The existing methods for capturing multi-scale time characteristics, especially in long-term prediction of time series, are not satisfactory. In this paper, LWSpace is introduced, which is a time series prediction model integrating wavelet decomposition and selective state space, especially for multi-scale time and long horizon prediction. Our approach consists of four key components: (1) a Wavelet Decomposition Module that extracts frequency components at multiple scales, (2) a Scale-Specific Selective State Space (S4) mechanism that processes different frequency bands with specialized recurrent dynamics, (3) a Cross-Scale Attention Integration module that enables information exchange between scales, and (4) an Adaptive Horizon Prediction framework for efficient multi-horizon forecasting. The experiment based on six common benchmark data sets in this paper proves the practical availability of LWSpace and its superiority compared with other common methods. In the horizon range selected in the experiment, MSE is increased by 8.5% on average and MAE by 7.2% on average. In addition, the robustness of time distortion and noise disturbance to the model has been proved theoretically, and it is found that it still maintains good performance on real time series data in the empirical study.