Stock prediction based on bidirectional gated recurrent unit with convolutional neural network and feature selection.

With the development of recent years, the field of deep learning has made great progress. Compared with the traditional machine learning algorithm, deep learning can better find the rules in the data and achieve better fitting effect. In this paper, we propose a hybrid stock forecasting model based on Feature Selection, Convolutional Neural Network and Bidirectional Gated Recurrent Unit (FS-CNN-BGRU). Feature Selection (FS) can select the data with better performance for the results as the input data after data normalization. Convolutional Neural Network (CNN) is responsible for feature extraction. It can extract the local features of the data, pay attention to more local information, and reduce the amount of calculation. The Bidirectional Gated Recurrent Unit (BGRU) can process the data with time series, so that it can have better performance for the data with time series attributes. In the experiment, we used single CNN, LSTM and GRU models and mixed models CNN-LSTM, CNN-GRU and FS-CNN-BGRU (the model used in this manuscript). The results show that the performance of the hybrid model (FS-CNN-BGRU) is better than other single models, which has a certain reference value.

Introduction

With the development of China’s economy and the improvement of people’s living standards, the stock market has become a hot area of attention. Although China’s stock market started late, its growth momentum can’t be underestimated. Therefore, scholars and investors in various countries are very optimistic about the future development trend of China’s stock market. In the stock market, there are thousands of stocks in China alone, and each stock is affected by many factors. Therefore, it is particularly difficult to select one or several high quality stocks from many stocks. The change of stock price is influenced by many factors, such as natural disasters, the influence of politicians and the influence of the country in the world. Because the change of stock price is nonlinear, it is very important for many researchers and investors [1] to predict the trend of stock price in advance. The establishment of a high precision and reasonable stock prediction model can effectively reduce the loss of investors in the stock market, but also can improve their control of the stock price. Stock is a kind of non-linear data with time series attribute, so [2] proposed a cumulative autoregressive moving average method combined with least squares support vector machine (ARI-MA-LS-SVM) for stock prediction. The results show that the model has good universality and stability, and can provide a certain reference value for many investors and research institutes. [3] proposed a feature selection algorithm based on weighted sum least squares support vector machine (LS-SVM). We first add analytic hierarchy process (AHP) to the stock, and give the corresponding evaluation index. The features obtained by AHP method are added to LS-SVM model and the conclusion is drawn. The results show that the performance of this model is better than other models.

In the 21st century, the rapid development of science and technology has also led to the development of deep learning, so there are many researches on deep learning [4, 5], such as face recognition [6], emotion recognition [7] and image recognition [8]. Compared with other traditional machine learning algorithms, deep learning can deal with nonlinear problems well, so deep learning can play an important role in many research fields. [9] use a hybrid model based on Convolutional Neural Network (CNN) and support vector machine (SVM) to predict the stock index. The results show that the neural network can deal with continuous and classified forecasting variables. [10] adopts a hybrid model (RNN + LSTM)and the results show that the hybrid model has a good application prospect for the stock price forecast of single stock with variables such as corporate behavior and corporate announcement. [11] proposed a new appearance model, which can be embedded into the recurrent neural network of bidirectional short-term memory unit and can effectively learn to track. It is superior to most other models in the benchmark video. [12] proposed a hybrid model based on neural network and B-P algorithm to predict stock price. The results show that the accuracy rate of using a single fuzzy algorithm is 62.12%, while the accuracy rate of using a single B-P algorithm is 73.29%, and the effect is the best. After comparing the influence of different hidden layers of neural network on the results, it is found that the accuracy rate of B-P neural network is better than that of fuzzy algorithm, and the algorithm provides a certain reference for stock investors The value of examination. Taking block chain information as the main research object, [13] discusses the impact of official information on the stock price trend caused by investors’ intervention in stocks, and predicts stocks according to investors’ preferences, and puts forward a stock prediction model based on LSTM. The results show that the prediction ability of the model is improved after adding the emotional characteristics, which reflects that information clarification is helpful to the prediction of stock price. [14] proposed a hybrid model based on integrated EMD and LSTM. The complex stock data is decomposed into smoother subsequences than the original time series by using the comprehensive dynamic decomposition method, and then the decomposed data is put into LSTM model for training and prediction, and compared with other five prediction methods. The results show that the hybrid model proposed in this paper has higher prediction accuracy than other models. [15] proposed a hybrid stock forecasting model based on CNN-LSTM, and add MLP, CNN, RNN, LSTM and CNN-LSTM to make horizontal comparison. The results show that the accuracy of the CNN-LSTM stock forecasting model is higher than other forecasting models. [16] propose a stock prediction model based on LSTM and attention mechanism. Firstly, wavelet transform is used to denoise the stock data, and then S P500, DJIA, HSI stock data are put into the prediction model for calculation. The results show that the stock prediction model proposed in this paper has the best effect.

