Descriptive statistics for forecasting errors.

LSTM (Long Short-Term Memory Network) is currently extensively utilized for forecasting financial time series, primarily due to its distinct advantages in separating the long-term from the short-term memory information within a sequence. However, the experimental results presented in this paper indicate that LSTM may struggle to clearly differentiate between these two types of information. To overcome this limitation, we propose the ARMA-RNN-LSTM Hybrid Model, aimed at enhancing the separation between the long-term and short-term memory information on top of LSTM framework. The experiment in this paper is inspired by an observation: when LSTMs and RNNs are respectively used to forecast the same time series that contains only short-term memory information, LSTMs exhibit significantly lower forecasting accuracy than RNNs, and we attributed this to LSTMs potentially misclassifying some short-term memory information as long-term during forecasting process. Further, we speculate that this confusion might also arise when LSTMs are used to forecast the time series containing both the long-term and short-term memory information. To verify the aforementioned hypothesis and improve the forecasting accuracy for financial time series, this paper combines RNNs with LSTMs, proposing a method of ARMA-RNN-LSTM Hybrid Modelling, and conducts an experiment with stock index prices. Eventually, the experiment results show that the ARMA-RNN-LSTM Hybrid Model outperforms standalone RNNs and LSTMs in forecasting stock index series containing both long-term and short-term memory information, confirming that the ARMA-RNN-LSTM Hybrid Model has effectively enhanced the separation between the long-term and short-term memory information within sequence. This hybrid modelling approach has innovatively addressed the issue of the confusion between the long-term and the short-term memory information in a sequence during LSTM’s forecasting process, improving the accuracy of forecasting financial time series, and demonstrates that neural network’s forecasting errors is a area worth to explore in the future.