At present, time series prediction methods are widely applied for Human–Computer Intelligent Systems in various fields such as Finance, Meteorology, and Medicine. To enhance the accuracy and stability of the prediction model, this paper proposes a time series prediction method called RAdam-Dual stage Attention mechanism-Nested Long Short-Term Memory (RAdam-DA-NLSTM). First, we design a Nested LSTM (NLSTM), which adopts a new internal LSTM unit structure as the memory cell of LSTM to guide memory forgetting and memory selection. Then, we design a self-encoder network based on the Dual stage Attention mechanism (DA-NLSTM), which uses the NLSTM encoder based on the input attention mechanism, and uses the NLSTM decoder based on the time attention mechanism. Additionally, we adopt the RAdam optimizer to solve the objective function, which dynamically selects Adam and SGD optimizers according to the variance dispersion and constructs the rectifier term to fully express the adaptive momentum. Finally, we use multiple datasets, such as PM2.5 data set, stock data set, traffic data set, and biological signals, to analyze and test this method, and the experimental results show that RAdam-DA-NLSTM has higher prediction accuracy and stability compared with other traditional methods.