Microsoft Word - cet-01.docx CHEMICAL ENGINEERING TRANSACTIONS VOL. 46, 2015 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Peiyu Ren, Yancang Li, Huiping Song Copyright © 2015, AIDIC Servizi S.r.l., ISBN 978-88-95608-37-2; ISSN 2283-9216 Forecast of Opening Stock Price Based on Elman Neural Network Jun Zheng Baotou Teachers’ College Network Information Center, Inner Mongolia, Baotou, 014030. zhengjun_025@163.com Elman Neural Network is a typical regression nerve network which is highly applicable in processing sequential data. In order to predicate accuratelythe fluctuation of stock prices, Elman Neural Network is applied in the forecast of the opening price of SSE (Shanghai Stock Exchange). This paper establishes mathematical models for the input layer, the hidden layer, connection layer and the output layer based on Elman Neural Network. The opening prices of SSE of 337 trading days from December, 2012 to April, 2014 are selected as the raw data for stimulated forecast, and its result proves the validity of this forecast model. 1. Research questions Stocks have existed for over 200 years since Britain firstly issued shares in 1773, and have had an inestimable influence on the development of market economy. China’s security market came into being in the early 1990s; although it has only developed for a little more than 20 years, great achievements have been made (ChongwenZhong (2014)) reported: there are over 2000 listed companies in Shanghai Stock Exchange and Shenzhen Stock Exchange and more than 50 million shareholders. China’s stock market has taken preliminary shape and is gradually becoming an essential part of the security business or even the whole financial sector; in the meantime, stock investing has become an important part of the daily life of a growing number of people. However, the stock market constantly changes, sometimes going up and sometimes going down, which makes stock investing highly risky. With an increase in stock investing activities, an effective stock forecasting method is in urgent need, with which the trend of stock market can be predicted so that investors can avoid risks and enjoy higher rate of return. The stock value is significantly influenced by policy changes, interest rate changes, economic cycles and human manipulation. The entire stock market can be seen as a complicated non-linear system. Since Elman Neural Network has a strong non-linear approximation ability with features like self-learning and self-adaptation (S.C. Kremer (1995), Chun-Fei Hsu (2014)) reported, it will be very effective in predicting the opening price of the stock market. 2. Overview of Elman Neural Network Elman Neural Network is a typical locally recurrent globally feed-forward network (D. P. Mandic and J. A. Chambers (2001)) reported. It was put forward in 1990 by J. L. Elmanfor speech processing, and later, on the basis of it, Pham et al introduced a modified Elman network, which is considered by most scholars as the standard Elman network. The feedback connections between and within layers in the Elman network enable it to show the time delay between the input and output, so it has a local memory function. The Elman network is widely employed in many fields such as sequence analysis, system identification and control (Jujie Wang et (2014), Penghua Li et (2014) Anqi Cui, Hua Xu and Peifa Jia (2011) reported, AksoySaadettin and Muhurcu Aydin (2011), Ciarlini P and Maniscalco U (2008)); its mathematical model is normally written as: y(k) = g (w3(w1xc(k) + w2u(k − 1))), xc(k) = α. xc(k − 1) + x(k − 1) (1) DOI: 10.3303/CET1546095 Please cite this article as: Zheng J., 2015, Forecast of opening stock price based on elman neural network, Chemical Engineering Transactions, 46, 565-570 DOI:10.3303/CET1546095 565 http://www.sciencedirect.com/science/article/pii/S0925231214001684 http://www.sciencedirect.com/science/article/pii/S1568494614003019 http://www.sciencedirect.com/science/article/pii/S0142061513004377 http://www.sciencedirect.com/science/article/pii/S0957417410015277 http://www.sciencedirect.com/science/article/pii/S0957417410015277 http://www.sciencedirect.com/science/article/pii/S0957417410015277 3. Establishing stock forecasting model based on Elman Neural Network 3.1 Overall structure of the model The structure of the proposed Elman Neural Network model is demonstrated as follows: Figure 1: Overall structure of Elman Neural Network 3.2 The input layermodel In this study, the closing prices of the first six trading days are utilized to predict the closing price of the seventh trading day. In accordance with the actual demand mentioned above, the number of nodes in the input layer is set as 6. Therefore, the mathematical model of input in the input layer is defined as: Input ik (1)(t) = [Rk (t), Uk(t)] T (2) In Equation 2, i stands for the number of nodes in the input layer, the value interval of which is 1≤i≤6 in this model, i∈ N; k refers to the number of input samples; t refers to the number of iterations; R k(t) stands for the input of sample space; Uk(t) stands for the input in the connection layer. The mathematical model of output