A Granular Prediction Model of Time Series Integrating LSTM and Mathematical Morphology

Time series data are prevalent across various fields, including environmental science, energy, finance, and medicine. The long-term prediction of such data is crucial for practical applications like investment decision-making and environmental management. This study develops a novel granular prediction model (IG-MM-LSTM) for time series prediction, which integrates mathematical morphology (MM) with long shortterm memory (LSTM) networks. First, we derive interval-based granular representations of the original time series to reduce data dimensionality while preserving critical temporal patterns. Then, by applying MM decomposition techniques, we decompose the series into a stationary long-term baseline component and a non-stationary short-term residual component, suppressing noise while capturing local features. Moreover, LSTM is employed to predict the baseline and residual components separately, capturing their unique temporal features to form the final prediction results in the form of information granules. Experiments on six datasets demonstrate that IG-MM-LSTM outperforms autoregressive integrated moving average (ARIMA), support vector regression (SVR), backpropagation neural network (BPNN), and LSTM in prediction accuracy and effectively captures the main fluctuation ranges.