Excursion Depth and the Limits of Boosted Trees on a Drifting Target: The S&P 500 Level as a Stress Test Asset

Gradient-boosted tree ensembles are widely fitted to economic and financial series that trend, yet a regression tree predicts an average of its training targets and cannot follow a target that rises above its training range. This study measures how much of the forecast error of such ensembles that restriction accounts for, and what the available correction costs. It is a diagnostic study rather than a forecasting one: the log level of the S&P 500 is used as a stress test asset because it drifts steadily beyond any training window. The log index is forecast from five United States macroeconomic indicators lagged one month, over January 2003 to January 2026, at seven rolling origins under two training window rules. We define excursion depth, the distance of a test target beyond the training target range, computed in a backtest from the targets alone. Four boosting implementations are compared with a ridge regression, linear leaf boosting, a linear trend, a random walk with drift, and anchored residual boosting (ARB), which fits the ensemble to the residual of a ridge anchor. The error gap between unanchored and anchored boosting widens with excursion depth, from 0.0065 to 0.1498 in root mean squared error between the shallowest and deepest thirds of beyond-range months, and it tracks depth and not forecast horizon when both are controlled. Diebold–Mariano tests reject equal accuracy for one of the four families and not for their average. Ridge alone is ahead of three of the four anchored ensembles under the expanding origin, while linear leaf boosting leaves the range without the same gain, so a linear term fitted to the whole window is what matters. Inside the training range, unanchored boosting remains more accurate for three of the four families. The random walk with drift is the most accurate forecast of the level, and on monthly log returns no model improves on the historical mean. The results identify the conditions under which boosted trees are an unsuitable estimator for a level target, and excursion depth locates those conditions in a backtest before any model is fitted.