A typical way to predict the remaining useful life (RUL) of bearings is to predict certain health indicators (HIs) according to the historical HI series and forecast the end of life (EOL). The autoregressive neural network (ARNN) is an early idea to combine the artificial neural network (ANN) and the autoregressive (AR) model for forecasting, but the model is limited to linear terms. To overcome the limitation, this paper proposes an improved autoregressive integrated moving average with the recurrent process (ARIMA-R) method. The proposed method adds moving average (MA) components to the framework of ARNN, adding the long-range dependence and nonlinear factors. To deal with the recursive characteristics of the MA term, a process of MA component estimating is constructed based on the expectation-maximum method. In the concrete realization of the method, the rotation tree (RTF) is introduced in place of ANN to improve the prediction performance. The experiment on FEMTO datasets reveals that the proposed ARIMA-R method outperforms the ARNN method in terms of predictive performance evaluation indicators.