Analysis of stock index with a generalized BN-S model: an approach based on machine learning and fuzzy parameters

Abstract

In this paper we implement a combination of data-science and fuzzy theory to improve the classical Barndorff-Nielsen and Shephard model, and implement this to analyze the S&P 500 index. We preprocess the index data based on fuzzy theory. After that, S&P 500 stock index data for the past 10 years are analyzed, and a deterministic parameter is extracted using various machine and deep learning methods. The results show that the new model, where fuzzy parameters are incorporated, can incorporate the long-term dependence in the classical Barndorff-Nielsen and Shephard model. The modification is based on only a few changes compared to the classical model. At the same time, the resulting analysis effectively captures the stochastic dynamics of the stock index time series.

Keywords:

• Barndorff-Nielsen and Shephard model
• Lévy process
• fuzzy sets
• machine learning
• stock index

Acknowledgments

This work is supported in part by the National Key Research and Development Program of China (2017YFB1401801), National Natural Science Foundation of China (71774042, 71532004) and China Scholarship Council (201906120273). The authors would also like to thank the anonymous reviewers for their careful reading of the manuscript and for suggesting points to improve the quality of the paper.

Data availability statement

The data that support the findings of this study are openly available in S&P 500 at https://finance.yahoo.com/.

Table 7. Evaluation of calculation results within 5 year (Train set: 11/01/2015–10/09/2018, Test set: 10/10/2018–10/30/2020).

Table 8. Evaluation of calculation results within 6 year (Train set: 11/01/2014–10/09/2018, Test set: 10/10/2018–10/30/2020).

Table 9. Evaluation of calculation results within 7 year (Train set: 11/01/2013–12/21/2017, Test set: 12/22/2017–10/30/2020).

Table 10. Evaluation of calculation results within 8 year (Train set: 11/01/2012–12/21/2017, Test set: 12/22/2017–10/30/2020).

Table 11. Evaluation of calculation results within 9 year (Train set: 11/01/2011–10/13/2016, Test set: 10/14/2016–10/30/2020).