RETRACTED

Mathematical Problems in Engineering and the authors have retracted the article titled “A Bimodel Algorithm with Data-Divider to Predict Stock Index” [1] due to errors identified in the figures and data by the authors.

The programs used were modified by the authors during the study, and it was identified that Figures 2 and 3 in the published article do not correspond with the test sets. Figures 4, 5, 8, and 9 are incorrect as a result of this error.

The authors apologized and requested the retraction of the article, which has been in agreement with the editorial board.

Mathematical Problems in Engineering
Volume 2018 (2018), Article ID 3967525, 14 pages
https://doi.org/10.1155/2018/3967525

Research Article

A Bimodel Algorithm with Data-Divider to Predict Stock Index

Zhaoyue Wang, Jinsong Hu, and Yongjie Wu

School of Computer Science & Engineering, South China University of Technology, Guangzhou, Guangdong 510006, China

Correspondence should be addressed to Jinsong Hu; cshjs@scut.edu.cn

Received 12 August 2017; Accepted 30 January 2018; Published 5 March 2018

Academic Editor: Daniela Boso

Copyright © 2018 Zhaoyue Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

There is not yet reliable software for stock prediction, because most experts of this area have been trying to predict an exact stock index. Considering that the fluctuation of a stock index usually is no more than 1% in a day, the error between the forecasted and the actual values should be no more than 0.5%. It is too difficult to realize. However, forecasting whether a stock index will rise or fall does not need to be so exact a numerical value. A few scholars noted the fact, but their systems do not yet work very well because different periods of a stock have different inherent laws. So, we should not depend on a single model or a set of parameters to solve the problem. In this paper, we developed a data-divider to divide a set of historical stock data into two parts according to rising period and falling period, training, respectively, two neural networks optimized by a GA. Above all, the data-divider enables us to avoid the most difficult problem, the effect of unexpected news, which could hardly be predicted. Experiments show that the accuracy of our method increases 20% compared to those of traditional methods.

1. Introduction

People have been trying to predict stock prices or indexes since a successful prediction means huge income. However, from the point of view of system theory, the formation mechanism of stock price is a nonlinear system with a high degree of complexity [1], so it is difficult to predict. With the development of neural networks, its strong nonlinear fitting ability has shown huge potential in stock prediction. According to predicted objects about stocks, there are two primary methods to construct neural networks models for stock prediction.

Most scholars prefer the first method, predicting an exact stock price or index (exact prediction for short). Qiu et al. tried to predict the return of Nikkei 225 index by combining the performance of the accuracy of prediction and run time and concluded that the hybrid of genetic algorithm (GA) and backpropagation (BP) provides more accurate forecasting of future values than other prediction models [2] do. In J. Wang and J. Wang’s paper, they introduced the stochastic time effective neural network with principal component analysis model to forecast the indexes of Shanghai Stock Exchange (SSE), Hong Kong Hang Seng 300 Index (HS300), Standard & Poor’s 500 Index (S&P500), and Dow Jones Industrial Average Index (DJIA). Their results show that the proposed neural network model improves the accuracy of forecasting results [3]. In Al-Hnaity and Abbod’s paper, they proposed a hybrid ensemble model based on BP neural network and EEMD to predict FTSE100 closing price. The results show that this method can effectively reduce the stock price prediction error [4]. The accuracy of this kind of prediction methods seems very high, but it is still not enough to help stock investors to make a decision since the fluctuation of a stock price or index usually is no more than 1% in a day (that is to say, prediction accuracy should be up to 99.5%).

The others, a few scholars, prefer the rise or fall of a stock index (trend prediction for short) to its exact numerical value. In Wang et al.’s paper, they used an NNK-ELM model which is based on market news and stock prices to forecast Hong Kong stock indexes. The prediction results show that the proposed method is better than the traditional BP algorithm in trend prediction accuracy [5]. Sun and Gao directly used the forecast accuracy of the stock trend as the criterion of their model. They proposed a hybrid BP neural network combining adaptive particle swarm optimization algorithm (HBP-PSO) to predict the stock price of “Zhong Guo Yi Yao” (600056). The results support that the trend prediction accuracy of HBP-PSO is better than that of the simple neural network [6]. Using this criterion can ensure the prediction accuracy of the up and down signals of stock price to reduce the possibility of trading errors.

