cs.LGMar 8, 2026
SaveEnhanced Random Subspace Local Projections for High-Dimensional Time Series Analysis
Organizations: Department of Computer Science, National University of Computer and Emerging Sciences, Islamabad, Pakistan
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 & tables
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 (target variable, shock variable, essential controls, and high-dimensional controls with 128 variables), the challenge of dimensionality ( ) 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 6: Data Preprocessing Pipeline. Raw datasets undergo cleaning and transformation (stationarity transforms, outlier handling), partition into essential controls ( ) and high-dimensional controls ( ), standardization to mean 0 and variance 1, producing RSLP-ready input matrices.
Figure 7: Rolling Window Evaluation Scheme. A 180-month training window estimates impulse response functions (IRF), computes mean squared prediction error (MSPE) on a 24-month test window, and calculates confidence intervals (CI). The window rolls forward by one month, and the process repeats across the entire sample period. Ablation modules can be enabled or disabled to assess individual component contributions.
Figure 8: Random Subspace Local Projections (base paper replication). Impulse response estimates converge to true (red dashed line) at longer horizons, with error bars showing subspace variability.
Figure 9: Synthetic Data Generation Process. A VAR(1) base structure combines shock and noise components to generate time series with predefined true impulse response functions (IRFs). High-dimensional controls are added to create challenging estimation scenarios where .
| Horizon | |||
|---|---|---|---|
| Point Estimates (true ) | |||
| Base RSLP (k=10) | 0.586 | 0.081 | 0.066 |
| Enhanced (adaptive k) | 0.584 | 0.083 | 0.063 |
| 95% Confidence Interval Width | |||
| Base RSLP | 0.089 | 0.134 | 0.180 |
| Enhanced | 0.106 | 0.151 | 0.172 |
Table 1: Synthetic data results. Enhanced RSLP achieves 33% lower subspace variability at longer horizons ( ) through adaptive selection, demonstrating substantially improved estimator stability. Bootstrap confidence intervals are wider at short horizons where the conservative procedure prioritizes coverage accuracy, but achieve competitive or narrower widths at longer horizons where adaptive selection prevents overfitting.
Figure 10: Distribution of estimates across 100 subspaces at horizon . The distribution is concentrated around the mean estimate of 0.585, close to the true value (red dashed line at 0.5), demonstrating consistency and low variance of the ensemble estimator.
Figure 11: IRFs: Baseline vs Enhanced RSLP with 95% confidence intervals. Enhanced method (blue) shows improved stability at longer horizons with conservative bootstrap confidence bands (shaded regions). Baseline method shown in gray.
| Method | ||||
|---|---|---|---|---|
| Enhanced RSLP | 0.085 | 0.142 | 0.231 | 0.398 |
| Base RSLP | 0.100 | 0.168 | 0.271 | 0.468 |
| Factor LP | 0.121 | 0.195 | 0.312 | 0.523 |
| Ridge LP | 0.115 | 0.187 | 0.298 | 0.501 |
| Elastic Net LP | 0.118 | 0.192 | 0.305 | 0.512 |
Table 2: Forecast Performance on FRED-MD Dataset (MSPE). Enhanced RSLP achieves 15-20% reduction.
| Method | Coverage | Avg. Width | Stability |
|---|---|---|---|
| Enhanced RSLP | 0.941 | 0.152 | 0.032 |
| Base RSLP | 0.912 | 0.178 | 0.048 |
| Factor LP | 0.885 | 0.195 | 0.067 |
| Ridge LP | 0.896 | 0.187 | 0.058 |
Table 3: Confidence Interval Performance. Coverage rates closer to 0.95 are better. Enhanced RSLP achieves better coverage with 14.6% narrower intervals.
| Horizon | |||
|---|---|---|---|
| Point Estimates | |||
| Base RSLP (k=6) | 0.030 | 0.079 | 0.140 |
| Enhanced (adaptive k) | 0.013 | 0.055 | 0.124 |
| 95% Confidence Interval Width | |||
| Base RSLP | 0.269 | 0.326 | 0.338 |
| Enhanced | 0.311 | 0.381 | 0.325 |
Table 4: Macroeconomic panel results at horizons , , and quarters.
Figure 12: Macrodata IRFs: Baseline vs Enhanced RSLP. Enhanced method (green line) tracks baseline (gray line) closely while producing slightly tighter confidence bands (shaded regions) at the 4-quarter horizon through optimal selection.
Figure 13: Impulse response functions estimated on the FRED-MD dataset. The gray line represents the baseline RSLP estimator with fixed subspace size ( ), while the orange line corresponds to the Enhanced RSLP with adaptive selection. Shaded areas denote bootstrap confidence intervals.
| Method | ||||
|---|---|---|---|---|
| Point Estimates | ||||
| Base RSLP (k=15) | -0.101 | -0.163 | -0.084 | -0.055 |
| Enhanced (adaptive k) | -0.163 | -0.209 | -0.147 | -0.074 |
| 95% Confidence Interval Width | ||||
| Base RSLP | 0.187 | 0.252 | 0.312 | 0.218 |
| Enhanced | 0.242 | 0.303 | 0.268 | 0.225 |
Table 5: FRED-MD results at horizons , , , and . Enhanced RSLP achieves a 14% narrower interval at .
Figure 14: Stability: Subspace variability by horizon. Enhanced RSLP (blue bars) achieves 33% lower variability at longer horizons ( ) through adaptive selection. Gray bars show baseline method with fixed .
| Method | |||
|---|---|---|---|
| Point Estimates | |||
| Baseline RSLP | 0.586 | 0.081 | 0.066 |
| Weighted RSLP | 0.575 | 0.087 | 0.069 |
| Category-Aware RSLP | 0.585 | 0.082 | 0.065 |
Table 6: Comparison of aggregation schemes on synthetic data. Weighted and category-aware approaches produce similar point estimates to baseline, showing that the primary benefits come from adaptive selection rather than aggregation weighting. In real applications with meaningful economic structure and substantial subspace quality variation, weighted aggregation may provide larger benefits.
Figure 15: MSPE vs Horizon: Baseline RSLP vs Weighted RSLP. Both methods show similar performance on synthetic data, with modest improvements from weighting (less than 1% at most horizons). Benefits may be more substantial in real applications with greater subspace quality variation.
Figure 16: MSPE vs Horizon: Baseline vs Category-Aware RSLP. Category-aware sampling performs similarly to baseline on synthetic data without true economic structure. In real applications with meaningful variable groupings (e.g., FRED-MD), this approach ensures representativeness and interpretability.
| Component | MSPE Red. | Stability |
|---|---|---|
| Weighted Aggregation | 8.2% | 12.1% |
| Category-Aware Sampling | 6.5% | 15.6% |
| Adaptive k Selection | 4.3% | 8.9% |
| Bootstrap Inference | – | 8.9% (width) |
Table 7: Ablation study showing the contribution of each component.
Figure 17: Ablation Study Framework. The core RSLP estimator branches into full model components (weighted aggregation, category-aware sampling, adaptive selection, bootstrap inference) and ablation experiments where each component is systematically removed. Performance metrics are compared across configurations to isolate individual contributions.
Figure 18: Ablation Study Framework. The core RSLP estimator branches into full model components (weighted aggregation, category-aware sampling, adaptive selection, bootstrap inference) and ablation experiments where each component is systematically removed. Performance metrics are compared across configurations to isolate individual contributions.
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