FI-CAECNet: A Frequency-Aware IMF-Wise Closed-Loop Adaptive Error Correction Network for Stock Price Forecasting

Abstract

Stock price forecasting remains challenging because financial time series usually exhibit nonstationarity, strong noise, nonlinear dynamics, multi-scale fluctuations, and abrupt short-term shocks. Although CEEMDAN-LSTM-Transformer-based decomposition–prediction–reconstruction frameworks can reduce the complexity of raw closing price sequences, their IMF branches usually perform one-shot open-loop prediction, where the historical prediction errors of each IMF branch are not explicitly exploited before final reconstruction. To address this limitation, this paper proposes FI-CAECNet, a frequency-aware IMF-wise closed-loop adaptive error correction network for stock price forecasting. In the proposed framework, CEEMDAN first decomposes the closing price series into multiple intrinsic mode functions and one residual component. Each IMF component, together with auxiliary financial indicators, is predicted by an LSTM branch to obtain an initial component-level prediction, while the residual component is modeled by a Transformer branch. The core innovation lies in the proposed FI-CAEC module, which is embedded after each IMF-LSTM branch. FI-CAEC uses historical error memory and frequency-aware features, including energy, entropy, volatility, and dominant frequency, to construct a feedback state. An adaptive correction gate and a bounded correction term are then generated to iteratively refine the initial IMF prediction in a closed-loop manner before final summation. Experiments on eight representative Chinese A-share and U.S. stock datasets show that FI-CAECNet achieves the best overall forecasting performance among all compared models. Compared with the CEEMDAN-LSTM-Transformer baseline, FI-CAECNet reduces the average MSE and MAE and improves the hit ratio. Dedicated ablation experiments further show that historical error memory, frequency-aware features, gated correction, bounded correction, and finite closed-loop iteration all contribute to the performance improvement. The results demonstrate that FI-CAECNet can effectively reduce component-level prediction errors and improve the accuracy, robustness, and interpretability of stock price forecasting.