Abstract

This study proposes a hybrid approach to analyze and forecast non-stationary financial time series by combining statistical models with deep neural networks. A model is introduced that integrates three key components: the Generalized Autoregressive Score (GAS) model, which captures volatility dynamics; an attention mechanism (ATT), which identifies the most relevant features within the sequence; and a Long Short-Term Memory (LSTM) neural network, which receives the outputs of the previous modules to generate price forecasts. This architecture is referred to as GAS-ATT-LSTM. Both unidirectional and bidirectional variants were evaluated using real financial data from the Nasdaq Composite Index, Invesco QQQ Trust, ProShares UltraPro QQQ, Bitcoin, and gold and silver futures. The proposed model’s performance was compared against five benchmark architectures: LSTM Bidirectional, GARCH-LSTM Bidirectional, ATT-LSTM, GAS-LSTM, and GAS-LSTM Bidirectional, under sliding windows of 3, 5, and 7 days. The results show that GAS-ATT-LSTM, particularly in its bidirectional form, consistently outperforms the benchmark models across most assets and forecasting horizons. It stands out for its adaptability to varying volatility levels and temporal structures, achieving significant improvements in both accuracy and stability. These findings confirm the effectiveness of the proposed hybrid model as a robust tool for forecasting complex financial time series. © 2025 by the authors.