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Forecasting the Dynamic Correlation of Stock Indices Based on Deep Learning Method

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Abstract

With the economic globalization, it is important to accurately estimate and predict the correlation between global stock markets for the efficient asset allocation around the globe. While practitioners may resort to various GARCH-type models for correlation forecasting, the forecasting accuracy is still not very satisfactory. For the first time, this paper introduces a deep learning method into the research of stock market correlation. A hybrid DCDNN model is developed based on the RDNN (recurrent deep neural network) and DCC-GARCH models. Deep learning is then devised to forecast the prediction error of the DCC-GARCH model in order to improve the prediction accuracy of stock market correlation. An autoencoder is also introduced in the empirical study to extract useful features of the stock index data. Then, the correlations among the stock markets in China, Hong Kong, the United States and Europe are predicted and tested. We show that the accuracy of the DCDNN model is significantly higher than that of the DCC-GARCH model. The results indicate that the introduction of deep learning can help improve the efficacy of existing correlation forecasting methods.

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The data that support the findings of this study are available from the corresponding author upon request.

References

  • Aladesanmi, O., Casalin, F., & Metcalf, H. (2019). Stock market integration between the UK and the US: Evidence over eight decades. Global Finance Journal, 41, 32–43.

    Article  Google Scholar 

  • Allard, A.-F., Iania, L., & Smedts, K. (2020). Stock-bond return correlations: Moving away from “one-frequency-fits-all” by extending the DCC-MIDAS approach. International Review of Financial Analysis, 71, 101557. https://doi.org/10.1016/j.irfa.2020.101557

    Article  Google Scholar 

  • Alp, T., & Demetrescu, M. (2010). Joint forecasts of Dow Jones stocks under general multivariate loss function. Computational Statistics & Data Analysis, 54(11), 2360–2371.

    Article  Google Scholar 

  • Baek, Y., & Kim, H. Y. (2018). ModAugNet: A new forecasting framework for stock market index value with an overfitting prevention LSTM module and a prediction LSTM module. Expert Systems with Applications, 113, 457–480.

    Article  Google Scholar 

  • Basher, A., & Sadorsky, P. (2016). Hedging emerging market stock prices with oil, gold, VIX, and bonds: A comparison between DCC, ADCC and GO-GARCH. Energy Economics, 54, 235–247.

    Article  Google Scholar 

  • Bekaert, G., Hodrick, R. J., & Zhang, X. (2009). International stock return comovements. Journal of Finance, 64(6), 2591–2626.

    Article  Google Scholar 

  • Bekiros, S. (2014). Nonlinear causality testing with stepwise multivariate filtering: Evidence from stock and currency markets. The North American Journal of Economics and Finance, 29, 336–348.

    Article  Google Scholar 

  • Bonga-Bonga, L. (2018). Uncovering equity market contagion among BRICS countries: An application of the multivariate GARCH model. The Quarterly Review of Economics and Finance, 67, 36–44.

    Article  Google Scholar 

  • Celık, S. (2012). The more contagion effect on emerging markets: The evidence of DCC-GARCH model. Economic Modelling, 29(5), 1946–1959.

    Article  Google Scholar 

  • Chen, Y. H., He, K. J., & Tso, G. K. F. (2017). Forecasting crude oil prices: A deep learning based model. Procedia Computer Science, 122, 300–307.

    Article  Google Scholar 

  • Chiang, T. C., Lao, L., & Xue, Q. (2016). Comovements between Chinese and global stock markets: Evidence from aggregate and sectoral data. Review of Quantitative Finance and Accounting, 47(4), 1003–1042.

    Article  Google Scholar 

  • Chong, E., Han, C., & Park, F. C. (2017). Deep learning networks for stock market analysis and prediction: Methodology, data representations, and case studies. Expert Systems with Applications, 83, 187–205.

    Article  Google Scholar 

  • Daníelsson, J. (2008). Blame the models. Journal of Financial Stability, 4(4), 321–328.

    Article  Google Scholar 

  • Deng, K. (2018). Another look at large-cap stock return comovement: A semi-markov-switching approach. Computational Economics, 51(2), 227–262.

    Article  Google Scholar 

  • Efimova, O., & Serletis, A. (2014). Energy markets volatility modelling using GARCH. Energy Economics, 43, 264–273.

    Article  Google Scholar 

  • Engle, R. F. (2002). Dynamic conditional correlation: A new simple class of multivariate GARCH models. Journal of Business and Economic Statistics, 20(3), 339–350.

    Article  Google Scholar 

  • Fei, P., Ding, L., & Deng, Y. (2010). Correlation and volatility dynamics in REIT returns: Performance and portfolio considerations. Journal of Portfolio Management, 36(2), 113–125.

    Article  Google Scholar 

  • Fischer, T., & Krauss, C. (2018). Deep learning with long short-term memory networks for financial market predictions. European Journal of Operational Research, 270(2), 654–669.

    Article  Google Scholar 

  • Gers, F. A., Schmidhuber, J., & Cummins, F. (2000). Learning to forget: Continual prediction with LSTM. Neural Computation, 12(10), 2451–2471.

    Article  Google Scholar 

  • Güloğlu, B., Kaya, P., & Aydemir, R. (2016). Volatility transmission among Latin American stock markets under structural breaks. Physica a: Statistical Mechanics and Its Applications, 462, 330–340.

    Article  Google Scholar 

  • Hochreiter, S., & Schmidhuber, J. (1997). Long short-term memory. Neural Computation, 9(8), 1735–1780.