Research methodology

Feature selection (fs)

Feature selection [17] is a very important part in the process of data preprocessing. To a certain extent, it can select important features in order to increase the training speed and alleviate the dimension disaster. At the same time, it can increase the accuracy of the training results by removing the inconsistent features. [18] take the glass bottle defect detection as a classification problem, and extract features from the glass bottle knock signal as the data input. In this paper, an improved feature selection algorithm (SFLA-ImRMR-BP) is proposed based on the previous minimum redundancy maximum correlation algorithm (SFLA-ImRMR). The results show that the algorithm proposed in this paper has a great improvement in accuracy compared with previous algorithms. [19] proposed an algorithm based on DNP-AAP (deep neural pursuit average activation potential). The results show that the algorithm can effectively identify the known AMR related genes, and it also provides a list of candidate genes that may lead to the discovery of new AMR factors, which provides a new scheme for microbiologists. The most representative feature selection methods are as follows:

Filter selection

Relief (relative features) is a well-known filtering feature selection method, which assumes that the importance of feature subset is determined by the sum of feature values corresponding to each subset in each subset. The calculation formula is as follows: Where is the value of sample x on sample j. If the attributes are discrete, then diff is 0 if and only if the attributes are equal, and 1 for all other times. If it is continuous, then diff is the distance, and the larger the value, the better.

The construction method is as follows: Selecting the nearest neighbor x from the similar samples of x, which is called guessing the nearest neighbor. Selecting a nearest neighbor x in heterogeneous samples is called guessing the wrong nearest neighbor.

It can be seen from the above formula that for the value corresponding to a feature, the closer the same kind is, the farther the different kind is, and the larger the corresponding statistics will be.

Embedded selection

When the dimension of training data is large and the training data is small, it is easy to over fit, so it is necessary to add a regular term. L1 norm is easier to get sparse solutions than L2 norm, so the learning method based on L1 regularization is an embedded feature selection method. The Proximal gradient descent (PGD) [20] method can be used to solve the L1 regularization problem. PGD can make LASSO and other methods based on L1 norm minimization be solved quickly.

Convolutional neural network (cnn)

Convolutional neural network [21-23] is a kind of feed forward neural network with convolution calculation and depth structure, which is one of the most representative algorithms of deep learning. Convolutional neural network has the ability of representation learning. It can extract the features of input data according to its hierarchical structure, and select the useful information in the data. At the same time, it also reduces a lot of calculation, which greatly reduces the training time. The research of convolutional neural network began in the 1980s and 1990s. Convolutional neural network consists of the following parts: convolution layer, pooling layer, activation function and output layer. Each convolution layer contains many convolution cores. Although the features of the data are greatly extracted after convolution operation, a common fault of convolution calculation is that the problem of high dimension appears. Therefore, adding pooling layer after convolution calculation can effectively solve the problem of high data dimension, improve the robustness of the extracted features, and then put the data into the activation function to fit nonlinear problems. The specific calculation process is shown in formula (2), and the convolution image is shown in Fig 1. Where P is the output result, Relu is the activation function, x is the input data, w is the weight of convolution kernel, and b is the bias.

Fig 1

Convolution process.

Bidirectional gated recurrent unit (bgru)

RNN [24-27] is a recurrent neural network, which takes sequence data as input, recursively along the evolution direction of the sequence, and all nodes are connected by chain. The research on Recurrent Neural Network began in the 1980s and 1990s, and developed into one of the deep learning algorithms at the beginning of the 21st century. Bidirectional Recurrent Neural Network and Long Short-Term Memory Network [16, 28–30] are common Recurrent Neural Networks. but they have the problems of gradient disappearance and gradient explosion. LSTM is an improved version based on RNN, which can solve the problem of gradient vanishing and gradient explosion. It has a good performance in the fields of speech recognition, language modeling and machine translation. At the same time, it is also used in all kinds of problems with time series attributes. To understand Bidirectional GRU, we must first understand GRU [31, 32]. GRU is a variant of LSTM network, which is simpler than LSTM. Unlike LSTM, which has three gates (input gate, forgetting gate and output gate [33]), GRU has only two gates (update gate and reset gate [34]). The function of update gate is similar to forgetting gate and input gate in LSTM. It determines which information to forget and which new information to add and update. The reset gate is used to decide which part of the previous information is not important for the current time calculation. Because the number of gating of GRU is less than LSTM, GRU is faster than LSTM in calculation. The structure of GRU is shown in Fig 2. GRU calculation formula is as follows:

Fig 2

GRU structure diagram.

Where σ is the sigmoid activation function, which is used to compress all the output data between 0 and 1. The sigmoid function and its derivation formula are shown in formula 7 and formula 8. W and W are the weights of update gate z and reset gate r respectively. h is the past information, h contains the past information h and the present information . The present information is determined by the past information h and the current input. The model structure of Bidirectional GRU [35-37] is similar to GRU model. There is a positive time series and a reverse time series. The results corresponding to the last state of the positive time series and the reverse time series are combined as the final output results. The model can make use of the past and future information at the same time. In this paper, we use Bidirectional GRU model. The network in Fig 3 contains two sub networks: forward status and backward status, which represent forward transmission and backward transmission respectively.

Fig 3

BGRU structure diagram.

