Enhanced forecasting of stock prices based on variational mode decomposition, PatchTST, and adaptive scale-weighted layer

TL;DR

This paper tackles the challenge of forecasting stock index prices under non-stationary, nonlinear dynamics by proposing a decomposition-then-predict framework that combines Variational Mode Decomposition (VMD), PatchTST, and an Adaptive Scale-Weighted Layer (ASWL). Each stock index price series is decomposed into intrinsic mode functions (IMFs) via VMD, with PatchTST employed to model temporal patterns for every IMF, and a scale-aware ASWL modifies the training loss to account for IMF magnitudes. The authors demonstrate that VMD+PatchTST outperforms several strong baselines and other VMD-based configurations, and that adding ASWL yields additional reductions in forecasting error across SP500, DJI, SSEC, and FTSE, including sizable MSE improvements for both low- and high-frequency components. This work provides a robust, decomposition-based approach for financial time series forecasting and suggests broad applicability to other non-stationary multivariate domains where scale-aware learning can improve predictive accuracy and stability.

Abstract

The significant fluctuations in stock index prices in recent years highlight the critical need for accurate forecasting to guide investment and financial strategies. This study introduces a novel composite forecasting framework that integrates variational mode decomposition (VMD), PatchTST, and adaptive scale-weighted layer (ASWL) to address these challenges. Utilizing datasets of four major stock indices--SP500, DJI, SSEC, and FTSE--from 2000 to 2024, the proposed method first decomposes the raw price series into intrinsic mode functions (IMFs) using VMD. Each IMF is then modeled with PatchTST to capture temporal patterns effectively. The ASWL module is applied to incorporate scale information, enhancing prediction accuracy. The final forecast is derived by aggregating predictions from all IMFs. The VMD-PatchTST-ASWL framework demonstrates significant improvements in forecasting accuracy compared to traditional models, showing robust performance across different indices. This innovative approach provides a powerful tool for stock index price forecasting, with potential applications in various financial analysis and investment decision-making contexts.

Figures (6)

• Figure 1: The flowchart of the proposed framework
• Figure 2: The architecture of PatchTST
• Figure 3: The Adaptive scale-weighted layer
• Figure 4: The decomposed components of the fifth period SP500 by VMD
• Figure 5: Forecasting results of IMFs for the fifth period SP500 using VMD+PatchTST