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

TL;DR

An enhanced Random Subspace Local Projection (RSLP) framework designed to deliver robust impulse response estimation in the presence of hundreds of correlated predictors is proposed, which substantially improve estimator stability at longer forecast horizons while providing more reliable finite-sample inference.

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.

Figures (18)

• Figure 1: Enhanced RSLP System Architecture. The framework consists of four layers: Input Layer (FRED-MD dataset), Preprocessing Layer (stationarity transforms, missing value handling, standardization), Feature Engineering Layer (variable partitioning into essential and high-dimensional controls), and Enhanced RSLP Core Modules (category-aware sampling, local projection estimation, weighted aggregation, and bootstrap inference).
• Figure 2: Enhanced RSLP Solution Overview. Given inputs at time $t$ (target variable, shock variable, essential controls, and high-dimensional controls with 128 variables), the challenge of dimensionality ($q=128 > T=200-500$) causes LP regression instability. The solution breaks controls into random subspaces using category-aware sampling (Step 1), estimates local projections in each subspace (Step 2), and combines estimates using weighted aggregation (Step 3), producing impulse response functions with bootstrap confidence intervals.
• Figure 3: Overview of two core components of the enhanced RSLP framework.
• Figure 4: Adaptive $k$ Selection Module. The module evaluates a grid of candidate $k$ values, tests each using cross-validation, computes validation metrics, selects the optimal $k^*$ minimizing prediction error, and outputs horizon-specific subspace sizes.
• Figure 5: Bootstrap Inference Module. The aggregated impulse response estimate $\hat{\beta}_h$ undergoes moving block bootstrap sampling, RSLP re-estimation for each bootstrap sample, distribution analysis, and confidence interval construction using percentile or BCa methods.