Causal Forces: Structuring Knowledge for Time Series Extrapolation

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 longerrange 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.