Multi-Scale Signal Decomposition and Sparrow Search Algorithm–Optimized BiLSTM for Time Series Forecasting

Time series forecasting presents considerable challenges in real-world applications due to the inherent volatility, sophistication, and nonlinearity of time series data. These factors hinder the development of models that are both accurate and robust, particularly in highly dynamic and variable scenarios. This paper proposes a hybrid approach that leverages Variational Mode Decomposition (VMD) and the Sparrow Search Algorithm (SSA) to improve the predictive performance of bidirectional long short-term memory networks (BiLSTM). First, VMD is applied to decompose the original input signal into multiple frequency components, thereby reducing noise interference. Subsequently, the SSA algorithm is employed to optimize the hyperparameters of the BiLSTM model, further enhancing its capacity for effective data processing. Experimental results demonstrate that the approach delivers markedly improved performance over other established baseline models. Relative to the ideal baseline model (VMD-SSA-LSTM), the proposed model achieves approximately a $14.3 \%$ decrease in mean absolute error (MAE) and roughly an $11.2 \%$ reduction in mean absolute percentage error (MAPE) and attains the highest coefficient of determination ($R^{2}$) value. These findings demonstrate exceptional accuracy and reliability, positioning the suggested model as a practical and effective solution for predicting complex time series.