A FUZZY NEURAL NETWORK MODEL FOR FORECASTING STOCK PRICE
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1 A FUZZY NEURAL NETWORK MODEL FOR FORECASTING STOCK PRICE Li Sheng Institute of intelligent information engineering Zheiang University Hangzhou, 3007, P. R. China ABSTRACT In this paper, a neural network-driven fuzzy reasoning system for stock price forecast is proposed on the basis of improved Takagi-Sugeno reasoning model. The experimental result shows that the fuzzy neural network has such properties as fast convergence, high precision and strong function approximation ability and is suitable for real stock price prediction. Keywords: Fuzzy logic, neural network, forecasting stock price INTRODUCTION With the continual development of social economy, high-speed increase takes place in the emerging capital markets in the developing countries. Today, stock investment has become an important means of individual finance. Apparently, it is significant for investors to estimate the stock price and select the trading chance accurately in advance, which will bring high return to stockholders. In the past long-term trading process, many technical analysis methods for stock market such as K-line figure and moving average etc. were put forward. These methods are based on the statistical data generally. However, stock market is a nonlinear system in fact due to the political, economical and psychological impact factors. Thus, it is difficult for us to use traditional analysis tools to make stock transaction decision accurately. Moreover, there is usually remarkable difference in the analysis conclusions of various persons using even the same tool, which demonstrates they are not suited to be used by common investors without professional knowledge and experience. Recently, artificial neural network, a commonly used nonlinear function approximation tool, has shown huge advantages in forecasting, style identification, optimization technique and signal processing for its good properties such as nonlinear, flexible and valid self-organization study et al. Back-propagation (BP) neural network, a typical case of neural networks, is used most widely and is more mature than other networks. Unlike the classic mathematic methods, BP networks can establish function approximation for specific input and output relationship without a certain model. Therefore, we attempt to set up a BP ANN model for stock price prediction. Nevertheless, traditional BP network has some weaknesses that it is easy to relapse
2 into local minimum point and computation convergence speed is somewhat slower, which affect the enhancement of reliability and precision of prediction model. So, we intend to combine fuzzy reasoning theory with neural network in order to improve the precision and convergence speed of prediction model. Thus, a neural network-driven fuzzy reasoning system is proposed on the basis of improved Takagi-Sugeno reasoning model. The system consists of P+ neural networks, the networks NN ~NN P denote the functions in the conclusion parts of the P rules respectively, NN P+ is used to calculate the fitness of each rule corresponding to input vector. FUZZY NEURAL NETWORK SYSTEM As to an n-input and single output fuzzy system, a regular style of fuzzy rules is: If x is A, x is A,, x n is A n, then y is B. where A, A,, A n and B is fuzzy subsets. In the conclusion part, the model substituting fuzzy set B with a function is commonly called Takagi-Sugeno (TS) model. If x is A, x is A,,x n is A n, then y=f (x). Where f (x) is a linear combination of input variables, namely f ( x) = c x + c x + + c x () The model divide input space into linear spaces because the input variables are independent each other. When we use the two models abovementioned to divide input space into nonlinear spaces, it is necessary to have a elaborate division of it. But, it will result in the rapid increase of fuzzy rules. To avoid the happening of such a situation, it is convenient to adopt the number of following model: n n + c n+ If X, then y = f (X ) () P Where X= (x, x,, x n ), P is a partial space divided from input space. In the formula (), the membership function cannot be determined as formula independently, so we only acquire the oint membership function in the condition part using neural networks, similarly, the function in the conclusion part can be expressed by neural networks. Thus, a fuzzy system based on neural network is proposed and its structure is showed in Figure.
