Journal of Zhejiang University-SCIENCE A

, Volume 11, Issue 9, pp 677–682 | Cite as

Utility water supply forecast via a GM (1,1) weighted Markov chain

  • Yi-mei Tian
  • Hai-liang Shen
  • Li Zhang
  • Xiang-rui Lv


This paper describes the procedure of using the GM (1,1) weighted Markov chain (GMWMC) to forecast the utility water supply, a quantity that usually has significant temporal variability. The GMWMC is formulated into five steps: (1) use GM (1,1) to fit the trend of the data, and obtain the relative error of the fitted values; (2) divide the relative error into ‘state’ data based on pre-set intervals; (3) calibrate the weighted Markov chain model: herein the parameters are the pre-set interval and the step of transition matrix (TM); (4) by using auto-correlation coefficient as the weight, the Markov chain provides the prediction interval. Then the mid-value of the interval is selected as the relative error for the data. Upon combining the data and its relative error, the predicted magnitude in a specific time period is obtained; and, (5) validate the model. Commonly, static intervals are used in both model calibration and validation stages, usually causing large errors. Thus, a dynamic adjustment interval (DAI) is proposed for a better performance. The proposed procedure is described and demonstrated through a case study, which shows that the DAI can usually achieve a better performance than the static interval, and the best TM may exist for certain data.

Key words

Dynamic adjustment interval (DAI) Forecast GM (1,1) Markov chain Water supply 

CLC number



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Copyright information

© Zhejiang University and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yi-mei Tian
    • 1
  • Hai-liang Shen
    • 2
  • Li Zhang
    • 1
  • Xiang-rui Lv
    • 1
  1. 1.College of Environmental Science & EngineeringTianjin UniversityTianjinChina
  2. 2.School of EngineeringUniversity of GuelphGuelphCanada

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