Multiscale Portfolio Optimization via ICEEMDAN and Hilbert Spectral Analysis

Traditional portfolio optimization assumes homogeneous correlation structures across time scales, conflating high-frequency noise with persistent long-term trends. We introduce a scale-diversified portfolio construction framework that decomposes multivariate asset returns into intrinsic mode functions using Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise, classifies components into fast, medium, and slow frequency bands via Hilbert spectral analysis, optimizes portfolios independently at each scale with Ledoit-Wolf covariance shrinkage, and aggregates scale-specific portfolios through inverse-volatility weighting. Testing on 12 exchange-traded funds over 2019–2024 with 15-day rebalancing, the scale-diversified strategy achieves Sortino ratio 0.72 and Sharpe ratio 0.78, outperforming four canonical baselines: equal-weight (0.48), minimum variance (0.21), classical mean-variance (0.37), and risk-parity (0.48). Out-of-sample validation with training on 2019–2023 and testing on 2024–2025 yields test-period Sortino ratio 1.15 versus training-period 0.52, with maximum drawdown reduction from -26% to -5% and bootstrap one-tailed p = 0.044 for positive performance differential. Performance extends to 20 ETFs (Sortino 0.71 vs equal-weight 0.41) but exhibits regime-dependence, underperforming minimum variance in the low-volatility 2014–2018 period (annualized volatility 9.8% vs 3.1%) where Sortino ratio reaches 0.35 versus 0.52. Results indicate scale decomposition provides statistically significant risk-adjusted return improvements in volatile markets. JEL Classification: G11 , C58 , C61 , G17 , C22 , C14