For most stock investors, forecasting whether a stock price or index will rise or fall (trend prediction) is enough to make a decision, buying or selling. Therefore, the second method is more practical than the first. However, the second way does not yet work very well. One important reason is that different periods of a stock market, for example, rising period and falling period, have different inherent laws and scholars usually use a single neural networks model and the same set of parameters to deal with the different periods [5, 6]. Another reason, the most difficult problem, is the effect of unexpected news, which could hardly be predicted. Recently, some scholars try to deal with the problem through collecting and mining present financial information [7, 8]. However, the effect of the information is difficult to quantize and the relationship between present information and future news is uncertain.

In this paper, we developed a data-divider to divide a set of historical stock data into two parts according to rising period and falling period, training, respectively, two neural networks optimized by a GA. Above all, the data-divider enables us to avoid the most difficult problem, the effect of unexpected news. Experiments show that the accuracy of our method increases 20% than those of traditional methods.

2. The General Frameworks of the Bimodel Algorithm with Data-Divider

The whole framework of the bimodel algorithm with data-divider (BADD) is shown as Figure 1. In Figure 1, arrow lines show directs of data flows. Arrow dotted lines indicate adjusting parameters. In the stage of training neural networks, GA optimizes parameters of BP1 and BP2 separately. After the stage, GA does not work.

Figure 1: The general framework of BADD. BP1 and BP2 are two BP neural networks. GA is a genetic algorithm.

In the following paragraphs, we will give details of all components of Figure 1 sequentially.

3. Input and Output

The input of Figure 1, real historical data, include current and previous two day’s closing values and volumes and current day’s KDJ index, MACD index, and RSI. The output of Figure 1 is predictive data, tomorrow’s closing value.

According to Joseph E. Granville’s theoretical research on volume-price relationship, volume is the leading indicator of stock price, so this paper uses volume as an important factor of the input. Based on the practical experience of stock exchange, too “old” stock data usually is insignificant for stock forecasting. Therefore, this paper chooses previous two days’ closing price and volume as two of input variables.

The Stochastic Oscillator (KDJ), including value, value, and value, is a momentum indicator [9]. When value, value, and value are all above 50, the stock market is in a bullish mood. When they are all below 50, the stock market is in a bearish mood. This paper treats as an input variable.

The moving average convergence (MACD) is widely used for medium- and long-term stock forecasting. Observing a MACD line, we can easily find out the bullish signal and the bearish signal. Therefore, this paper chooses the MACD value as an input variable.

The Relative Strength Index (RSI) defines a trading rule to measure the speed and change of price movements [9]. Therefore, this paper chooses RSI as part of the input.

As three typical reference indicators, MACD, RSI, and KDJ have become an essential reference standard for many stock traders. So, these three indicators also have psychological significance to a certain extent.

4. Data-Divider

As two different stages, rising period and falling period have different inherent laws. If we use the same neural network with the same parameters to predict stock, these complex data will easily cause the overfitting problems and reduce the neural network prediction accuracy. So, this paper proposes a data-divider to divide a historical data set into two different training data sets and use two models to train separately.

However, these data should not be roughly divided once and for all since the accidental fluctuation of stock markets complicate stock data. A long stock period include some short rising periods and falling periods, which may be nested within each other. Further, there is always a long-term rising with some small range fluctuations which will not affect the general trend. The falling period is so too.

The presented data-divider, as Figure 2 shows, can reduce the complexity of a data set and improve the prediction accuracy of neural networks. From this figure, we can see that those data in a small range of fluctuation (around 2%) are retained, for the reason that stock with absolutely monotonic trend without any fluctuation does not exist in actual stock market. Additionally, the data-divider “ignores” the data of big unexpected news making violent changes (the index drop or rise over 2%). That is to say, we do not try to predict the effect of big unexpected news but predict the following trend.

