GARCH-FIS: A Hybrid Forecasting Model with Dynamic Volatility-Driven Parameter Adaptation

Stock price forecasting is hindered by the heteroscedastic nature of financial time series, in which turbulent and tranquil regimes alternate. Although the Long Short-Term Memory (LSTM) network is widely used for this task, its gates are oblivious to such volatility variation, so memory retention remains fixed regardless of market conditions. A common remedy is to supply volatility estimates as an additional input feature, yet this leaves the internal memory dynamics untouched. Instead, volatility can serve as a direct regulatory signal over the gate activation itself. This paper presents the Gsigmoid-LSTM model, which embeds Generalized Autoregressive Conditional Heteroscedasticity (GARCH(1,1))-derived volatility estimates into the LSTM forgetting gate through the Gsigmoid activation function, a volatility-adaptive variant of the sigmoid that combines a volatility adjustment factor with slope regulation via a learnable parameter. The model thereby automatically prioritizes recent information during turbulent periods while preserving long-term dependencies in stable markets. In the engineering application of daily stock price forecasting, extensive experiments, including activation function comparisons, baseline evaluations, and ablation studies, demonstrate that this structural gating modification effectively improves forecasting accuracy and robustness. The proposed model significantly outperforms a feature-level fusion baseline carrying the same volatility signal on all five datasets, as confirmed by Diebold-Mariano tests with all p<0.01, attains the best average rank of 1.00 in the Friedman test across nine models, and achieves the lowest MSE and MAE on all five datasets.

Financial time series exhibit multi-scale, high-noise, and non-stationary volatility dynamics. Decomposition--integration frameworks built on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) have advanced this field, yet existing CEEMDAN hybrids remain unstable: high-frequency mode mixing contaminates downstream predictors, and the heterogeneous volatility of decomposed components is not matched by any volatility-adaptive mechanism. To address these gaps, this paper proposes CEEMDAN-SE-SSA-VMGL. CEEMDAN adaptively decomposes the original series, and sample-entropy-driven K-means clustering groups the intrinsic mode functions into high-, mid-, and low-frequency and residual components. Singular spectrum analysis (SSA) is then applied to the high-frequency group, whose singular-value decomposition of the trajectory matrix and principal-component reconstruction decouple intertwined pseudo-oscillatory modes and alleviate mode mixing. We further design a plug-and-play robust LSTM variant, the volatility-modulated GARCH-LSTM (VMGL), which embeds a differentiable GARCH(1,1) layer inside the LSTM cell as a risk gate; the estimated conditional volatility multiplicatively scales the forget-gate activation, letting memory decay adapt to the instantaneous volatility while remaining fully end-to-end trainable. Component predictions are linearly combined. On five US and Chinese financial series (CSI 300, CSI 500, AAPL, GOOGL, S&P 500), the proposed model is compared with eleven benchmark architectures, lowering the forecasting error by 9% to 24% relative to the best benchmark and by 60% to 70% relative to a standard LSTM. Diebold--Mariano and model-confidence-set (MCS) tests confirm the statistical significance and stability of the gains, spectral analyses verify the SSA denoising efficacy, and backtesting demonstrates the framework's economic utility.

The problem of time-series forecasting in non-stationary and complex environments is a challenging task in machine learning, especially with heterogeneous numerical and textual data present. Traditional statistical models like AutoRegressive Integrated Moving Average (ARIMA) are based on the assumptions of linearity and stationarity, whereas recurrent neural networks like Long Short-Term Memory (LSTM) models do not necessarily represent distributional properties in highly volatile settings. This paper proposes a hybrid model that combines Generative Adversarial Networks (GANs) with Natural Language Processing (NLP)-based sentiment analysis to enable sentiment-conditioned time-series prediction. The model integrates adversarial learning on numerical sequences with contextual sentiment representations derived from unstructured text, enabling them to be jointly modelled to capture temporal dynamics and exogenous information. These results demonstrate the promise of hybrid generative and language-aware methods to enhance prediction robustness in non-stationary environments.