Selecting predictors one at a time to separate signals from correlated proxies

Economic datasets often contain many indicators describing overlapping activity: housing permits, housing starts, monetary aggregates and financial conditions. Selecting a compact regression from these candidates is difficult because a variable can track the outcome without contributing independently once other predictors are included.

In a preprint revised on November 3, 2026, George Kapetanios, Vasilis Sarafidis and Alexia Ventouri propose Boosting with Multiple Testing, or BMT. They combine theoretical results, simulations and two U.S. applications to investigate whether sequential testing can distinguish regression signals from correlated proxies. The supplied source is a preprint, not evidence of peer-reviewed validation.

Why proxies complicate selection

The paper defines a true signal as a variable with a nonzero coefficient in the specified data-generating regression. A proxy has a zero coefficient but is correlated with signals, allowing it to appear informative when considered separately.

This distinction is model-dependent. Selecting a predictor does not establish that it causes the outcome, and recovering nonzero regression coefficients does not by itself identify policy effects.

BMT starts with any compulsory controls chosen in advance. It tests each candidate conditional on those controls and selects only the variable with the largest absolute conventional least-squares t statistic, provided that statistic exceeds a multiple-testing threshold. It then retests the remaining candidates conditional on the enlarged model.

The process stops when none passes. Even the first admission requires passing the threshold, which depends on the number of remaining candidates and investigator-chosen calibration parameters.

The intuition is straightforward: once a genuine signal enters, a related proxy may lose its apparent contribution. But ordinary BMT never removes an admitted variable. A proxy entering early can therefore remain in the final model.

What the guarantees require

The authors establish exact recovery with probability approaching one as sample size and the candidate pool grow, under stated conditions. These include having every true signal among the candidates, sufficiently detectable effects, restrictions on regression-score dependence and distributional tails, and covariance bounds that exclude relevant near-singular designs.

With multiple signals, an additional ordering condition matters: after conditioning on any incomplete subset of true signals, at least one remaining signal must have a larger absolute population score than every proxy, by a margin exceeding sampling error. Correlated predictors or common factors alone do not ensure this condition.

Separate results allow some proxies to remain while retaining all signals and excluding pure noise. Those results fix both signal and proxy counts. A growing-signal extension needs additional restrictions.

After exact selection, the authors also establish the same first-order coefficient distribution as least squares fitted to the true model, under further fixed-dimensional moment conditions. This inference result is pointwise, not uniform near selection boundaries, and does not extend to growing signal dimension.

Importantly, the selection theorems do not establish finite-sample family-wise error control at the nominal calibration level for every adaptive path. They also do not validate heteroskedasticity-robust or serial-correlation-robust testing for the high-dimensional selection step.

Strong simulations, not universal dominance

The main reported comparison covers 108 designs with four true signals, varying sample sizes, candidate counts and local or global factor dependence. Each design uses 2,000 replications.

Across these designs, BMT has the highest median Matthews correlation coefficient, a balanced measure of selection accuracy, at 0.987. Its median exact-recovery rate is 0.889, and its median coefficient root mean squared error is the lowest among the compared specifications, at 0.324.

The comparison includes OCMT, factor-adjusted GOCMT, Lasso variants, Adaptive Lasso, MCP and SCAD. Rankings vary: Adaptive Lasso with the one-standard-error tuning rule, MCP and SCAD also perform well. Better selection does not translate into uniformly better forecasts.

Two retesting variants can remove early proxies under separate assumptions. However, additional simulations show their tradeoff: retesting can also delete genuine variables whose conditional contributions are weak.

Forecasting illustrations and their limits

For U.S. air emissions, BMT selects Midwest housing permits as its sole additional indicator from 245 candidates, alongside compulsory controls. It records the lowest forecast errors in the reported comparisons. However, those comparisons hold specifications selected using the full sample fixed while reestimating coefficients on earlier observations; they are not fully recursive selection exercises.

The inflation application does repeat selection and estimation at 36 recursive forecast origins. Without compulsory inflation terms, BMT delivers the best one-quarter-ahead forecasts among the compared methods, averaging two selected predictors. Its out-of-sample R-squared is 38.58% relative to the zero-change benchmark.

That advantage does not hold across targets, horizons or control specifications. Longer-horizon results are mixed, and larger compulsory inflation-control blocks can worsen performance. The evidence supports BMT as a promising sparse-selection alternative, not a universally superior forecasting method or a route from predictive associations to causal conclusions.