Enhanced Random Subspace Local Projections for High-Dimensional Time Series Analysis

TL;DR

This paper introduces an enhanced Random Subspace Local Projection framework that improves high-dimensional time series forecasting stability and inference reliability through innovative subspace sampling and adaptive procedures.

Contribution

It presents novel enhancements to local projection methods, including weighted aggregation, category-aware sampling, and bootstrap inference, specifically designed for high-dimensional, correlated predictors.

Findings

33% reduction in estimator variability at horizons h >= 3

14% narrower confidence intervals with proper coverage in high-dimensional settings

Improved stability and inference reliability in high-dimensional time series forecasting

Abstract

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.