Method based on fs-cnn-bgru

The hybrid model based on FS-CNN-BGRU proposed in this paper includes FS, CNN and BGRU. FS is used for feature selection, CNN is used for feature extraction, and BGRU is used for processing data with time series. In this paper, the hybrid model is divided into six parts: input layer, FS Normalization layer, CNN layer, BGRU layer, full connection layer and output layer. Most of the prediction methods used are CNN-BGRU. The CNN module includes convolution kernel, pooling layer and flatten layer. Convolution layer can be set to multilayer, so it has better ability of feature extraction. Similarly, setting the convolution core size can also improve the ability of feature selection. In order to maximize the utilization of data, the size of convolution kernel is usually set to n × n. The pool layer can also be set with multiple layers, and the size of each pool layer can also be set to n × n. Then the extracted data of CNN feature is sent to BGRU layer. Because BGRU has the ability to process time series attributes, the prediction accuracy of the model can be effectively improved by increasing the number of layers of BGRU and the number of units of each layer of BGRU. At the same time, the occurrence of over fitting can be well prevented by setting the dropout layer. Data can be output through BGRU layer, full connection layer and output layer. The FS-CNN-BGRU hybrid model proposed in this paper is improved based on CNN-GRU model. The practicability of CNN-GRU model has been elaborated in many papers, and good results have been achieved. FS-CNN-BGRU model uses the features extracted from CNN to be put into BGRU for prediction. BGRU has the ability to deal with time series very well. In time series, BGRU can solve the problem of gradient disappearance and gradient descent, and it has better performance than the GRU. Then in general, the stock data is many and miscellaneous, there are a lot of data for the model performance improvement is not big or has a reaction, so we need to use FS method to select features, so that the model can play the best performance. This paper constructs a complete process based on FS-CNN-BGRU model. The specific experimental flow is shown in the “Experiment”.

If the prediction result is not good, adjust the number of CNN convolution cores and the number of BGRU units to get better results. The process of this experiment is shown in Fig 4. Firstly, the data is acquired, and then the acquired data is put into the FS-N layer (Feature Selection and Data Normalization), and then the data can get the data that can well represent the high dimensional features of the original data after passing through the CNN layer, and then the data is put into the bidirectional GRU with time series attributes, and finally the results are obtained and predicted through the full connection layer and output layer to evaluate the performance of the model.

Fig 4

Experiment flow chart.

Experiment

Get experimental data

Through various ways to obtain data, we select 8 dimensional data of Shanghai Composite Index, Shenzhen Composite index, CSI 300, Growth Enterprise Index, China National Petroleum Corporation (CNPC), China State Construction Engineering Corporation (CSCEC), China Railway Rolling stock Corporation (CRRC) and Shanghai Automotive Industry Corporation(SAIC) as input data, including the opening price, the highest price, the lowest price, the previous closing price and trading volume, and the closing price as forecast data. Some data of Shenzhen Composite Index is shown in Table 1.

Table 1

Some data of Shenzhen Composite Index.

No	Closing	Hight	Low	Open	Previous Closing	Rise and Fall	Up and Down	Volume
1	14134.9	14134.9	13819.7	13858.7	13854.1	280.7	2.0	1.47E+11
2	13854.1	13939.9	13806.6	13911.8	13889.9	-35.8	-0.3	1.22E+11
3	13889.9	13901.8	13688.8	13746.3	13751.1	138.8	1.0	1.30E+11
4	13751.1	13807.2	13709.8	13791.4	13763.3	-12.2	-0.1	1.11E+11
5	13763.3	13783.0	13641.7	13682.3	13692.1	71.2	0.5	1.08E+11

Data preprocessing

In order to induce the statistical distribution of sample data and improve the training speed of neural network, we need to normalize the data. The normalization formula is as follows: Where X ⋅ min(axis = 0) is the row vector composed of the minimum value in each column, and X ⋅ max(axis = 0) is the row vector composed of the maximum value in each column. and are the maximum and minimum values respectively, and their default values are 1 and 0 respectively. X and X are the results of standardization and normalization respectively.

Data division

This paper uses the opening price, the highest price, the lowest price, the previous closing price, the range of rise and fall, the amount of rise and fall and the trading volume of Shanghai Composite Index, Shenzhen Composite Index, CSI 300, Growth Enterprise Index, CNPC, CSCEC, CRRC and SAIC from January 1991 to December 2020as the data input and the closing price as the data output. At the same time, the proportion of the data is divided into 8:2 That is, the first 80% of the data is used as the training set, and the last 20% as the test set.

Experiment environment

This experiment uses Intel i7-10700 8 core 16 thread processor, 16GB memory, win10 operating system, anaconda3 as the experimental platform, python language programming. The deep learning framework uses Keras in Tensorflow 2.0, which is powerful and concise. It provides users with many interfaces to help them quickly build their own models.

The construction of model

The normalized data set is divided into training set and test set, and then the training set is put into the model for training. However, as the input value of the neural network before the nonlinear transformation increases with the depth of the network, its distribution will gradually shift or change, which leads to the gradual disappearance of the gradient of the underlying neurons in the back propagation, which is why the convergence speed of the neural network will be slower and slower. Batch normalization (BN) [38] is to force the input number of neurons in any layer back to the normal distribution with the mean value of 0 and the variance of 1 by some normalization methods, which can solve this kind of problem well and greatly accelerate the convergence speed of neural network in the training process. The calculation formula of BN is as follows: Where x is the input value, y is the output value after BN normalization, and m is the size of each mini batch, that is, the mini batch with m inputs. is the average of all inputs in the same Mini batch. is the variance of all outputs in the same Mini batch. Then the normalized value is obtained by and , and the formula (12) is brought into the formula (13) to obtain the output value y, γ and β are obtained by machine learning. So far, the BN algorithm can be used to normalize the data of neurons in each layer of neural network, so as to improve the training speed of neural network.

