Decomposition by causal forces: a procedure for forecasting complex time series

Causal forces are a way of summarizing forecasters' expectations about what will happen to a time series in the future. Contrary to the common assumption for extrapolation, time series are not always subject to consistent forces that point in the same direction. Some are affected by conflicting causal forces; we refer to these as complex time series. It would seem that forecasting these time series would be easier if one could decompose the series to eliminate the effects of the conflicts. We hypothesized that a time series could be effectively decomposed when (1) uncertainty is high, (2) forecasters can use domain knowledge to decompose the problem such that different forces can be identified for two or more component series, (3) the causal forces imply trends that differ in direction, and (4) it is possible to obtain forecasts for each component that are more accurate than the forecast for the global series. Forecast accuracy for the components can be assessed by testing how well they can be forecast on early hold-out data. When such data are not available, historical variability may be an adequate substitute. We tested decomposition by causal forces on 12 complex annual time series for automobile accidents, airline accidents, personal computer sales, airline revenues, and cigarette production. The length of these series ranged from 16 years for airline revenues to 56 years for highway safety data. We made forecasts for one to ten horizons, obtaining 800 forecasts through successive updating. For nine series in which the conditions were completely or partially met, the forecast error (median absolute percentage error, MdAPE) was reduced by more than half. For three series in which the conditions were not met, decomposition by causal forces had little effect on accuracy.