DBC-LSTM-ARIMA as a Dynamic Bi-Directional Coupling and Jointly-Optimized Hybrid Approach for Stock Price Prediction

Accurate stock price prediction is urgently needed for economic and algorithmic investment, yet prices are highly non‑linear, non‑stationary, and regime‑switching, which makes reliable forecasting very challenging. To address this issue, we propose Dynamic Bi‑directionally Coupled Long Short‑Term Memory–AutoRegressive Integrated Moving Average (DBC‑LSTM‑ARIMA), a hybrid model that couples an AutoRegressive Integrated Moving Average (ARIMA) backbone with a Long Short‑Term Memory (LSTM) network under a non‑anchored Walk‑Forward Optimization (WFO) protocol. In each sliding window, ARIMA first models short‑run linear dynamics and produces one‑step forecasts and residuals. These residuals, together with price history and market covariates, are fed forward into the LSTM, while the LSTM’s one‑step prediction errors are injected back into ARIMA as an exogenous correction, forming a bi‑directional feedback loop. Both components are trained with a unified window‑level loss and alternating updates, and their outputs are combined through an adaptive convex fusion weight determined from recent errors. Extensive experiments on three Chinese A‑share stocks (BYD, China Unicom, Ping An Bank), three overseas blue‑chip stocks (BP p.l.c., Apple Inc., Citigroup Inc.), and six additional A‑share stocks from diverse industries show that DBC‑LSTM‑ARIMA consistently outperforms seven state‑of‑the‑art baselines in terms of Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and coefficient of determination (R²), while maintaining moderate computational cost suitable for rolling deployment.