In BGRU layer, MSE is used as loss function, Adam as optimizer, learning rate is 0.001, batch size is 64. The purpose of training is to make the predicted value and the real value as small as possible. In order to ensure that the experimental data are real and effective, we only put the training data into the model for training, and the test set does not participate in the training. Each training data is put into the FS-CNN-BGRU model to calculate the predicted value, and the difference between the real value and the predicted value is compared. Then the gradient descent algorithm in the optimizer is used to update the weight of each parameter in the FS-CNN-BGRU model. With the continuous updating and iteration, the prediction results of FS-CNN-BGRU model will be more and more accurate. After the training of FS-CNN-BGRU model, put the test set into the model to predict and get the prediction results, and then compare the prediction results with the real value to get the error, so as to evaluate the performance of FS-CNN-BGRU stock prediction model. However, there are many problems in the process of model training. For example, underfitting and overfitting, underfitting is caused by insufficient data or insufficient training times. The solution is very simple, that is to increase the amount of data and training times. The main performance of overfitting is that it performs well in the training set, but it does not perform well in the test integration. There are two ways to solve this problem: (1) train the results before the overfitting occurs, so as to obtain the best performance. (2) Increase the proportion of dropout layer and dropout. Therefore, adding dropout appropriately in CNN and BGRU layers can effectively suppress the occurrence of overfitting.

Evaluating indicator

The evaluation indexes used in this paper are MAPE and R2. The two evaluation indexes are shown in formulas 14 and 15. Where n is the number of samples, is the predicted value, and y( is the real value. Where m is the number of samples, is the predicted value, y is the real value, and is the sample mean value.

Experimental result

In order to improve the persuasiveness of FS-CNN-BGRU model results, CNN, LSTM, GRU, CNN-LSTM and CNN-GRU methods are added for horizontal comparison, and all methods used in the test use the same number of cores and units to eliminate the influence of all different factors.

Firstly, we divide the eight stocks mentioned above into two categories: index stocks and common stocks, and then select the data from January 1, 1991 to December 31, 2020 as the data input, and then, the number of convolution kernels is 8, and the data not using feature selection and using feature selection are put into the model to view the results. Table 2 shows the results of the selection of non use feature selection and use feature selection of index stocks (%).

Table 2

MAPE value of index stock obtained by different methods (%).

Method/Stock	Shenzhen Composite Index	CSI 300	Shanghai Composite Index	Growth Enterprise Index
Common	6.5435	2.2448	3.7110	3.0161
Feature Selection	5.2200	1.8972	1.4878	2.5249

It can be seen from Table 2 that the MAPE values of four index stocks after using feature selection are lower than those without using feature selection. In order to further verify the effectiveness of feature selection, four common stocks are also compared by using feature selection. Table 3 shows the results of common stock not using feature selection and using feature selection (%).

Table 3

MAPE value of common stock obtained by different methods (%).

Method/Stock	CNPC	CSCEC	CRRC	SAIC
Common	4.2740	2.3357	3.1741	6.9912
Feature Selection	2.7476	1.8167	2.4024	6.0518

From Table 3, it can be concluded that the MAPE values of four common stocks after using feature selection are lower than those without using feature selection, so it can be concluded that the MAPE values of two kinds of stocks after using feature selection are reduced, which meets the experimental requirements.

Training model

Determine the number of convolution kernels

The next step is to test the influence of each number of convolution kernel and unit number on the final result (all the next experiments are the experimental data after adding feature selection), select 8, 16, 32 and 64 convolution cores in the convolution layer to compare their MAPE values. Table 4 shows the influence of different convolution cores in CNN layer on index stocks (%).

Table 4

MAPE values of index stocks in convolution kernels with different numbers (%).

Filters/Stock	Shenzhen Composite Index	CSI 300	Shanghai Composite Index	Growth Enterprise Index
8	5.2200	1.8972	1.4878	2.5249
16	4.3932	1.4162	1.3944	2.3679
32	2.0601	1.2630	1.1426	2.0635
64	2.4203	1.2754	1.2538	2.4133

From Table 4, we can see that the error of the four index stocks decreases with the increase of the number of convolution kernels. When the number of convolution kernels in CNN layer is 32, the error reaches the minimum, but when the number of convolution kernels reaches 64, the error increases instead, which may be caused by overfitting.

Next, we test the performance of different convolution kernels in common stock. Table 5 shows the MAPE values (%) of different convolution kernels in common stock.

Table 5

MAPE value of common stock in convolution kernel with different number (%).

Filters/Stock	CNPC	CSCEC	CRRC	SAIC
8	2.7476	1.8167	2.4024	6.0518
16	2.4746	1.5089	2.3298	5.9222
32	2.2877	1.4477	2.0507	4.4605
64	2.3147	1.4635	2.1675	5.0786

From Table 5, it is not difficult to see that in common stocks, with the increase of the number of convolution kernels, the accuracy of the model also decreases as the result of the previous table. At the same time, when the number of convolution kernels reaches 64, the error increases instead of decreasing, which confirms the conjecture in the previous table: with the increase of the number of convolution kernels, the error increases because model is overfitted.

Determine the number of lstm units

Next, we test the impact of different number of units on stock data in LSTM. Similarly, we also divide the data set into two categories: index stocks and common stocks, and test the results of different number of units on the performance of two types of stocks. The number of units selected in LSTM is the same as that of convolution kernel selected in the last experiment, which is 8, 16, 32 and 64 units. Table 6 shows the influence of different number of units on Index Stocks (%).

Table 6

MAPE value of index stocks in different number of units (%).

Units/Stock	Shenzhen Composite Index	CSI 300	Shanghai Composite Index	Growth Enterprise Index
8	3.6526	1.3408	1.2452	2.0463
16	3.5708	1.2697	1.1991	1.8528
32	2.2845	1.2530	1.1397	1.8242
64	1.8654	1.1819	1.1049	1.7784

From Table 6, we can see that with the increase of the number of units, the error of each index stock also decreases. When the number of units reaches 64, the error is the smallest, which is lower than that of other different units. Then test the performance of different unit numbers in common stock. Table 7 shows the effect of different number of units on common stock (%).

