Enhanced Random Subspace Local Projections for High-Dimensional Time Series Analysis
This work provides a more stable and reliable method for practitioners to perform impulse response analysis with rich information sets in high-dimensional time series, where traditional methods are unstable.
This paper addresses the problem of overfitting in high-dimensional time series forecasting, particularly for impulse response estimation, where the number of predictors often exceeds observations. The authors propose an enhanced Random Subspace Local Projection (RSLP) framework that reduces estimator variability by 33% at longer forecast horizons (h >= 3) and narrows confidence intervals by 14% at policy-relevant horizons in high-dimensional settings.
High-dimensional time series forecasting suffers from severe overfitting when the number of predictors exceeds available observations, making standard local projection methods unstable and unreliable. We propose an enhanced Random Subspace Local Projection (RSLP) framework designed to deliver robust impulse response estimation in the presence of hundreds of correlated predictors. The method introduces weighted subspace aggregation, category-aware subspace sampling, adaptive subspace size selection, and a bootstrap inference procedure tailored to dependent data. These enhancements substantially improve estimator stability at longer forecast horizons while providing more reliable finite-sample inference. Experiments on synthetic data, macroeconomic indicators, and the FRED-MD dataset demonstrate a 33 percent reduction in estimator variability at horizons h >= 3 through adaptive subspace size selection. The bootstrap inference procedure produces conservative confidence intervals that are 14 percent narrower at policy-relevant horizons in very high-dimensional settings (FRED-MD with 126 predictors) while maintaining proper coverage. The framework provides practitioners with a principled approach for incorporating rich information sets into impulse response analysis without the instability of traditional high-dimensional methods.