### Mathematical Biosciences and Engineering

2021, Issue 4: 3323-3347. doi: 10.3934/mbe.2021166
Research article Special Issues

# Stock price forecasting based on Hausdorff fractional grey model with convolution and neural network

• Received: 14 March 2021 Accepted: 08 April 2021 Published: 15 April 2021
• Forecast of stock prices can guide investors' investment decisions. Due to the high-dimensional and long-memory characteristics of stock data, it is difficult to predict. The fractional grey model with convolution (FGMC (1, m)) can be used to predict time series, because of its memory and ability to process high-dimensional data. However, the FGMC (1, m) model has some disadvantages, including complex calculation, loss of information, and approximate background values. In this paper, Hausdorff fractional derivative and Newton-Cotes formula are used to optimize these shortcomings and can get a Hausdorff fractional grey model with convolution (HFGMC (1, m)) model. The HFGMC (1, m)-LLE-BP model is proposed in this paper. HFGMC (1, m) provides a solution that can reduce the complexity of the cumulative generator matrix calculation and preserve the global information of the sequence. Newton-Cotes formula is used to calculate the background value, which can solve the shortcomings of approximate background values. The HFGMC (1, m) model is used to predict the linear component of the sequence, and the BP neural network is used to predict the nonlinear component of the sequence. In addition, because of the high-dimensional and nonlinear characteristics of stock data, a local linear embedding (LLE) algorithm is used to remove redundant information in high-dimensional non-linear data. The experimental results show that the HFGMC (1, m)-LLE-BP model is effective for predicting the stock price in different trends.

Citation: Wenhua Dong, Chunna Zhao. Stock price forecasting based on Hausdorff fractional grey model with convolution and neural network[J]. Mathematical Biosciences and Engineering, 2021, 18(4): 3323-3347. doi: 10.3934/mbe.2021166

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• Forecast of stock prices can guide investors' investment decisions. Due to the high-dimensional and long-memory characteristics of stock data, it is difficult to predict. The fractional grey model with convolution (FGMC (1, m)) can be used to predict time series, because of its memory and ability to process high-dimensional data. However, the FGMC (1, m) model has some disadvantages, including complex calculation, loss of information, and approximate background values. In this paper, Hausdorff fractional derivative and Newton-Cotes formula are used to optimize these shortcomings and can get a Hausdorff fractional grey model with convolution (HFGMC (1, m)) model. The HFGMC (1, m)-LLE-BP model is proposed in this paper. HFGMC (1, m) provides a solution that can reduce the complexity of the cumulative generator matrix calculation and preserve the global information of the sequence. Newton-Cotes formula is used to calculate the background value, which can solve the shortcomings of approximate background values. The HFGMC (1, m) model is used to predict the linear component of the sequence, and the BP neural network is used to predict the nonlinear component of the sequence. In addition, because of the high-dimensional and nonlinear characteristics of stock data, a local linear embedding (LLE) algorithm is used to remove redundant information in high-dimensional non-linear data. The experimental results show that the HFGMC (1, m)-LLE-BP model is effective for predicting the stock price in different trends.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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