Figure 2: The data-divider.

5. Data Normalization

Sigmoid function is used as the activation function between the input layer and the hidden layer. The formula of this function is

Because the range of this function is between 0 and 1 and when the range is and , the trend of this function is smooth. However, stock data are very complicated. For example, trading volume could be very large, even reaching the level of , but the value of MACD is under the level of . After normalization, these data are unified into the same reference frame, which makes the calculation of next step easier.

We normalized input data to the range of . The normalization function is

is the result; is the value before normalizing; is the max value of the range.

6. The Approach to Combine BPNN and GA

BP neural network (hereinafter called BPNN) can achieve good results in stock forecasting [10–13]. On the one hand, BPNN may fast converge to a local optimal solution, but it can not ensure a globally optimal solution because of the problem of the local optimum. On the other hand, genetic algorithm (hereinafter called GA) can search the whole space, but its convergence rate is slow. GA-BP algorithm combines the two methods to fast obtain the global optimal solution. There are two different approaches to combine BPNN and GA.

First approach uses BPNN to optimize several different initial values and then obtains several local extreme values. GA combines these extreme values to get better values. However, this approach shows serious premature convergence and easily falls into local optimal solution [14].

Second approach uses a GA to obtain some low-precision solutions firstly. Starting from these solutions, BPNN makes local search to obtain some high-precision solutions. From the point of view of neural networks, the search of the GA is to obtain a group of better initial weights of the neural network than random initial weights. The local search by BPNN is to revise this group of initial weights and obtain the global optimal result. As a result, this approach got a better global solution than the first approach. Therefore, in this paper, we used the second approach. Figure 3 is the flow chart of the second approach.

Figure 3: The second approach to combine BPNN and GA.

6.1. Momentum Factor

Using momentum factor can not only minimize the error of the network, which easily falls into local minimum, but also speed up the convergence process of the algorithm [15]. After using momentum factor, the change of weight is

In this formula, is the momentum factor, with a domain of . If and are both positive or negative, this formula will accelerate convergence; if it is not the case, the speed of convergence will be reduced and greater stability will be achieved without falling into a local minimum. A dynamic method is adopted in choosing an appropriate momentum factor:

where is the number of iterations. A large momentum factor can speed up convergence in the BP algorithm. As the number of iterations increases, the momentum factor decreases. Therefore, the volatility of results is minimized.

6.2. L2 Regularization

The L2 Regularization can reduce weights, reducing the complexity of the network. This method can avoid overfitting problems caused by high network complexity and increases the accuracy of prediction. The formula of L2 Regularization is

where is the cost function and is the number of input vectors.

6.3. Details of the GA

Since this paper takes into account not only the error of the prediction results but also the trend prediction accuracy, the following fitness function is proposed:

where is the ideal output and is the prediction result. represents the result of trend prediction.

This paper uses the adaptive crossover rate and mutation rate algorithm mentioned in [16]. The formulae of this algorithm are

and represent the upper and lower limits of the value of crossover rate, respectively; and represent the upper and lower limits of the mutation rate value, respectively; is the maximum fitness of the population; is the average fitness; is the fitness of the individual currently in crossover process. This algorithm increases the crossover rates and mutation rates of individuals whose fitness values lie between and and decreases those of individuals whose fitness values lie between and . As a result, dominant individuals are retained, and disadvantaged individuals are changed.

The remainder stochastic sampling with replacement (RSSR) selection operator [17] is used and its basic steps are as follows.

Let the population size be and the sum of all individual fitness be sum. is defined as the fitness of the th individual, and the survival expectation of the th individual has the following explicit form:

Let be the new fitness of the th individual. Remaining individuals are generated by ordinary roulette method.

Compared with conventional roulette methods, this selection operator reduces the selection error so that individuals with fitness above average can survive to the next generation and increases population diversity. Therefore, the premature convergence problem of GA can be improved.

