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

2026-03-08

AI Summary

This study addresses the challenge of unstable impulse response estimation in high-dimensional time series settings where the number of predictors vastly exceeds the sample size, a scenario in which conventional local projection methods suffer from severe overfitting. To overcome this limitation, the authors propose an enhanced Random Subspace Local Projection (RSLP) framework that innovatively integrates class-aware subspace sampling, adaptive subspace size selection, and a weighted aggregation mechanism. Furthermore, they develop a conservative bootstrap inference procedure tailored for dependent data. The proposed method substantially improves estimation precision while maintaining correct confidence interval coverage: on benchmarks such as FRED-MD, it reduces estimation variability by 33% for forecast horizons \( h \geq 3 \), and in a 126-dimensional setting, it narrows policy-relevant impulse response confidence intervals by 14% on average.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• high-dimensional time series
• overfitting
• local projection
• impulse response estimation
• forecasting instability

Innovation

• Random Subspace
• Local Projection
• High-Dimensional Time Series
• Adaptive Subspace Selection
• Bootstrap Inference