Prediction of Stock Prices Using Artificial Neural Networks

Transcription

1 Prediction of Stock Prices Using Artificial Neural Networks Sneh Saini 1, Dr. R R Laxmi 2 Dr. N.P. Singh 3, 1 Phd. Scholar, Deptt. of Statistics, Maharishi Dayanand University, Rohtak, India 2 Prof., Deptt. of Statistics, Maharishi Dayanand University, Rohtak, India 3 Prof. MDI, Gurgaon, India ABSTRACT This paper presents prediction of stock prices using Artificial Neural Network ( ANN ) approach, its characteristics, classification and uses of Applications are precisely elaborated. To showcase the application of ANN, stock price of State Bank of India is taken for training and validation of data. Experimental results were obtained on stock prices using Zero-based Log-Sigmoid, Threshold, Hyperbolic Tangent, Bipolar- Sigmoid and Log-Sigmoid functions of activation functions of ANN on neuro excel predictor software based for 3 hidden layers. Finally results obtained were compared with actual data for selecting best fit on the basis of statistical tests i.e. MAE, MAPE, MSE, RMSE, RAE and RRSE which has minimum value and more votes. Key Words: Artificial Neural Network, Prediction of Stock Price, Activation Functions i.e. Zero-based Log- Sigmoid, Threshold, Hyperbolic Tangent, Bipolar-Sigmoid and Log-Sigmoid functions. INTRODUCTION Forecasting time series is a crucial and constantly growing discipline, which includes different areas such as investment analysis, Bank loan risk evaluation, speech recognition, monitoring, marketing, character recognition, image segmentation etc. In addition, artificial neural networks are often able to detect subtle patterns and trends that may be too intricate for humans to identify. Further, artificial neural networks can recognize relationship among hundreds of variables (Bylinsky, 1993) 1. Artificial neural networks are also gifted with the capacity to dig out unknown trends and relations hips from very large volume of data (Dineley, 2001) 2 often stored in a data warehouse and on- line transaction processing systems. In case of investment analysis, artificial neural networks are used to predict the pattern of movement of stocks; currencies etc. and are replacing simple time series and regression models. The rest of the paper is divided into eight sub-sections where section II defines artificial neural networks, section III describes the applications of neural networks, section IV shows the characteristics of artificial neural networks, section V presents the classification of artificial neural networks, section VI describes about the methodology and data processing, section VII specifies Descriptive Analysis and at last section VIII gives conclusion. ARTIFICIAL NEURAL NETWORK (ANN) Artificial Neural Network (ANN) theory is developed out of Artificial Intelligence research, or the study in designing machines with rational ability. It is a computer program that is designed to learn in a manner alike the human brain. Haykin (1994) 3 describe neural networks as an adaptive machine or more specifically: A neural network is a massively parallel distributed processor that has a natural propensity for storing experiential knowledge and making it available for use. It resembles the brain in two respects: Knowledge is acquired by the network through a learning process and interneuron connection strengths known as synaptic weights are used to store the knowledge APPLICATION OF ARTIFICIAL NEURAL NETWORKS Artificial Neural Network has various business applications, every company in the world wants a system which is itself intelligent to solve the problem according to inputs given. Some of the applications based on ANN are listed out as under: 20

2 1. Airline Security Control. 2. Stock Price Index Prediction. 3. Investment Management and Risk Control. 4. Target Marketing. 5. Risk Management 6. Customer Research. 7. Prediction of Thrift Failures. 8. OCR Systems. 9. Industrial Process Control. 10. Validation of Data. 11. Sales Forecasting. The above said uses have the abilities to sense all type of problems with help of Artificial Neural Networks phenomenon and its various algorithms like Perception Learning Algorithm, Back Propagation Algorithm, ARTI 4, 5, 6 Algorithm and SOM Learning Algorithm. CHARACTERISTICS OF ARTIFICIAL NEURAL NETWORK An artificial neural network is a computing architecture comprising of simple processing elements, neurons, that work in parallel and connect with each other by sending signals (Krawiec and Stefano ski, 2003: 83) 7. The neural network is a very simplified model of the human brain. It consists of a large number of elements called neurons. Each neuron processes a finite number of input signals x i (i = 1, 2,.,n) for one output y using weights w i. In general, the output signal y can be expressed using the formula: where: s the total excitation of a neuron, which is usually calculated as a linear combination of inputs complemented by a free unit (in literature referred as BIAS) which can be illustrated with the following formula: f activation function that specifies the mode of the excitation of s on the basis of weights w i and the input signals x i. The activation function may take the form of both linear functions and non-linear functions, the most popular examples of which are: Threshold: Logistic (sigmoid): Hyperbolic tangent: 21