An arithmetic crossover operator [18] is used. In the case of longer chromosome, this method will generate better individual and avoid massive destruction of chromosome. Meanwhile, its computing efficiency is high. So, this method fits real-coded chromosomes better. The main operation is

In these two formulae, is a random parameter and or means a gene (a real number) on the chromosome of the individual to crossover before crossover. or means the gene after crossover.

Mutation operator plays a vital role in maintaining population diversity. A suitable mutation operator can greatly improve premature convergence problem of genetic algorithm. According to Bitwise mutation operator, for every gene on a chromosome, a random value is calculated, if is larger than the probability of mutation, another random number is calculated and added to the gene value. A mutation probability that is too high or too low will cause problem like heavy loss of excellent genes or premature convergence. Therefore, to keep a proper mutation probability, this paper chooses adaptive mutation probability.

7. Simulations

In this paper, the data-divider can divide a stock data set into two different data subsets, the rising one and the falling one. So, our system includes two models, rising model and falling model. The falling data set trains falling model and the rising data set trains the rising model. The following experiments will test them, respectively. A conventional method (called single model method in this paper), which uses the same neural network with the same parameter to train historical data, was used for comparison.

This paper focuses on actual stock exchange, which is nothing more than buying or selling. It is an obvious buying signal for the stock traders when the price trend of a stock is rising. And when the price trend of the stock is falling, the stock trader will sell it. In fact, the stock trader is more concerned about the future price trend of a stock, so this paper uses not only average error and maximum error as the criterion of experimental results, but also the accuracy of trend prediction as the criterion.

The formula of the error calculation is

where is the actual closing price and is the prediction result. The following formula was used to judging the trend prediction result

7.1. Trend Forecast for Rising Model in a Long Period of Index

The SSE index from 13 October 2009 to 29 January 2016 (1533 groups of samples) was selected as a training set. SSE indexes in four long periods which match the rising model from 15 June 2016 to 29 November 2016 were selected as test sets.

With the same GA-BP algorithm, the results of the rising model (one part of bimodel) and the single model are, respectively, listed in Table 1.

Table 1: Results of the rising model and the single model.

Average error
Maximum error
Trend accuracy

Rising model
0.00548318728116
0.0232548639991
0.745454545455

Single model
0.00688573345702
0.031534665601
0.6

In Figures 4 and 5, green lines represent closing prices, blue points represent prediction results and red points represent real closing prices. For each day, if the red point and the blue point are on the same side, it means that this trend prediction is accurate.

Figure 4: Rising model.

Figure 5: Single model.

From Table 2, we can easily see that, in four periods, trend prediction accuracy of the rising model method is about 20% higher than that of the single model method. These results prove that rising model can obtain not only lower prediction error but also higher accuracy of trend prediction. In the figure of single model, for most days, the red point is close to blue point but they are on the different side of the green line, which means prediction failure. So, the single model method may mislead the operation of the stock traders. Oppositely, in the figure of rising model, even if two points are far away, they are still on the same side of the green line, which means prediction success. So rising model, that is, the bimodel method, can greatly reduce misleading signals.

Table 2: Real data and prediction results of the rising model and the single model.

