Adaptive Hybrid Markov Chain–LSTM Framework for Multi-Horizon Wind Speed Forecasting with Bias–Variance Optimization

The coexistence of stochastic regime transitions and nonlinear temporal dependencies has made accurate wind speed forecasting in complex terrain remains challenging. This study proposes an adaptive hybrid Markov Chain–Long Short-Term Memory (MC–LSTM) framework for multi-horizon wind speed forecasting, designed to address the limitations of standalone statistical and deep learning models. While Markov models capture stochastic state transitions effectively, they struggle with long-term dependencies, whereas LSTM networks model temporal patterns but may exhibit smoothing effects and error accumulation over extended horizons. To overcome these limitations, a bias–variance optimization perspective is introduced to guide the integration of both models within a unified adaptive ensemble framework. Using high-resolution NASA POWER hourly wind data for a complex terrain site, the proposed model dynamically adjusts the contribution of each component across forecasting horizons (t+1, t+3, t+6, and t+24). The results show that the hybrid framework consistently outperforms individual models in terms of RMSE, MAE, and coefficient of determination (R²), while exhibiting slower error propagation across increasing forecast horizons. Statistical validation using the Diebold–Mariano test confirms the significance of performance improvements. The findings highlight that the proposed framework provides a more stable and generalizable forecasting approach by balancing model bias and variance, making it suitable for power system planning and renewable energy integration under uncertain wind conditions.