Abstract: Time series forecasting can provide insights into future trends and patterns,which is crucial for various applications.For example,weather forecast,power load forecast,etc.However,existing time series prediction models suffer from problems such as large model parameters,high computational complexity,and insufficient utilization of frequency domain information in data.To address these issues,a new model based on state space is proposed for long-term time series prediction.The model firstly uses multi-level wavelet decomposition to decouple the original time-series data into multiple sub sequences of different frequency bands.Secondly,it designs independent bidirectional Mamba modules for each subsequence to capture its unique dynamic patterns.Finally,the prediction results of each frequency band are accurately fused into the final prediction through wavelet reconstruction.Experimental results on seven publicly available datasets,including ETT,show that the method achieves optimal performance at multiple prediction lengths,with an average MSE reduction of 4.12% compared to the current best baseline model.This method has demonstrated its effectiveness and potential for practical applications on time series public datasets.

Key words: Time series prediction, Multi resolution wavelet decomposition, State space model, Linear model, Power load forecasting