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Long Short-Term Memory Networks with Multiple Variables for Stock Market Prediction

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Abstract

Long short-term memory (LSTM) networks have been successfully applied to many fields including finance. However, when the input contains multiple variables, a conventional LSTM does not distinguish the contribution of different variables and cannot make full use of the information they transmit. To meet the need for multi-variable modeling of financial sequences, we present an application of multi-variable LSTM (MV-LSTM) network for stock market prediction in this paper. The network consists of two serial modules: the first module is a recurrent layer with MV-LSTM as its recurrent unit, which is able to encode information from each variable exclusively; the second module employs a variable attention mechanism by introducing a latent variable and enables the model to measure the importance of each variable to the target. With these two modules, the model can deal with multi-variable financial sequences more effectively. Moreover, a statistical arbitrage investment strategy is constructed based on the prediction model. Extensive experiments on the large-scale Chinese stock data show that the MV-LSTM network has a higher prediction accuracy and provides a better statistical arbitrage investment strategy than other methods.

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Notes

  1. Vectors are assumed to be in column form in this paper.

  2. http://www.csindex.com.cn/en.

  3. https://www.joinquant.com/.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61976174), the Nature Science Basis Research Program of Shaanxi (No. 2021JQ-055), the Ministry of Education of Humanities and Social Science Project of China (No. 22XJCZH004) and the Scientific Research Project of Shaanxi Provincial Department of Education (No. 22JK0186).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Fei Gao, Jiangshe Zhang, Chunxia Zhang, Shuang Xu & Cong Ma

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Appendix A Evaluation Metrics

Appendix A Evaluation Metrics

Several evaluation metrics used in this paper are defined as follows.

  1. (1)

    Max drawdown: Max drawdown (MDD) measures the maximum fall in the value of an investment. It is calculated by the difference between the value of the lowest trough and that of the highest peak before the trough, i.e.,

    $$\begin{aligned} {\mathrm{MDD}} = \mathop {max}\limits _{0 \le t_1 \le t_2 \le T} \frac{V_{t_1}-V_{t_2}}{V_{t_1}}, \end{aligned}$$

    where T is the length of trading period, \(V_{t_1}\) and \(V_{t_2}\) are the values of the investment at the time \(t_1\) and \(t_2\), respectively. A low MDD value indicates slight fluctuations in the investment value and, therefore, a low degree of risk, and vice versa.

  2. (2)

    Sharpe ratio: Sharpe ratio measures the performance of an investment compared to a risk-free asset, after adjusting for its risk. It is defined as the excess return for per unit of risk, i.e.,

    $$\begin{aligned} {\mathrm{Sharpe \ ratio}} = \frac{R_p-R_f}{\sigma _p}, \end{aligned}$$

    where \(R_p\) is the expected return of the investment, \(R_f\) is the risk-free rate, and \(\sigma _p\) is the standard deviation of the investment return. The higher the ratio, the greater the investment return relative to the amount of risk, and thus, the better the investment.

  3. (3)

    Sortino ratio: Sortino ratio is an improvement of Sharpe ratio. It only considers the downside risk rather than the total risk like Sharpe ratio, since upside risk is beneficial. It is calculated as

    $$\begin{aligned} {\mathrm{Sortino\ ratio}} = \frac{R_p-R_f}{\sigma _d}, \end{aligned}$$

    where \(\sigma _d\) is the standard deviation of the downside risk deviation. Like Sharpe ratio, a higher Sortino ratio indicates a better investment.

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Gao, F., Zhang, J., Zhang, C. et al. Long Short-Term Memory Networks with Multiple Variables for Stock Market Prediction. Neural Process Lett 55, 4211–4229 (2023). https://doi.org/10.1007/s11063-022-11037-8

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