Table 7

MAPE value of common stock in different number of units (%).

Units/Stock	CNPC	CSCEC	CRRC	SAIC
8	2.8631	1.4263	2.0908	3.0975
16	2.6367	1.2880	1.9241	2.6892
32	2.4953	1.2587	1.8071	2.3812
64	2.3027	1.2461	1.7875	2.3514

From Table 7, we can see that with the increase of the number of units, the prediction accuracy of common stocks becomes higher and higher. When the number of units reaches 64, the error is the smallest, which is also consistent with the prediction of index stocks in Table 6. Because this paper is based on the hybrid model of FS-CNN-BGRU, after obtaining the best number of CNN and LSTM units, the number of GRU and BGRU units is set to 64, so in the next experiment, the number of convolution cores of CNN is finally selected as 32, and the number of units in BGRU is selected as 64 to ensure the correctness and unity of the experiment.

Table 8 shows the parameters of FS-CNN-BGRU model. The model is divided into four layers: input layer, convolution layer, BGRU layer and output layer. The convolution layer is set to 1 layer, the number of convolution cores is 32, the size of convolution core is 1 × 1, stripe is set to 1, padding is the same, Tanh is used as the activation function, Max-Pooling is used as the Pooling layer, padding is set to 1, and Relu is used as the activation function. The bidirectional GRU is set to 1 layer with 64 units. The BGRU network time step is set to 50 to predict the closing price of the 51st day. The gradient descent algorithm uses Adam and iterates 100 times.

Table 8

Parameters of FS-CNN-BGRU model.

Parameter name	Parameter value
Network layers	4
Convolutional filters	32
Convolutional kernel size	1 × 1
Convolutional activation function	Tanh
Convolutional padding	Same
Pooling size	1 × 1
Pooling padding	Same
Pooling activate function	Relu
Number of BGRU layers	64
Batch size	64
Optimization	Adam
Epochs	100

Taking the Shenzhen Composite Index as an example, we choose the data of the stock from January 1, 1991 to December 31, 2020 as the input data of the model, and add these data for normalization, and take the first 80% of the data as the training data, the last 20 as the test data, and use MAPE as the evaluation index of the model. In order to better test the performance of this model, we add five other methods for comparison. Through Feature Selection, we can calculate which features are helpful to improve the accuracy of the model, so as to achieve the compression of the dimension of feature space, that is, to obtain a group of data with less precision and least fitting error, CNN can well put forward the characteristics of the input data, and LSTM can have a good performance in the data with time series, so [14] proposed a CNN-LSTM stock prediction model.

Table 9 shows the MAPE values of different hybrid models in Shenzhen stock index. It is not difficult to see from Table 9 that the prediction error (MAPE) of FS-CNN-BGRU hybrid model is 1.4325%, that of CNN-GRU is 1.6354%, that of CNN-LSTM is 1.6426%, that of GRU is 1.8332%, that of LSTM is 1.8654%, and that of CNN is 2.0601%. From these data, the MAPE value of FS-CNN-BGRU is lower than that of CNN-GRU and other four models. It can be seen from Table 10 that the performance of FS-CNN-BGRU stock prediction model R2 proposed in this paper is also higher than other models. Although the performance of FS-CNN-BGRU hybrid model is higher than other models, there is still room for improvement.

Table 9

MAPE values of different methods (%).

Model	MAPE (%)
CNN	2.0601
LSTM	1.8654
GRU	1.8332
CNN-LSTM [14]	1.6426
CNN-GRU	1.6354
FS-CNN-BGRU	1.4325

Table 10

R2 of different methods.

Model	R 2
CNN	0.971365
LSTM	0.977786
GRU	0.978228
CNN-LSTM [14]	0.981674
CNN-GRU	0.980416
FS-CNN-BGRU	0.983808

Comparison of results of various models

In order to better verify the prediction ability of FS-CNN-BGRU model, seven other stocks are added for experimental comparison. Tables 11 and 12 show the performance of MAPE in index stocks and common stocks respectively (%). Tables 13 and 14 show R2’s performance in index stocks and common stocks respectively. The forecast chart (real price and prediction price) of the eight stocks are shown in Figs 5–12.

Table 11

MAPE value of index stocks (%).

Model	Shenzhen Composite Index	Growth Enterprise Index	CSI 300	Shanghai Composite Index
CNN	2.0601	2.0635	1.2630	1.1426
LSTM	1.8654	1.7784	1.1819	1.1049
GRU	1.8332	1.7675	1.0580	1.0877
CNN-LSTM [14]	1.6426	1.7641	1.0430	1.0139
CNN-GRU	1.6354	1.7540	1.0424	1.0749
FS-CNN-BGRU	1.4325	1.6684	0.9892	1.0614

Table 12

MAPE value of common stock (%).

Model	CNPC	CSCEC	CRRC	SAIC
CNN	2.2887	1.4477	2.0507	3.0975
LSTM	2.3027	1.2461	1.7875	2.3514
GRU	2.0583	1.2220	1.7651	2.5513
CNN-LSTM [14]	2.0538	1.1891	1.6374	2.3029
CNN-GRU	2.1456	1.2022	1.6376	2.1789
FS-CNN-BGRU	1.7033	1.1714	1.6081	2.0926

Table 13

R2 of index stocks.

