On the forecasting of high‐frequency financial time series based on ARIMA model improved by deep learning

Through empirical research, it is found that the traditional autoregressive integrated moving average (ARIMA) model has a large deviation for the forecasting of high‐frequency financial time series. With the improvement in storage capacity and computing power of high‐frequency financial time series, this paper combines the traditional ARIMA model with the deep learning model to forecast high‐frequency financial time series. It not only preserves the theoretical basis of the traditional model and characterizes the linear relationship, but also can characterize the nonlinear relationship of the error term according to the deep learning model. The empirical study of Monte Carlo numerical simulation and CSI 300 index in China show that, compared with ARIMA, support vector machine (SVM), long short‐term memory (LSTM) and ARIMA‐SVM models, the improved ARIMA model based on LSTM not only improves the forecasting accuracy of the single ARIMA model in both fitting and forecasting, but also reduces the computational complexity of only a single deep learning model. The improved ARIMA model based on deep learning not only enriches the models for the forecasting of time series, but also provides effective tools for high‐frequency strategy design to reduce the investment risks of stock index.