Decomposition-Integration Framework Coupling SSA with a Volatility-Adaptive LSTM for Stock Price Forecasting

01 ABSTRACT

The paper introduces a decomposition-integration framework that decomposes financial series with CEEMDAN, groups intrinsic mode functions via sample-entropy-driven K-means clustering, applies singular spectrum analysis to the high-frequency group to mitigate mode mixing, and designs VMGL, which embeds a differentiable GARCH(1,1) layer in the LSTM cell so memory decay adapts to instantaneous volatility. The authors report 9%–24% lower error than the best of eleven benchmarks and 60%–70% lower than a standard LSTM on five US and Chinese series, supported by Diebold-Mariano and MCS tests. These gains are the authors' reported results under their experimental setup and require independent replication and broader market validation.

02 KEY FINDINGS

1. CEEMDAN decomposition is followed by sample-entropy-based clustering into high-, mid-, low-frequency and residual groups; the high-frequency group is reconstructed via SSA principal components to decouple pseudo-oscillatory modes.
2. VMGL embeds a differentiable GARCH(1,1) layer inside the LSTM cell as a risk gate, multiplicatively scaling forget-gate activation by conditional volatility while remaining end-to-end trainable.
3. On CSI 300, CSI 500, AAPL, GOOGL and S&P 500, forecasting error is 9%–24% lower than the best benchmark, with statistical tests supporting significance.