    Article  Google Scholar 

  • Hu, Y., Ni, J., & Wen, L. (2020). A hybrid deep learning approach by integrating LSTM-ANN networks with GARCH model for copper price volatility prediction. Physica A-Statistical Mechanics and its Applications, 557, 124907. https://doi.org/10.1016/j.physa.2020.124907

    Article  Google Scholar 

  • Huang, W. (2007). Financial integration and the price of world covariance risk: large vs. small-cap stocks. Journal of International Money and Finance, 26(8), 1311–1337.

    Article  Google Scholar 

  • Kim, H. Y., & Won, C. H. (2018). Forecasting the volatility of stock price index: A hybrid model integrating LSTM with multiple GARCH-type models. Expert Systems with Applications, 103, 25–37.

    Article  Google Scholar 

  • Kleć, M., & Koržinek, D. (2014). Unsupervised feature pre-training of the scattering wavelet transform for musical genre recognition. Procedia Technology, 18, 133–139.

    Article  Google Scholar 

  • Krauss, C., Do, X. A., & Huck, N. (2017). Deep neural networks, gradient-boosted trees, random forests: Statistical arbitrage on the S&P 500. European Journal of Operational Research, 259(2), 689–702.

    Article  Google Scholar 

  • Lago, J., Ridder, F. D., & Schutter, B. D. (2018). Forecasting spot electricity prices: Deep learning approaches and empirical comparison of traditional algorithms. Applied Energy, 221, 386–405.

    Article  Google Scholar 

  • Lee, H.-T. (2010). Regime switching correlation hedging. Journal of Banking & Finance, 34(11), 2728–2741.

    Article  Google Scholar 

  • Nair, V., Hinton, G.E. (2010). Rectified linear units improve restricted boltzmann machines. In Proceedings of the twenty seventh international conference on machine learning (ICML-10), pp. 807–814.

  • Öztek, M. F., & Öcal, N. (2016). The effects of domestic and international news and volatility on integration of Chinese stock markets with international stock markets. Empirical Economics, 50(2), 317–360.

    Article  Google Scholar 

  • Panda, A. K., & Nanda, S. (2017). Short-term and long-term Interconnectedness of stock returns in Western Europe and the global market. Financial Innovation, 3(1), 2199–4730.

    Article  Google Scholar 

  • Sezer, O. B., Gudelek, M. U., & Ozbayoglu, A. M. (2020). Financial time series forecasting with deep learning : A systematic literature review: 2005–2019. Applied Soft Computing. https://doi.org/10.1016/j.asoc.2020.106181

    Article  Google Scholar 

  • Shiferaw, Y. A. (2019). Time-varying correlation between agricultural commodity and energy price dynamics with Bayesian multivariate DCC-GARCH models. Physica A-Statistical Mechanics and Its Applications, 526, 120807. https://doi.org/10.1016/j.physa.2019.04.043

    Article  Google Scholar 

  • Turban, E., Sharda, R., & Delen, D. (2011). Decision support and business intelligence systems (9th ed.). Pearson Prentice Hall.

    Google Scholar 

  • Turgutlu, E., & Ucer, B. (2010). Is global diversification rational? Evidence from emerging equity markets through mixed copula approach. Applied Economics, 42(5), 647–658.

    Article  Google Scholar 

  • Wang, K.-M. (2013). Did Vietnam stock market avoid the “contagion risk” from China and the US? The contagion effect test with dynamic correlation coefficients. Quality & Quantity, 47(4), 2143–2161.

    Article  Google Scholar 

  • You, L., & Daigler, R. T. (2010). Is international diversification really beneficial? Journal of Banking & Finance, 34(1), 163–173.

    Article  Google Scholar 

  • Zhang, X., Zhu, Y. M., & Yang, L. S. (2018). Multifractal detrended cross-correlations between Chinese stock market and three stock markets in The Belt and Road Initiative. Physica A: Statistical Mechanics and Its Applications, 503, 105–115.

    Article  Google Scholar 

  • Zhao, Y., Li, J. P., & Yu, L. (2017). A deep learning ensemble approach for crude oil price forecasting. Energy Economics, 66, 9–16.

    Article  Google Scholar 

Download references

Acknowledgments

We would like to thank the Editor and the anonymous referees for their insightful comments and suggestions for the revision of this paper. Any remaining errors are our responsibility. This research was supported by National Natural Science Foundation of China (No. 71601159), National Social Science Fund of China (No. 19ZDA074) and Fundamental Research Funds for the Central Universities (No. JBK2107035).

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Authors and Affiliations

  1. School of Finance, Southwestern University of Finance and Economics, Chengdu, 611130, China

    Jian Ni & Yue Xu

Authors
  1. Jian Ni
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  2. Yue Xu
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Contributions

Jian Ni & Yue Xu Contributions Conceptualization, Methodology, Resources, Supervision, Writing—review & editing: Jian Ni; Data curation, Formal Analysis, Writing – original draft, Software, Validation, Visualization: Yue Xu.

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Correspondence to Yue Xu.

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The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Correspondence to Yue Xu.

Appendices

Appendix A

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Table 3 Descriptive statistics of the returns of every 20 days
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3.

Appendix B

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Table 4 Tuning hyperparameters for models
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Ni, J., Xu, Y. Forecasting the Dynamic Correlation of Stock Indices Based on Deep Learning Method. Comput Econ 61, 35–55 (2023). https://doi.org/10.1007/s10614-021-10198-3

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