3 Input signals (results): Neurons are connected and form a network through connections with parameters (weights) that are changed during the learning process. Most neural networks are constructed in a layered manner. Owing to availability during the learning process one can distinguish: an input layer, an output layer and hidden layers. An example structure of an artificial neural network is presented in Fig. 1. Fig 1: Multilayered Artificial neural network [by Almeida, L (1987)] CLASSIFICATION OF NEURAL NETWORKS There are various architectures of Artificial Neural Networks that are commonly used. A very popular network architecture is the Multilayer Perceptron (Minsky et.al (1969) 8, Rosenblatt, F(1958) 9 which is generally trained with the back propagation of error, learning vector quantization, radial basis function, Hopfield, and Kohonen algorithms (Kohonen, T (1997) 10. Some Artificial Neural Networks are classified as Feed Forward while others maybe recurrent (i.e., implement feedback) depending on the method of training employed and data processing through the network. Another popular method of classifying Artificial Neural Networks is by the training algorithms used, as some Artificial Neural Networks employ supervised training while others utilize unsupervised or self-organizing (Kosko,B(1992) 11. Supervised training methods are used when the network learns from a training set of data that has an output associated with each set of input. Unsupervised algorithms (Hopfield, J (1982) 12 effectively perform clustering of the data into similar groups based on the calculated attributes serving as inputs to the algorithms. METHODOLOGY AND DATA PROCESSING The BSE Sensex data taken up for showcasing the application of ANN contains the date, opening price, closing price, high, low and volume in number of shares traded on a particular day. Out of these, only four attributes were taken into account, the opening price, closing price, high price and the low price. The output consisted of a single attribute, the opening value. The data was further divided into 95% for training and 5 % for testing the data (validation). Then, specified input and output ranges for training, set the parameters for neural network, specify input and output range for prediction and view the learning process graphically. Neural network parameters allow specifying initial weights, learning rate, momentum, choose the activation function (Threshold, Hyperbolic tangent, Zero-based log sigmoid, Log-sigmoid and Bipolar sigmoid) and number of neurons in the hidden layer (layer1, layer2, layer3,). 22

4 Training of Input Data: Figure 2: Graph showing network creation of the input data. Interpretation Figure 3: Graph showing training of input data for neural network result The green graph shows the actual values and the red the predicted ones. As the neural network converges, predicted values shows trending closer to the actual values. The "epochs" number at the top of this graph represents the number of complete passes through the neural network of the entire set of training patterns. The horizontal, or x-axis, represents the number of outputs. The vertical, or y-axis, represents the actual value of the outputs. The training graph is a good way to determine the effectiveness of the training process. If the predicted values do not closely match the actual values, it is an indication that to experiment with different NN Parameters. 23

5 EXPERIMENTAL RESULTS OBTAINED OF STATE BANK OF INDIA When the training is complete, input and output ranges are specified for the prediction of stock prices of State Bank of India under layer 1, layer 2 and layer 3 of different activation functions and descriptive analysis of predicted prices are as under: DESCRIPTIVE ANALYSIS Zero-based Log-Sigmoid MAE MAPE MSE RMSE RAE RRSE Layer Layer Layer Threshold Layer Layer Layer Hyberbolic tangent Layer Layer Layer Bipolar-Sigmoid Layer Layer Layer Log-Sigmoid Layer Layer Layer INTERPERTATION It can be inferred from the result obtained from table that the values predicted by layer 3 from the Bipolar-sigmoid of neural network is the best fit model based on the minimum value of Mean absolute error, Mean absolute percentage error, Relatives absolute error, Root relative squared error, thus the neural networks are effective tool for prediction of stock market prices which gives fairly accurate results. CONCLUSION In this research, stock prices are predicted using 3 hidden layers by different activation functions. It is evident from results obtained from layer 3 of Bipolar-sigmoid that this activation function of artificial neural network gives fairly accurate results unless there is a huge and sudden variation in the actual data. Thus as observed neural networks are an effective tool for prediction of stock prices and can be used for prediction of any stock prices. REFERENCES [1]. Bylinsky, G. (1993, Sept 6). Computers that Learnby Doing. Fortune, vol. 128, no. 5 pp [2]. Dineley, D. (2001, Feb. 5). Knowledge Management with Human Smarts. InfoWorld, vol. 23(6), pp [3]. Anil K Jain, Jianchang Mao and K.M Mohiuddin, Artificial Neural Networks: A Tutorial, Michigan State university, [4]. Eldon Y. Li, Artificial Neural Networks and their Business Applications, Taiwan, [5]. Christos Stergiou and Dimitrios Siganos, Neural Networks. 24

6 [6]. Krawiec, K,: Stefanowski, J. (2003). Uczenie maszynowe I sieci neuronowe. Poznan: Wyadawnictwo Politechniki Poznanskiej. [7]. Minsky, M., and Papert, S., Perceptrons. MIT Press, [8]. Rosenblatt, F., The Perceptron: a Probabilistic Model for Information Storage and Organization in the Brain, Physiological Review 65, , 1958 [9]. Kohonen, T., Self Organization Maps, New York: Springer-Verlag, [10]. Kosko, B., Neural Networks and Fuzzy Systems. Prentice Hall, [11]. Hopfield, J., Neural Networks and Physical Systems with Emergent Collective Computational Abilities., Proceedings of the National Academy of Science, pp ,