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Causal Forces: Structuring Knowledge for Time-series Extrapolation


  • JS Armstrong

    (The Wharton School - University of Pennsylvania)

  • Fred Collopy

    (Case Western Reserve University)


This paper examines a strategy for structuring one type of domain knowledge for use in extrapolation. It does so by representing information about causality and using this domain knowledge to select and combine forecasts. We use five categories to express causal impacts upon trends: growth, decay, supporting, opposing, and regressing. An identification of causal forces aided in the determination of weights for combining extrapolation forecasts. These weights improved average ex ante forecast accuracy when tested on 104 annual economic and demographic time series. Gains in accuracy were greatest when (1) the causal forces were clearly specified and (2) stronger causal effects were expected, as in longer- range forecasts. One rule suggested by this analysis was: “Do not extrapolate trends if they are contrary to causal forces.” We tested this rule by comparing forecasts from a method that implicitly assumes supporting trends (Holt’s exponential smoothing) with forecasts from the random walk. Use of the rule improved accuracy for 20 series where the trends were contrary; the MdAPE (Median Absolute Percentage Error) was 18% less for the random walk on 20 one-year ahead forecasts and 40% less for 20 six-year-ahead forecasts. We then applied the rule to four other data sets. Here, the MdAPE for the random walk forecasts was 17% less than Holt’s error for 943 short-range forecasts and 43% less for 723 long-range forecasts. Our study suggests that the causal assumptions implicit in traditional extrapolation methods are inappropriate for many applications.

Suggested Citation

  • JS Armstrong & Fred Collopy, 2004. "Causal Forces: Structuring Knowledge for Time-series Extrapolation," General Economics and Teaching 0412003, EconWPA.
  • Handle: RePEc:wpa:wuwpgt:0412003
    Note: Type of Document - pdf; pages: 17

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    References listed on IDEAS

    1. Fred Collopy & J. Scott Armstrong, 1992. "Rule-Based Forecasting: Development and Validation of an Expert Systems Approach to Combining Time Series Extrapolations," Management Science, INFORMS, vol. 38(10), pages 1394-1414, October.
    2. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
    3. Armstrong, J. Scott & Collopy, Fred, 1992. "Error measures for generalizing about forecasting methods: Empirical comparisons," International Journal of Forecasting, Elsevier, vol. 8(1), pages 69-80, June.
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    Cited by:

    1. Armstrong, J. Scott & Collopy, Fred & Yokum, J. Thomas, 2005. "Decomposition by causal forces: a procedure for forecasting complex time series," International Journal of Forecasting, Elsevier, vol. 21(1), pages 25-36.
    2. JS Armstrong, 2004. "Forecasting for Environmental Decision Making," General Economics and Teaching 0412023, EconWPA.
    3. Fred Collopy & J. Scott Armstrong, 1992. "Rule-Based Forecasting: Development and Validation of an Expert Systems Approach to Combining Time Series Extrapolations," Management Science, INFORMS, vol. 38(10), pages 1394-1414, October.
    4. JS Armstrong & Fred Collopy, 2004. "Integration of Statistical Methods and Judgment for Time Series," General Economics and Teaching 0412024, EconWPA.
    5. J. S. Armstrong & R. Brodie, 2005. "Forecasting for Marketing," General Economics and Teaching 0502018, EconWPA.

    More about this item


    Causal forces Combining Contrary trends Damped trends Exponential smoothing Judgment Rule-based forecasting Selecting methods;

    JEL classification:

    • A - General Economics and Teaching

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