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Use of Partial Cumulative Sum to Detect Trends and Change Periods for Nonlinear Time Series


  • Berlin Wu

    (Department of Mathematics, National Chengchi University, Taiwan)

  • Liyang Chen

    (Department of Mathematics, National Chengchi University, Taiwan)


Because the structural change of a time series from one pattern to another may not switch at once but rather experience a period of adjustment, conventional change point detection may be inappropriate under some circumstances. Furthermore, changes in time series often occur gradually so that there is a certain amount of fuzziness in the change point. For this, considerable research has focused on the theory of change period detection for improved model performance. However, a change period in some small time interval may appear to be negligible noise in a larger time interval. In this paper, we propose an approach to detect trends and change periods with fuzzy statistics using partial cumulative sums. By controlling the parameters, we can filter the noises and discover suitable change periods. Having discovered the change periods, we can proceed to identify the trends in the time series. We use simulations to test our approach. Our results show that the performance of our approach is satisfactory.

Suggested Citation

  • Berlin Wu & Liyang Chen, 2006. "Use of Partial Cumulative Sum to Detect Trends and Change Periods for Nonlinear Time Series," Journal of Economics and Management, College of Business, Feng Chia University, Taiwan, vol. 2(2), pages 123-145, July.
  • Handle: RePEc:jec:journl:v:2:y:2006:i:2:p:123-145

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    References listed on IDEAS

    1. Van Cutsem, Bernard & Gath, Isak, 1993. "Detection of outliers and robust estimation using fuzzy clustering," Computational Statistics & Data Analysis, Elsevier, vol. 15(1), pages 47-61, January.
    2. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
    3. Balke, Nathan S, 1993. "Detecting Level Shifts in Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 81-92, January.
    4. Ploberger, Werner & Kramer, Walter & Kontrus, Karl, 1989. "A new test for structural stability in the linear regression model," Journal of Econometrics, Elsevier, vol. 40(2), pages 307-318, February.
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    More about this item


    fuzzy time series; change periods; partial cumulative sums; trend; noise;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C42 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Survey Methods


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