Asymmetric Errors in Extrapolation: An Empirical Analysis of Causes

Extrapolation forecasts fall outside of estimated prediction intervals more often than would be expected on the basis of statistical theory. One reason is that while prediction intervals are generally assumed to be symmetric, forecast errors are often asymmetric. We examined three possible explanations for asymmetry in the forecasts for ratio-scaled data. First, because the series are bounded on the low side, but not on the high side, large errors are more likely to occur when the actual value exceeds the forecast. Second, because the forces acting on a series change over time, there is a tendency for the actuals to regress to the mean. As a result, actuals will tend to be in the direction opposite to the forecasted trend. Third, because extrapolation methods do not generally incorporate knowledge of causal forces when estimating the trend in a series, these forces tend to make the actuals depart from the forecasts in the direction of those forces. We tested for these three effects using 12,808 ex-ante extrapolation forecasts from 44 annual economic series and nine monthly series on personnel decisions. The effects, which are large and statistically significant, enable us to specify some of the conditions under which confidence intervals can be improved by permitting them to be symmetric.