Working condition fluctuations, noise interference and other factors result in complex information in the high-frequency vibration signals of rolling bearings, making it difficult for the modeling of degradation processes to accurately reflect actual degradation trends, thus reducing the accuracy of remaining life predictions for the bearings. To address this issue, this paper proposes a long-range time-series correlation prediction method for bearing remaining life based on a signal decomposition network. The method uses a time series decomposition algorithm to break down vibration signals into trend, periodic, and residual components, effectively filtering out redundant information. For the rapid degradation to failure stages, a feature extraction model based on a long short-term memory network autoencoder is designed to derive health indicators with strong monotonicity and trend. Finally, a deep temporal autoregressive neural network model is developed to predict trends in these health indicators and to output the probability distribution of remaining life predictions. Experimental results show that the health indicators constructed in this study exhibit strong trends and monotonicity. Compared to other methods, the proposed remaining life prediction method achieves significantly higher accuracy.