in the input layer is defined as: Output ik (1) (t) = Input ik (1) (t) (3) 3.3 The hidden layer model The hidden layer is a critical model that links the input layer and the output layer. The hidden layer determines the performance of the network model. The number of nodes in the hidden layer has a great impact on the model: excessive nodes will lead to not only excessive training time of the network, but also over-training of it, which causes bigger error and poorer generalization ability; on the other hand, inadequate number of nodes will lead to insufficient training of the network, causing poorer fault tolerance. Therefore, the key issue in designing the hidden layer model is to properly determine the number of nodes on the layer. According to the empirical formula M = √m + n + a (where m and n refer to the number of neurons in the output layer and the input layer respectively, and 1≤a≤10, a∈ C), and the experimental study, it can be seen that when the number of nodes in the hidden layer is 12, the network has the best performance, so the number of nodes in the hidden layer is determined as 12. Thus, the input model of the hidden layer is defined as: Input ik (2)(t) = ∑ ∑ ωil 1 (t)Rik (t) p l=1 6 i=1 + ∑ ωlk 2 (t)Ulk(t) p l=1 + θl(t) (4) In Equation 4, p refers to the number of nodes in the hidden layer, which is set as 12 in this case; i stands for the number of nodes in the input layer; k refers to the input sample; t stands for the number of iterations; ωil 1 (t) refers to the connection weight between the input layer and the hidden layer, while ωlk 2 (t) refers to the connection weight between the connection layer and the input layer; Ulk(t) stands for the output of the connection layer; θl(t) refers to the threshold value of the hidden layer. The output model of the hidden layer is defined as follows: Output lk (2) (t) = F(Input lk (2)(t)) (5) p refers to the number of nodes in the hidden layer, and p=12; F refers to the activation function, which is defined as follows: 566 F（x）= 2 1+e−2x − 1 (6) 3.4 The connection layer model The connection layer enables the forecast model to have dynamic feedback and storage memory. The input model of the connection layer is defined as: Input lk (c) (t) = Output lk (2)(t − 1), when t=1，Input lk (c) (1) = 0 (7) The output model of the connection layer is defined as: Ujk (t) = Inputlk (c) (t) (8) 3.5 The output layer model In this study, the opening prices of the first six trading days are utilized to predict the opening price of the seventh trading day, so there is only one output in the output layer, and the number of nodes in the output layer is 1. The mathematical model of input in the output layer is defined as: Input ak (3)(t) = ∑ ωla 3 (t)Output lk (2) (t) p l=1 + θa (t) (9) In this equation, a refers to the number of nodes in the output layer, and since the number of nodes in the output layer is 1, so a=1. k refers to the input sample; t stands for the number of iterations. The output model of the output layer is defined as: Output ak (3) (t) = g(Input ak (3)(t)) (10) In Equation 10, g is a linear function, which is defined as g(x) = x. 3.6 Network learning model After the mathematical model of every layer in the Elman network has been determined, the stock price forecasting model still requires the weight coefficient and the threshold between layers, both of which would be determined through learning. In this study, the gradient descent algorithm is utilized as the learning algorithm (Wei Wu,Dong-po Xu and Zheng-xue Li (2008)) reported. The principle of gradient descent method is that for function F(x), if there is definition at x0and it is differentiable, then F(x) decreases the fastest in the negative direction -∇F(x0 ) of gradient. In the training of the network, data transmit backward from the input layer, via the hidden layer and the connection layer, and are finally output via the output layer. Then, according to the gradient descent algorithm, weight coefficients and thresholds of the network are corrected layer by layer starting from the output layer in the direction of reducing errors (Qing Song (2010)) reported, and the following learning models can be derived from the gradient descent algorithm: The adjustment model of the connection weight ωil 1 (t) between the input layer and the hidden layer: ωil 1 (t + 1) = ωil 1 (t) + ∆ωil 1 (t + 1) (11) The adjustment model of the hidden layer threshold: θl (t + 1) = θl(t) + ∆θl(t + 1) (12) The adjustment model of the connection weight between the hidden layer and the output layer: ωla 3 (t + 1) = ωla 3 (t) + ∆ωla 3 (t + 1) (13) The adjustment model of the hidden layer threshold: θa(t + 1) = θa(t) + ∆θa(t + 1) (14) The adjustment model of the connection layer weight: ωlk 2 (t + 1) = ωlk 2 (t) + ∆ωlk 2 (t + 1) (15) 4. Training and Testing of the Forecast Model 4.1 Data source In this study, the opening prices of Shanghai Stock Exchange of 337 trading days from December, 2012 to April, 2014 are used as the source data. The data of the first 300 trading days are utilized as training samples for the Elman network model, to tune network model parameters; the data of the latter 37 trading days are utilized as testing samples, to test the network model that has been established. 