Modelling and forecasting high-frequency data with jumps based on a hybrid nonparametric regression and LSTM model

Abstract

High-frequency financial data is more difficult to predict than low-frequency data because it possesses nonlinearity, nonstationarity, higher volatility, and long memory and is frequently accompanied by the jump phenomena. In this paper, the nonparametric regression (NR) model based on kernel function is used to fit the nonlinear relationship between the nonstationary series Yt and its lagging series to model the trend of high frequency financial time series. Furthermore, the deep learning LSTM (long short-term memory) model is applied to capture the high volatility and frequent jumps of high frequency financial data and to improve the forecasting accuracy of the residual series. The results demonstrate that the hybrid NR and LSTM model has greatly improved the forecasting accuracy in several evaluation criteria. In comparison to NR, support vector machine (SVM), LSTM, ARIMA and NR-SVM models, the mean absolute error (MAE) of NR-LSTM has reduced by 89.78%, 97.85%, 86.48%, 32.47% and 89%, respectively. In addition, we have constructed the trading strategy for the Shanghai-Shenzhen 300 index by using the NR-LSTM model. The NR-LSTM model can continue to provide good returns even during a bear market, which can serve as a guide for investors. Furthermore, the NR-LSTM model also exhibits the best forecasting effect when we model the high-frequency data of Ping An bank in China, the FTSE 100 index in the UK, and the S&P 500 index in the US.