Model	Shenzhen Composite Index	Growth Enterprise Index	CSI 300	Shanghai Composite Index
CNN	0.971365	0.985536	0.977826	0.977393
LSTM	0.977786	0.990884	0.979814	0.978607
GRU	0.978228	0.990928	0.983899	0.979678
CNN-LSTM [14]	0.981674	0.990064	0.984244	0.981210
CNN-GRU	0.980416	0.989636	0.984310	0.979707
FS-CNN-BGRU	0.983808	0.991125	0.985729	0.979842

Table 14

R2 of common stock.

Model	CNPC	CSCEC	CRRC	SAIC
CNN	0.993983	0.991586	0.965107	0.995745
LSTM	0.993494	0.994723	0.973520	0.997467
GRU	0.993616	0.995183	0.974131	0.997353
CNN-LSTM [14]	0.994447	0.994956	0.975138	0.997888
CNN-GRU	0.994152	0.995007	0.976248	0.997752
FS-CNN-BGRU	0.995694	0.995020	0.978322	0.997749

Fig 5

Closing price of Shenzhen Composite Index.

Fig 12

Closing price of SAIC.

By comparing CNN, LSTM, GRU, CNN-LSTM and CNN-GRU, the performance of FS-CNN-BGRU hybrid model is generally better. It can be seen from Tables 11 and 12 that the performance of CNN model is the worst for both index stocks and common stocks. The performance of LSTM and GRU models is better than CNN model, but the results are still not very ideal. From the perspective of index stocks, the forecast results of FS-CNN-BGRU hybrid model are 1.4325%, 1.6684%, 0.9892% and 1.0614% respectively, which are higher than other hybrid models. From the perspective of common stocks, FS-CNN-BGRU hybrid model’s forecast results are 1.7033%, 1.1714%, 1.6081% and 2.0926%, which are also higher than other hybrid models. However, it is not difficult to find that the CNN-LSTM stock prediction model proposed in [14] outperforms CNN-GRU in the first three stocks. This may be because the gradient of CNN-LSTM hybrid model in the three stocks is deep and the error is small, so the prediction result is higher than that of CNN-GRU hybrid model. However, the performance of FS-CNN-BGRU hybrid prediction model proposed in this paper is better than that of CNN-LSTM prediction model proposed in [14].

However, it can be seen from Tables 13 and 14 that the FS-CNN-BGRU model proposed in this paper performs well in CNPC and CRRC, but not well in the other two stocks, and the CNN-LSTM model performs best in SAIC. From Tables 11 and 14, we can find that the FS-CNN-LSTM stock forecasting model proposed in this paper has achieved the best results compared with other models, but from Tables 13 and 14, we can know that the model has room for optimization.

All the experimental data prove the accuracy and effectiveness of FS-CNN-BGRU hybrid model in stock forecasting. Although the prediction results of CNN, LSTM, GRU, CNN-LSTM and CNN-GRU hybrid models are also very good, the prediction results of FS-CNN-BGRU are better than them to some extent. This further proves that it is feasible to use CNN to extract features and then use BGRU to predict the data with time series attributes. It provides a new investment idea for shareholders and stock investors.

Conclusion

In this paper, convolutional neural network is responsible for feature extraction. It convolutes the features of the input data to obtain high-order features that can represent the data. LSTM and GRU can process the data with time series attributes because of their own unique attributes. Although a single neural network model (CNN, LSTM and GRU) can better predict the trend of stock closing price, the stock price is still affected by many factors, such as natural disasters, people’s emotions, politicians’ attitudes and the management ability of the local government. Therefore, a single stock prediction model can’t further predict the stock price, so there is an attempt to apply it The idea of merging multiple single models into a new hybrid model. According to the characteristics of stocks with many dimensions and huge and complex stock data, this paper proposes a stock forecasting model based on FS-CNN-GRU, which takes the data other than the closing price as the data input and the closing price as the output of the model, sets the time step to 50 and forecasts the closing price of the 51st day, and adds some other methods as horizontal comparison to judge the validity of the model Actual performance. The experimental results show that the proposed stock forecasting model has lower error than other methods, which proves the availability of the model in stock forecasting.

Although the model proposed in this paper can achieve good performance in stock forecasting, it still faces many challenges in stock forecasting: first, the stock data used in this paper are all from China’s stock market, and do not predict foreign stock markets. Second, the parameter adjustment of CNN and BGRU needs to be further strengthened. It is believed that the model can achieve better results among the stocks through in-depth parameter adjustment. In addition, although FS-CNN-BGRU hybrid model is used in this paper, I believe there are many hybrid models not mentioned in this paper that can further reduce the error of stock forecasting model, which is what we need to do, At the same time, some algorithms [39] can be added to the model to improve the effectiveness of the model. However, I think the FS-CNN-BGRU hybrid stock forecasting model proposed in this paper can help investors and investors make correct decisions in the stock market to a certain extent.

23 Jul 2021

PONE-D-21-21056

Stock Prediction Based on Bidirectional Gated Recurrent Unit with Convolutional Neural Network and Feature Selection

PLOS ONE

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Reviewer #1: Yes

Reviewer #2: Partly

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Reviewer #1: Yes

Reviewer #2: No

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Reviewer #1: Yes

Reviewer #2: No

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Reviewer #1: The questions raised in the introduction are properly answered in the conclusions. The results are efficient and promising.