Time
Real closing price
Rising model
Single model

Prediction result
Prediction result

2016/6/15
2887.21
2846.836
2796.163

2016/6/16
2872.82
2883.434
2872.760

2016/6/17
2885.11
2863.198
2846.830

2016/6/20
2888.81
2890.223
2877.362

2016/6/21
2878.56
2883.827
2880.484

2016/6/22
2905.55
2884.713
2876.291

2016/6/23
2891.96
2905.169
2899.756

2016/6/24
2854.29
2887.931
2887.805

2016/6/27
2895.7
2863.445
2840.101

2016/6/28
2912.56
2890.929
2877.978

2016/6/29
2931.59
2896.139
2900.084

2016/6/30
2929.61
2919.562
2919.075

2016/7/1
2932.48
2900.068
2921.965

2016/8/2
2971.28
2962.792
2928.970

2016/8/3
2978.46
2989.999
2958.781

2016/8/4
2982.43
2990.815
2981.247

2016/8/5
2976.7
3000.188
2980.018

2016/8/8
3004.28
2994.374
2977.334

2016/8/9
3025.68
3024.378
3019.758

2016/8/10
3018.75
3029.842
3031.766

2016/8/11
3002.64
3022.079
3028.418

2016/8/12
3050.67
3016.695
3012.348

2016/8/15
3125.2
3052.524
3047.272

2016/8/16
3110.04
3134.624
3090.307

2016/8/17
3109.55
3095.069
3112.005

2016/9/30
3004.7
3020.829
3002.374

2016/10/10
3048.14
3025.421
3004.802

2016/10/11
3065.25
3070.946
3058.432

2016/10/12
3058.5
3061.450
3055.368

2016/10/13
3061.35
3054.349
3065.218

2016/10/14
3063.81
3068.503
3067.874

2016/10/17
3041.17
3057.303
3059.720

2016/10/18
3083.88
3046.384
3038.485

2016/10/19
3084.72
3089.847
3076.174

2016/10/20
3084.46
3075.266
3079.818

2016/10/21
3090.94
3084.724
3093.903

2016/10/24
3128.25
3107.663
3101.333

2016/11/4
3125.32
3165.698
3143.740

2016/11/7
3133.33
3138.868
3138.245

2016/11/8
3147.89
3152.136
3157.431

2016/11/9
3128.37
3164.585
3162.472

2016/11/10
3171.28
3167.704
3146.561

2016/11/11
3196.04
3187.292
3181.853

2016/11/14
3210.37
3215.444
3206.459

2016/11/15
3206.99
3225.372
3235.153

2016/11/16
3205.06
3203.528
3252.325

2016/11/17
3208.45
3224.321
3246.904

2016/11/18
3192.86
3227.154
3234.399

2016/11/21
3218.15
3224.297
3219.953

2016/11/22
3248.35
3248.086
3235.721

2016/11/23
3241.14
3259.562
3249.783

2016/11/24
3241.74
3258.817
3268.720

2016/11/25
3261.94
3271.736
3282.042

2016/11/28
3277
3279.733
3283.476

2016/11/29
3282.92
3299.852
3291.134

7.2. Trend Forecast for Rising Model in the Long Period of Individual Share

This paper selected the stock of industrial and commercial bank of China (ICBC) from 31 March 2008 to 07 April 2017 (2176 sets of data) as an experimental training set and selected the stock of ICBC from four long periods which match the rising model from 17 May 2017 to 12 October 2017 as test sets. The test sets have 49 groups.

With the same GA-BP algorithm, the result of the rising model method and that of the single model method are shown in Table 3.

Table 3: Results of the rising model and the single model.

Average error
Maximum error
Trend accuracy

Rising model
0.00961777468253
0.0291690512821
0.755102040816

Single model
0.0101503712662
0.0318118420168
0.591836734694

In Figures 6 and 7, green lines represent closing prices, blue points represent prediction results, and red points represent real closing prices. For each day, if the red point and the blue point are on the same side, it means that this trend prediction is accurate.

Figure 6: Rising model.

Figure 7: Single model.

From Tables 2 and 4, we can know that rising model can improve trend prediction accuracy not only in stock index but also in individual share. This model can keep error in a low level.

Table 4: The real data and prediction results of the rising model and the single model.

