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A novel stock indices hybrid forecasting system based on features extraction and multi-objective optimizer

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Abstract

The stock index is a barometer of the market economy. However, there are few reliable methods to forecast the stock market accurately and steadily owing to the complexity and non-linearity of the stock market. In this paper, a novel hybrid forecasting system is established based on the singular spectrum analysis (SSA), a novel multi-features extraction strategy, and the extreme learning machine (ELM) optimized by the multi-objective grey wolf optimizer (MOGWO). The raw stock data is firstly denoised by SSA. To make full use of data information, multiple feature extractors are constructed to obtain different features of the denoised data. The ELM optimized by MOGWO learns different features to acquire more satisfying prediction accuracy. The performance of the developed system has been comprehensively evaluated through three global stock indices datasets. Experimental results reveal that the proposed system has a great advantage over both conventional baseline models and advanced models proposed in recent years.

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Funding

National Natural Science Foundation of China (11701071).

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Authors and Affiliations

  1. School of Science, Beijing Jiaotong University, Beijing, China

    Xuerui Wang

  2. School of Statistics, Dongbei University of Finance and Economics, Dalian, China

    Xiangyu Li & Shaoting Li

Authors
  1. Xuerui Wang
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  2. Xiangyu Li
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  3. Shaoting Li
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Corresponding author

Correspondence to Shaoting Li.

Appendix A

Appendix A

Table 14 shows the hyperparameters of ARIMA and SSA-ARIMA, the order of the difference is determined by Augmented Dickey-Fuller (ADF) test, and the Akaike Information Criterion (AIC) is used to select the lag of periods and the lag of error components [76].

The hyperparameters of LSTM, IWFTS, SSA, ELM and MOGWO are listed in Table 15.

  1. (1)

    Because extracting nonlinear features of stock indices is not a complicated task, LSTM with a simple network structure is adopted in this paper. Meanwhile, a small learning rate (0.05) and a large number of iterations (5000) are adopted to ensure stable and effective extraction of nonlinear features.

  2. (2)

    To extract the trend feature effectively, the first-order difference of the stock data is calculated and divided into 10 equal-length domains, and the triangular membership function is selected to ensure that the first-order difference of the stock data has a reasonable degree of membership in each domain.

  3. (3)

    SSA has two important hyperparameters, but there is no uniform criterion to choose them. Generally, the larger the window length is, the finer the decomposition of the original sequence can be. However, choosing a large window length increases the amount of calculation and produces many singular values approaching 0, and their corresponding subsequences are usually noise sequences that should be removed. Therefore, we set the window length to 20 and select the first 7 subsequences to reconstruct the data (their singular values do not approach 0), which can effectively retain the main feature of stock indices.

  4. (4)

    There are 3 input variables for ELM, too many hidden neurons of ELM lead to overfitting. In addition, the experimental results show that ELM can better learn stock features when Sine is selected as the activation function [77].

  5. (5)

    MOGWO only needs to find 20 initial parameters of ELM, which is a simple task. Therefore, the hyperparameters of MOGWO set in this study are not large.

Table 14 Model hyperparameters I
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Table 15 Model hyperparameters II
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Wang, X., Li, X. & Li, S. A novel stock indices hybrid forecasting system based on features extraction and multi-objective optimizer. Appl Intell 52, 11784–11807 (2022). https://doi.org/10.1007/s10489-021-03031-9

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