Chaotic Time Series Forecasting Optimisation Based on Hybrid PSO Algorithm

The chaotic time series is widely applied in multiple forecasting situations under stochastic processes because of its irregular and disordered changing pattern. Although methods such as exponential smoothing and auto-regressive integrated moving average models are widely used for prediction, such methods still face problems from distorted signals, ineffective chaotic model training, and non-accurate forecasting results. To solve these problems, this research introduced a hybrid particle swarm optimisation method (HPSO) based on a Long Short-Term Memory (LSTM) model to improve parameter selection during phase space reconstruction (PSR) to enhance the performance of the Gated Recurrent Unit (GRU) neural network in forecasting chaotic time series. By optimising time delay and embedded dimension choices, the improved phase space reconstruction method enables better handling of non-linear relationships and complex patterns inherent in chaotic data generated by GRU model. With this optimisation, the new HPSO-GRU model can significantly improve forecasting accuracy metrics, providing a more efficient and resilient approach to chaotic time series prediction.