Time
Real closing price
Rising model
Single model

Prediction result
Prediction result

2017/5/17
4.96
5.072
5.020

2017/5/18
5
5.028
4.982

2017/5/19
4.98
5.021
5.022

2017/5/22
5.03
5.019
5.008

2017/5/23
5.1
5.055
5.058

2017/5/24
5.11
5.103
5.118

2017/5/25
5.16
5.129
5.129

2017/5/26
5.23
5.203
5.184

2017/5/31
5.25
5.240
5.241

2017/6/1
5.31
5.273
5.272

2017/6/2
5.3
5.300
5.318

2017/7/12
5.08
5.171
5.076

2017/7/13
5.16
5.156
5.094

2017/7/14
5.17
5.200
5.184

2017/7/17
5.34
5.220
5.198

2017/7/18
5.28
5.346
5.356

2017/7/19
5.27
5.364
5.295

2017/7/20
5.29
5.363
5.300

2017/7/21
5.33
5.355
5.309

2017/7/24
5.39
5.365
5.347

2017/7/25
5.48
5.413
5.403

2017/7/26
5.6
5.501
5.483

2017/7/27
5.53
5.591
5.586

2017/7/28
5.55
5.612
5.547

2017/7/31
5.51
5.616
5.563

2017/8/1
5.56
5.585
5.532

2017/8/2
5.7
5.599
5.572

2017/8/15
5.61
5.577
5.500

2017/8/16
5.63
5.657
5.617

2017/8/17
5.62
5.682
5.634

2017/8/18
5.62
5.669
5.641

2017/8/21
5.63
5.663
5.637

2017/8/22
5.69
5.660
5.637

2017/8/23
5.85
5.679
5.683

2017/8/24
5.92
5.778
5.810

2017/9/18
5.76
5.848
5.750

2017/9/19
5.78
5.792
5.732

2017/9/20
5.79
5.804
5.755

2017/9/21
5.95
5.819
5.761

2017/9/22
5.98
5.940
5.913

2017/9/25
6.11
5.995
5.930

2017/9/26
6.07
6.067
6.039

2017/9/27
6.02
6.071
6.011

2017/9/28
6.05
6.048
5.976

2017/9/29
6
6.044
5.992

2017/10/9
6.1
6.008
5.956

2017/10/10
6.14
6.110
6.033

2017/10/11
6.2
6.159
6.054

2017/10/12
6.21
6.188
6.123

7.3. Trend Forecast for Falling Model in the Long Period of Index

This paper selected the SSE index from 13 October 2009 to 29 January 2016 (1533 sets of data) as the experimental training set and selected the SSE index from three long periods which match the falling model from 15 July 2016 to 03 November 2016 as test sets. The test sets have 26 groups.

With the same GA-BP algorithm, the result of the falling model (another part of bimodel) method and that of the single model method are shown in Table 5.

Table 5: The results of the falling model and the single model.

Average error
Maximum error
Trend accuracy

Falling model
0.00575280455171
0.0189167045488
0.769230769231

Single model
0.0066222028267
0.0276437614071
0.461538461538

In Figures 8 and 9, green lines represent closing prices, blue points represent prediction results, and red points represent real closing prices. For each day, if the red point and the blue point are on the same side, it means that this trend prediction is accurate.

Figure 8: Falling model.

Figure 9: Single model.

From Table 6, we can know that falling model not only can keep error in a low level but also can improve the accuracy of trend prediction. According to the experimental results of 7.1 and 7.2, bimodel method, including rising model and falling model, reaches nearly 75% accuracy and keeps the error in a low level.

Table 6: The real data and predict results of the falling model and the single model.