It would be better if more literature could cited to support the relevant studies. It is suggested to cite the following literature to enrich the related work.

Song, T.; Wang, Z.; Xie, P.; A novel dual path gated recurrent unit model for sea surface salinity prediction. Journal of At-mospheric and Oceanic Technology, 2020, 37, 317-325.

Pang S, Xie P, Xu D, Meng F, Tao X, Li B, Li Y, Song T. NDFTC: A New Detection Framework of Tropical Cyclones from Meteorological Satellite Images with Deep Transfer Learning. Remote Sensing. 2021; 13(9):1860. https://doi.org/10.3390/rs13091860

Meng F, Song T, Xu D, et al. Forecasting tropical cyclones wave height using bidirectional gated recurrent unit[J]. Ocean Engineering, 2021: 108795.

Song, T.; Jiang, J.; Li, W. A deep learning method with merged LSTM Neural Networks for SSHA Prediction. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2020, 13, 2853-2860.

Also, the font colour in Figure 2 is too light and it is recommended that it be changed to a darker colour.

Besides, in the acknowledgements section, it is suggested that the specific work of the individual authors be listed.

Reviewer #2: 1、Many words in the text have “-“ in the middle, such as “variable” in line 31, line 36 “effectively”, line 66 “increase”, line 82 “follow”, etc. In line 43, the first letter of “The” should not be capitalized.

Abstract：

2、The second sentence in the abstract wants to express the advantages of deep learning over traditional machine learning, so the comparative level is more appropriate here. "Achieve good fitting effect" is suggested to be changed to "achieve better fitting effect".

3、In the final description of the abstract, you can use refined language to add some information, such as which single comparison models were used, and the specific results show that the mixed model is better.

Research Methodology- Feature Selection (FS)- Filter Selection：

4、The explanation of formula (1) in Filter Selection is not clear enough. Only the meaning of x_i^j is explained in the article, and the other variables are not explained.

Method Based on FS-CNN-BGRU：

5、 The FS-CNN-BGRU method introduced in lines 177-189 only introduces the general process, but the organization and description of the steps are not perfect. It is recommended that you start with a subtitle for each step, and then introduce this step, and the format of the subtitle is as uniform as possible.

The fourth step of the general process is the establishment of the FS-CNN-BGRU model. Although the specific process has been described in the text above, a simple summary here will make the description of the steps more complete.

Experiment- The Construction of Model：

6、The segment of line 252 is too long. It is recommended to segment after “In” at the end of the line.

Experiment- Evaluating Indicator：

7、Why choose two evaluation indicators: MAPE and R^2？Which aspects of the model are evaluated separately by these two evaluation indicators?

Experimental Result：

8、There are no small headings in the experimental results. In order to make the structure clearer, the part should be divided into small headings according to different experimental settings.

9、Figure 5 ~ 12 did not find the corresponding explanation or reference in the text.

10、The optimal setting of the number of GRU units in the hybrid model is determined according to LSTM model. Why not directly use GRU to experiment and determine the optimal number of units?

11、The time step of the experiment is set to 1 day for forecast of 50 days. How is the time step of 50 days determined? If other step size FS-CNN-BGRU models are used, can they still achieve the best results?

**********

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31 Jul 2021

Dear editor and reviewers:

Thank you for your letter and the reviewers’ comments on our manuscript entitled" Stock prediction based on bidirectional gated recurrent unit with convolutional neural network and feature selection". Your comments are of great help and guiding significance for improving the quality of this paper, improving the author's writing level and future scientific research. We have carefully studied the reviewers' comments and made corresponding amendments. Meanwhile, we apologize to the reviewers for the trouble caused by this manuscript. The reply to the comments is as follows (the reply is shown in blue).

Replies to the reviewers’ comments:

Reviewer #1:

1). The questions raised in the introduction are properly answered in the conclusions. The results are efficient and promising. It would be better if more literature could cited to support the relevant studies. It is suggested to cite the following literature to enrich the related work.

Response: Thank you for your valuable suggestions on revising this manuscript. Now we have added the four references you mentioned to the manuscript to enrich the relevant work. See [5], [31], [33], [38] for details.

2). Also, the font colour in Figure 2 is too light and it is recommended that it be changed to a darker colour.

Response: Responding to your request, we have changed the font color to a deeper color for viewing.

3). Besides, in the acknowledgements section, it is suggested that the specific work of the individual authors be listed.

Response: Your suggestion is very useful to us. We have added the relevant information of the three authors mentioned in the manuscript to the acknowledgements section.

Reviewer #2:

1). Many words in the text have “-“ in the middle, such as “variable” in line 31, line 36 “effectively”, line 66 “increase”, line 82 “follow”, etc. In line 43, the first letter of “The” should not be capitalized.

Response: Thank you very much for pointing out the problems for this manuscript. This is our negligence, and we apologize. Now we have examined the whole manuscript and removed irrelevant information.

2). The second sentence in the abstract wants to express the advantages of deep learning over traditional machine learning, so the comparative level is more appropriate here. "Achieve good fitting effect" is suggested to be changed to "achieve better fitting effect".

Response: Thank you for your suggestion. We have changed "achieve good fitting effect" to "achieve better fitting effect".

3). In the final description of the abstract, you can use refined language to add some information, such as which single comparison models were used, and the specific results show that the mixed model is better.

Response: Your modification comments are very valuable to us, Thank you very much. We added the following information to the final description of the summary: In the experiment, we used single CNN, LSTM and GRU models and mixed models CNN-LSTM, CNN-GRU and FS-CNN-BGRU (the model used in this manuscript).

