Dynamic forecasting for nonstationary high‐frequency financial data with jumps based on series decomposition and reconstruction

High‐frequency financial data generally possess nonlinear and nonstationary characteristics and usually contain jumping parts, which makes it difficult to establish an accurate forecasting model. In this paper, we first decompose the nonstationary high‐frequency financial time series through the variational mode decomposition (VMD), then construct the traditional autoregressive moving average (ARIMA) model on the trend and periodic items to capture the characteristics of the high‐frequency series, construct a deep learning long short‐term memory (LSTM) model on the disturbance item to fit the nonlinear trend of the data, and finally reconstruct the decomposed series by multiple linear regression. Through the Monte Carlo simulation and empirical data, it is found that under various evaluation criteria, the VMD‐LSTM model is more accurate in forecasting the nonstationary high‐frequency financial data with jumps, compared with the single ARIMA model, machine learning, and deep learning model. The VMD‐LSTM model has reduced 21.74%, 94.69%, and 48.57% on the mean absolute error (MAE) of forecasting compared with other models such as the ARIMA model, machine learning, and deep learning model. Furthermore, we construct a trading strategy for the ChiNext index based on the VMD‐LSTM model, which presents a good return and can provide investors with reasonable suggestions.