1467-9892.1990.tb00039.x
Jayawardena AW, Lai FZ (1989) Time-series analysis of water quality data in Pearl River, China. J Environ Eng ASCE 115(3):590–607
Kurunc A, Yurekli K, Cevik O (2005) Performance of two stochastic approaches for forecasting water quality and streamflow data from Yesilιrmak River, Turkey. Environ Model Softw 20(9):1195–1200. doi:10.1016/j.envsoft.2004.11.001
Kwiatkowski D, Phillips PCB, Schmidt P, Shin YC (1992) Testing the null hypothesis of stationarity against the alternative of a unit root—how sure are we that economic time series have a unit root. J Econom 54(1–3):159–178. doi:10.1016/0304-4076(92)90104-Y
Lawrance AJ, Lewis PAW (1985) Modeling and residual analysis of nonlinear autoregressive time-series in exponential variables. J R Stat Soc B Methodol 47(2):165–202
Li WK, McLeod AI (1988) ARMA modeling with non-Gaussian innovations. J Time Ser Anal 9(2):155–168. doi:10.1111/j.1467-9892.1988.tb00461.x
Mandelbrot B (1975) Limit theorems on the self-normalized range for weakly and strongly dependent processes. Z Wahrscheinlichkeitstheorie verw Gebiete 31(4):271–285. doi:10.1007/BF00532867
Mandelbrot B, Wallis JR (1968) Noah Joseph and operational hydrology. Water Resour Res 4(5):909–918. doi:10.1029/Wr004i005p00909
Mandelbrot B, Wallis JR (1969) Computer experiments with fractional Gaussian noises. 1. Averages and variances. Water Resour Res 5(1):228–241. doi:10.1029/Wr005i001p00228
Marivoet JL (1983) Real time water quality forecasting based on water quantity/quality relationship. IAHS-AISH pub 141 edn. International Association of Hydrological Sciences, Washington, DC, pp 395–404
McLeod AI, Li WK (1983) Diagnostic checking ARIMA time series models using squared-residuals autocorrelations. J Time Ser Anal 4:269–273. doi:10.1111/j.1467-9892.1983.tb00373.x
Montanari A, Rosso R, Taqqu MS (1997) Fractionally differenced ARIMA models applied to hydrologic time series: identification, estimation, and simulation. Water Resour Res 33(5):1035–1044. doi:10.1029/97wr00043
Mudelsee M (2007) Long memory of rivers from spatial aggregation. Water Resour Res 43(1). doi:10.1029/2006wr005721
Palma W (2007) Long-memory time series: theory and methods. Wiley series in probability and statistics. Wiley-Interscience, Hoboken
Worrall F, Burt TP (1999) A univariate model of river water nitrate time series. J Hydrol 214(1–4):74–90. doi:10.1016/S0022-1694(98)00249-2
Worrall F, Burt T (2004) Time series analysis of long-term river dissolved organic carbon records. Hydrol Process 18(5):893–911. doi:10.1002/Hyp.1321
Yu GH, Huang CC (2001) A distribution free plotting position. Stoch Environ Res Risk A 15(6):462–476. doi:10.1007/s004770100083
Yu GH, Chen HL, Wen WC (2002) A distribution-free method for forecasting non-Gaussian time series. Stoch Environ Res Risk A 16(2):101–111. doi:10.1007/s00477-002-0087-3
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Arya, F.K., Zhang, L. Time series analysis of water quality parameters at Stillaguamish River using order series method. Stoch Environ Res Risk Assess 29, 227–239 (2015). https://doi.org/10.1007/s00477-014-0907-2
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DOI: https://doi.org/10.1007/s00477-014-0907-2