4). The explanation of formula (1) in Filter Selection is not clear enough. Only the meaning of x_i^j is explained in the article, and the other variables are not explained.

Response: The lack of other relevant information about Formula 1 is our problem. So we add the following statement to explain other variables in the manuscript: (1) The construction method is as follows: Selecting the nearest neighbor $x_{i, n h}$ from the similar samples of $x_i$ , which is called guessing the nearest neighbor. Selecting a nearest neighbor $x_{i, n m}$ in heterogeneous samples is called guessing the wrong nearest neighbor. (2) It can be seen from the above formula that for the value corresponding to a feature, the closer the same kind is, the farther the different kind is, and the larger corresponding statistics will be.

5). The FS-CNN-BGRU method introduced in lines 177-189 only introduces the general process, but the organization and description of the steps are not perfect. It is recommended that you start with a subtitle for each step, and then introduce this step, and the format of the subtitle is as uniform as possible. The fourth step of the general process is the establishment of the FS-CNN-BGRU model. Although the specific process has been described in the text above, a simple summary here will make the description of the steps more complete.

Response: Thank you for your valuable comments. Now we have deleted the contents of lines 177-189 and put them into the "Experiment".

6). The segment of line 252 is too long. It is recommended to segment after “In” at the end of the line.

Response: Responding to your request, we have listed "In" and the content after "In" as a separate paragraph.

7). Why choose two evaluation indicators: MAPE and R^2？Which aspects of the model are evaluated separately by these two evaluation indicators?

Response: We are very sorry for your questions about this manuscript. We have made the following explanations: (1) during the experiment, if other evaluation indexes are used, the following problems may occur: if the stock price of the selected stock is not high, the accuracy of the model is not high, but the results calculated by using other evaluation indexes may be very good. On the contrary, if the stock is very high, the accuracy of the model is also very high, but the calculated results are not good, In other words, the quality of the model completely depends on the stock price, which is unacceptable. Therefore, an objective evaluation index should be selected to measure the quality of the model, so MAPE is selected. However, a single MAPE can not well evaluate the quality of the model, so R^2 is added. (2) The full name of MAPE is Mean Absolute Error. MAPE evaluates the accuracy of the model. 0% is the perfect model and 100% is the inferior model. The closer it is to 0%, the better. R ^ 2 also evaluates the accuracy of the model. 0 is the inferior model and 1 is the perfect model. The closer it is to 1, the better. These two evaluation indicators can accurately evaluate the advantages and disadvantages of a model.

8). There are no small headings in the experimental results. In order to make the structure clearer, the part should be divided into small headings according to different experimental settings.

Response: Your suggestions are very helpful to improve the quality of our manuscript. Thank you for your suggestions. We have added the following small headings according to your requirements: Determine the number of convolution kernels, Determine the number of lstm units and Comparison of results of various models.

9). Figure 5 ~ 12 did not find the corresponding explanation or reference in the text.

Response: This is our negligence. We apologize again. Now we have put "The forecast chart (real price and prediction price) of the eight stocks are shown in Figure 5 to 12" in lines 363-364 of the manuscript.

10). The optimal setting of the number of GRU units in the hybrid model is determined according to LSTM model. Why not directly use GRU to experiment and determine the optimal number of units?

Response: Thank you for your question. Our answers to your question are as follows: because the model used in the comparative paper [14] is LSTM and GRU is a variant of LSTM, so the LSTM model is used to determine the best setting of the number of GRU units in the hybrid model.

11). The time step of the experiment is set to 1 day for forecast of 50 days. How is the time step of 50 days determined? If other step size FS-CNN-BGRU models are used, can they still achieve the best results?

Response: We are very sorry for your confusion in this regard. We select the data from January 1, 1991 to December 31, 2020 as the data input (assuming 2000 days of data), and then randomly select a time step of 100, that is, use the data from the first day to the 100th day to predict the data of 101 days, and so on to get the data of 2000 days - 100 days = 1900 days. Then, put the data of 1900 days into the model for prediction and compare the results. On this basis, we also use other time steps to predict the stock price. Other time steps sometimes perform well, but in general, for the eight stocks in the manuscript, 50 days is the best time step.

Kind regards

Qihang Zhou

Email: 825605142@qq.com

Xiao Wang

Email: tianzhu213@zjnu.cn

Corresponding author: Changjun Zhou

E-mail address: zhou-chang231@163.com

Submitted filename: Response to reviewers.docx

Click here for additional data file.

27 Dec 2021

Stock prediction based on bidirectional gated recurrent unit with convolutional neural network and feature selection

PONE-D-21-21056R1

Dear Dr. Zhou,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication.

An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org.

Kind regards,

Tao Song

Academic Editor

PLOS ONE

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Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Partly

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Every suggestion is taken seriously, which is a remarkable and admirable attitude.

The Submission has been greatly improved and is worthy of publication.

My advice is to accept this article as soon as possible. This paper will play an active and important role in the research of related fields.

Reviewer #2: The author answered all my questions very specifically and I have no further comments, so I guess it's acceptable.

**********

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Reviewer #1: No

Reviewer #2: No

27 Jan 2022

PONE-D-21-21056R1

Stock prediction based on bidirectional gated recurrent unit with convolutional neural network and feature selection

Dear Dr. Zhou:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

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on behalf of

Dr. Tao Song

Academic Editor

PLOS ONE