Time
Real closing price
Falling model
Single model

Prediction result
Prediction result

2016/7/15
3054.3
3015.018
3053.366

2016/7/18
3043.56
3037.105
3070.031

2016/7/19
3036.6
3027.025
3052.860

2016/7/20
3027.9
3024.982
3043.598

2016/7/21
3039.01
3031.914
3032.450

2016/7/22
3012.82
3036.633
3059.587

2016/7/25
3015.83
3022.038
3013.960

2016/7/26
3050.17
3017.658
3029.422

2016/7/27
2992
3048.599
3074.710

2016/7/28
2994.32
3002.108
3006.372

2016/7/29
2979.34
2967.689
2988.813

2016/8/1
2953.39
2982.602
2964.578

2016/8/18
3104.11
3081.673
3127.543

2016/8/19
3108.1
3095.075
3124.608

2016/8/22
3084.81
3080.501
3125.914

2016/8/23
3089.71
3088.842
3089.085

2016/8/24
3085.88
3082.001
3100.461

2016/8/25
3068.33
3092.965
3093.066

2016/10/25
3131.94
3077.205
3153.576

2016/10/26
3116.31
3085.473
3148.972

2016/10/27
3112.35
3109.123
3122.424

2016/10/28
3104.27
3099.440
3114.055

2016/10/31
3100.49
3103.166
3103.392

2016/11/1
3122.44
3096.934
3106.386

2016/11/2
3102.73
3120.894
3148.097

2016/11/3
3128.94
3113.404
3112.531

7.4. Trend Forecast for Falling Model in a Long Period of Individual Share

This paper selected the stock of industrial and commercial bank of China (ICBC) from 31 March 2008 to 31 July 2015 (1768 sets of data) as an experimental training set and selected the stock of ICBC from three long periods which match the falling model from 11 August 2015 to 03 November 2017 as test sets. The test sets have 31 groups.

With the same GA-BP algorithm, the result of the falling model method and that of the single model method are shown in Table 7.

Table 7: Results of the falling model and the single model.

Average error
Maximum error
Trend accuracy

Falling model
0.0123645507535
0.0893076243902
0.870967741935

Single model
0.0151008394772
0.0921751707317
0.451612903226

In Figures 10 and 11, green lines represent closing prices, blue points represent prediction results, and red points represent real closing prices. For each day, if the red point and the blue point are on the same side, it means that this trend prediction is accurate.

Figure 10: Falling model.

Figure 11: Single model.

Form Tables 6 and 8, we can easily know that falling model can improve trend prediction accuracy not only in stock index but also in individual share. From the above experiments, these results prove the certain practical significance of the bimodel method.

Table 8: Real data and prediction results of falling model and single model.

Time
Real closing price
Falling model
Single model

Prediction result
Prediction result

2015/8/11
4.87
4.847
4.936

2015/8/12
4.8
4.773
4.869

2015/8/13
4.79
4.755
4.810

2015/8/14
4.77
4.768
4.798

2015/8/17
4.71
4.746
4.774

2015/8/18
4.63
4.693
4.706

2015/8/19
4.57
4.608
4.604

2015/8/20
4.55
4.523
4.524

2015/8/21
4.54
4.488
4.508

2015/8/24
4.1
4.466
4.478

2015/8/25
3.89
4.036
4.098

2015/9/7
4.52
4.609
4.835

2015/9/8
4.5
4.343
4.533

2015/9/9
4.5
4.462
4.499

2015/9/10
4.47
4.428
4.477

2015/9/11
4.43
4.419
4.452

2015/9/14
4.52
4.408
4.425

2015/9/15
4.54
4.458
4.491

2015/9/16
4.53
4.464
4.521

2015/9/17
4.52
4.495
4.536

2015/9/18
4.45
4.498
4.528

2015/9/21
4.42
4.436
4.458

2015/10/22
4.65
4.650
4.721

2015/10/23
4.61
4.581
4.685

2015/10/26
4.62
4.640
4.640

2015/10/27
4.63
4.615
4.634

2015/10/28
4.61
4.606
4.641

2015/10/29
4.58
4.590
4.624

2015/10/30
4.57
4.572
4.594

2015/11/2
4.52
4.559
4.576

2015/11/3
4.45
4.509
4.523

8. Conclusion

Stock prediction is an interesting and difficult question. Existing algorithms, including BP and many current algorithms, still could not provide helpful prediction results for stock investors. An important reason may be that stock data in a long period are too complex and include too many modes. The data-divider, which divides a complex data set into two simple sets, enables two “old” BP models to get satisfactory prediction results for the difficult question. It is interesting that “old” BP neural networks are still potential. An intelligent and self-adaptive data-divider is our future object.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

The authors would like to thank the Chinese National Natural Science Foundation (61370177), Guangdong industry-university-research (2012B090600017 and 2011B090400204), and Student Research Project of South China University of Technology (2016).

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