567 http://link.springer.com/search?facet-creator=%22Wei+Wu+%E5%90%B4%E5%BE%AE%22 http://link.springer.com/search?facet-creator=%22Dong-po+Xu+%E5%BE%90%E4%B8%9C%E5%9D%A1%22 http://link.springer.com/search?facet-creator=%22Zheng-xue+Li+%E6%9D%8E%E6%AD%A3%E5%AD%A6%22 http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=%22Authors%22:.QT.Qing%20Song.QT.&newsearch=true 4.2 Normalization of data Since the ranges of the data collected are not unitary but variable, on the one hand, the establishment of the network model and the prediction cannot be processed in a unified framework; on the other hand, while the data input into the network model are restricted in certain intervals, the data collected do not necessarily meet the requirement, so in order to unify the range of input data, the source data need normalization. The normalization method utilized in this study is to divide a vector by its length, so the result will stay between -1 and 1. The normalization model is described as follows: p′ = 2 × p−min(p) max(p)−min(p) − 1 (16) 4.3 Training of the forecast model The training of the forecast model refers to a procedure in which the model connection weight is adjusted iteratively according to training samples (Alex Aussem(1999)) reported. The purpose of the training is to find out the essential connection between the opening prices of the stock market (Pham D T and Liu X (1996)) reported. In this study, the opening prices of 337 trading days x1, x2…x300 are rearranged to form the following matrix: [ x1 x2 … x294 x2 x3 … x295 ⋮ x7 ⋮ x8 … ⋮ … x300 ] In this matrix, the vector of each column is an input sample. The first six elements in the column are input variables in the input layer and the last element (the seventh element) needs to be predicted. 4.4 Testing of the forecast model After the training of the network model, the network needs to be tested with testing samples. The opening prices ofShanghai Stock Exchange of the latter 37 out of the 337 trading days are utilized to test the forecast model. Before the testing, the testing samples need to be normalized according to Equation 16, and the output of the forecast model also needs to be reversely normalized in order to obtain normal data. The reversed normalization model is described as follows: p′ = 0.5(p + 1) × (max(p) − min(p)) + min(p) (17) 5. Analysis and evaluation of experiment results After training the Elman Neural Network established with the data of 300 trading days, and the training results and the actual results are shown in the following Fig 2: It can be seen from Fig 2 that the training results and the actual results match very well. In order to better evaluate the performance of the network, on the condition that parameters of the trained network model remain unchanged, the testing samples are utilized to test the established model. The test results are shown in Table 1 and Fig 3: 568 http://www.sciencedirect.com/science/article/pii/S0925231298001258?np=y Table 1: Test results Period forecasted value actual value absolute error relative error 307 2015.313425 2026.224 -10.9106 0.005384684 308 2030.474114 2019.98 10.49411 0.005195157 309 2024.298481 2017.22 7.078481 0.003509028 310 2020.816727 1987.679 33.13773 0.016671569 311 1995.641654 2050.827 -55.1853 0.026908826 312 2057.628295 2063.323 -5.6947 0.002759968 313 2067.806992 2070.574 -2.76701 0.001336348 314 2066.338839 2060.812 5.526839 0.002681874 315 2060.675963 2046.851 13.82496 0.00675426 316 2048.897426 2043.045 5.852426 0.00286456 317 2045.907503 2031.005 14.9025 0.007337502 318 2033.873784 2049.423 -15.5492 0.007587119 319 2052.027645 2063.497 -11.4694 0.005558213 320 2066.324399 2037.552 28.7724 0.014121062 321 2037.91241 2054.53 -16.6176 0.008088268 322 2056.821305 2100.651 -43.8297 0.020864815 323 2105.30551 2105.876 -0.57049 0.000270904 324 2104.624669 2130.368 -25.7433 0.012083983 325 2129.713469 2127.409 2.304469 0.001083228 326 2126.652801 2125.902 0.750801 0.000353168 327 2124.915249 2097.213 27.70225 0.013209077 328 2096.415877 2108.947 -12.5311 0.005941886 329 2108.457653 2091.48 16.97765 0.008117531 330 2089.618038 2085.98 3.638038 0.001744043 331 2083.092073 2062.787 20.30507 0.009843514 332 2062.427368 2068.084 -5.65663 0.002735204 333 2067.599232 2064.156 3.443232 0.001668106 334 2064.649926 2060.538 4.111926 0.001995559 335 2060.125047 2033.337 26.78805 0.013174426 336 2034.900326 2001.896 33.00433 0.016486534 337 2005.643197 2020.438 -14.7948 0.007322572 Figure 2: Test results of training data Figure 3: Test results It can be seen from Table 1 and Fig 3 that the predicted values and the actual values are very close; the biggest relative error is only 0.026908826, and the tendency of the predicted values is consistent with that of 569 the actual values. In summary, according to the experiment, the network model established on the basis of Elman Neural Network has good performance in predicting the opening price index of Shanghai Stock Exchange. 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