Public-Data Causal Multiscale Wavelet Spillover Learning for Stock Index Volatility Forecasting and Risk Early Warning

Accurate volatility forecasting and timely risk early warning are foundational requirements of financial risk management: Value-at-Risk estimates, portfolio risk limits, derivative hedging ratios, and stress-test scenario calibrations all depend on forward-looking volatility signals that remain reliable when market conditions depart from average. This paper develops a public-data causal multiscale wavelet spillover learning (CMWSL) framework that jointly addresses stock-index volatility forecasting and high-volatility early warning under strict walk-forward evaluation. CMWSL integrates three components: a heterogeneous autoregressive (HAR) persistence block as the dominant linear baseline, causal stationary wavelet transform (SWT) summaries that encode within-index multiscale market dynamics, and a cross-index spillover layer that tests whether medium- and long-scale wavelet energy from peer indices carries incremental risk-relevant information. The empirical analysis covers the S&P 500, Nasdaq-100, and Dow Jones Industrial Average over a 2513-step out-of-sample evaluation period from 2016 to 2025, with forecast horizons h∈{1,5,10} and OHLC-based volatility targets. All preprocessing, wavelet decomposition, calibration rules, and warning thresholds are re-estimated inside each rolling training window to eliminate look-ahead bias. HAR remains the strongest average model in the main Rogers–Satchell specification, confirming that daily index volatility risk is highly persistence-driven. The multiscale extension delivers statistically significant improvements at longer horizons, in richer public macro-financial information environments, and under the Parkinson target. Clark–West tests detect significant spillover gains in five of nine index–horizon cells (CW =4.83, p<0.001 for S&P 500 at h=10). Critically, tail-conditioned and rolling-window diagnostics show that multiscale and cross-index gains concentrate in upper-volatility regimes and synchronized stress episodes—precisely the conditions in which risk management decisions are most consequential. For market-risk early warning, a logistic classifier built on the same causal feature pipeline delivers the most stable precision–recall performance across all settings, providing an interpretable and operationally auditable alert mechanism suitable for practical risk monitoring.