3 Y P g g g P NN P+ NN NN NN P X Figure. A fuzzy neural network system The system consists of P+ neural networks, NN ~NN P denote the functions in the conclusions of the P rules, NN P+ is used to calculate the fitness of each rule corresponding to input vector. The output of the fuzzy system can be calculated by the following formula y = P = µ (3) g Where g is the output value of the network NN. The system is called an NN-driven fuzzy reasoning system. We stipulate three kind of function of the fuzzy system as follows: a. Determine the number of fuzzy rules by the use of K-means clustering method. b. Design and train the neural network NN P+ to calculate the fitness of each rule corresponding to input vector. c. Design and train the neural network NN to denote the nonlinear function in conclusion part in the fuzzy system. The steps of establishing and training the fuzzy system are as follows: a. Step. Collect training sample for the fuzzy system. b. Step. Use K-means method to cluster input vectors, and each cluster corresponds to a rule. Because the samples are clustered into P teams, there are P fuzzy rules for the fuzzy reasoning system. c. Step 3. Train the network NN P+, which have n inputs and P outputs in its structure. The training samples can be constructed using following method: 3
4 If the training sample X i is clustered into the S-th team, we have: i on = S ω = off S Namely, W = ) i i i i i i i ( ω, ω,, ω s, ω s, ω s+,, ω P T =,,, P (4) Where on/off correspond to or 0 respectively. But the output of the sigmoid function is not absolutely or 0. Here we replace them with 0.9/0., which can accelerate the training process of networks. Thus, we can construct training sample X, ) for the network NN P+. After a certain number of training, the final fitness ( i Wi vector U = µ, µ,, µ ) for each network NN (=,, P) ( P Step 4. Train the networks NN ~NN P. Assume that NN s corresponds to the S-th rule, thus, all of the samples in the S-th cluster is the training data for the network NN s. Then, back-propagation algorithm is applied to train the networks NN ~NN P. APPLICATION OF THE NOVEL PREDICTION MODEL Assume that x i is the data series of stock price, i=,,, N, N is the number of data samples. If the number of prediction stages is m, i.e., use x i-, x i-,, x i-m to forecast the value at time i. Here x i-, x i-,, x i-m is the input vector X, and x i is the prediction expected value Y. In the practice of predicting stock price using the fuzzy system aforesaid, the steps of application are as follows: Step. First, divide the samples into two teams by use of K-means clustering method. Step. Second, use clustered samples to train the networks NN ~NN P+, and all networks have two hidden layers. The determination of number of input neurons can be conducted using heuristic method empirically. The prediction stages vary from to 0 one by one to train networks, thus, we can determinate the stages with least error. Here, the final predicted stage m=4, the computation process is showed in Table. The number of output node is, accompanied with 5 nodes in each hidden layers. Step 3. We set that the training time is 000, momentum coefficient is 0.9, and the initial study factor is
5 Table. The determination of the input nodes SSE RES RES Note: SSE is the square sum of error for samples, RES is the ratio of maximum relative error for training samples, and RES is the ratio of maximum relative error for testing samples. Table. The contrast of actual value and prediction value of a stock Actual value Prediction Relative error value (%) The training processes of networks are as follows: Step. Initializing the parameters of the BP network. By using random number, the link weights and thresholds of the network are evaluated. Step. Construct study samples and use them as the input and output vectors of the network. Step 3. Carry on the self-study of network and gain the output vector and error of network. Step 4. Calculate the instantaneous gradient vector. Step 5. Carry out error back-propagation and revise the parameters of the networks. Step 6. While the absolute value of the error is less than the precision, stop the training process and turn to practice. Otherwise, turn to Step 3. We adopt the closing price data of the stock ZXTX of Shenzhen Stock Exchange in 00 as the experimental data, and the corresponding prediction results are shown in Table. CONCLUSION The experimental result shows that the fuzzy neural network has such properties as fast convergence, high precision and strong function approximation ability. Furthermore, it also demonstrates that the fuzzy neural network system is good at predicting stock price because of its non-strict requirement for input variables and not needing plenty of sample data, which ensure that it is suitable for actual forecasting and outperforms the classic prediction methods. 5
6 REFERENCES [] Wang, L. X., Mendel J. M., Fuzzy basis functions, universal approximation and orthogonal least-squares learning, IEEE Transaction on Neural Networks, 99(3), 807~84. [] Tong, R. M., A control engineering review of fuzzy systems, Automatic, 997, 3(6): 559~569. [3] Kim, K. H., Park, J. K., et al., Implementation of hybid short-term forecasting system using network and fuzzy expert systems. IEEE Transaction on Power Systems, 995, 0(3), 534~539. [4] Jang J-S R. ANFIS, adaptive-network-based fuzzy inference systems. IEEE Transaction on systems, Man., and Cybernetics, 993, 3 (3), 665~685. [5] Cybenko, G., Approximation by superpositions of a sigmoidal function, Math. Control Signals Syst., 989, vol, 303~34. [6] Wang, L. X., Mendel J. M., Back-propagation fuzzy system as nonlinear dynamic system identifiers, Proceeding of IEEE 99 International Conference on fuzzy systems, Mar., 99, 409~48. 6
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