Prediction scheme of stock price using multiagent

Transcription

1 Prediction scheme of stock price using multiagent system E. Kits&Y Katsuno School ofnformatics and Sciences, Nagoya University, Japan. Abstract This paper describes the prediction scheme of stock price by using multiagent systems. Agents predict the stock price according to their strategies which is defined from technical and fundamental parameters such as some index related to the stock price, the currency exchange rate of the Japanese Yen (JPY) against the US Dollar and so on. Agents are randomly generated to construct population and then, their strategies are improved by genetic algorithm. Finally, the strategy is employed for predicting the real stock price. 1 ntroduction n real stock market, a lot of market players such as scalpers, day traders, institutions and hedgers compete to exchange risk and return in ways that meet their objectives. Prediction of stock price is very important not only for the players but also for public citizen and governments. The prediction schemes of the stock price are briefly classified into the technical and the fundamental analysis schemes. n the technical analysis scheme, stock price is predicted from the past fluctuation of the price by using stock price chart and statistical schemes and computers. The basic idea of the technical analysis scheme that the price can be predicted from the past fluctuation of price was firstly inspired by Dau and then, Hamilton compiled related ideas into one book[l, 2, 3]. On the other hands, the stock

2 738 DataMining nitial population Day 2 Predicting stock price on next day 1 ~ Estimating fitness function on this day + 1Genetic Algorithms! Last day of learning process + Estimatingfitnessfunction on last day Figure 1: Learning process price strongly depends on several economic indicators such as interest rate, currency exchange rate, economic growth rate and so on and the management indices such as corporate performance, earning capacity and research and development. Therefore, in the fundamental analysis scheme, the stock price is predicted from the global and the domestic economy and corporate performance[4, 5]. n this paper, we will describe the prediction scheme of the stock price by using multi-agent system. The process is mainly composed of the learning and the prediction processes. n the learning process, the population is constructed with many agents. Each agent has a strategy to predict stock price according to technical and fundamental indices. The agents improve their strategy by using genetic algorithm for a certain period [6, 7, 8]. After the learning process, prediction process stars. This scheme is applied for predicting the stock price of the Toyota motor company. 2 Simulation process The simulation process is composed of learning and prediction processes. n the learning process, agents improve their strategy by using genetic algorithm for a certain period. Figure 1 shows briefly the flow of the learning

3 DataMining 739 Generating initial population F==l ti + Mutation Generating new population * Figure 2: Flowchart of genetic algorithm process. After the learning process, prediction process stars. n the prediction process, the strategies obtained in the learning process are applied for predicting the stock price at the period different from the learning process. n this section, we will describe genetic coding of the prediction strategy and the genetic operations such as the selection, the crossover and the mutation operations. 2.1 Prediction strategy Each agent will predict the stock price according to the following equation: e~+l = ek + go$ +gly +gzz + gsnhz +fj4~~ (1) where ek denotes the stock price at a day k. The variables x, y, z, nhzandkz are selected from the technical and the fundamental view-points. The parameter g~ (i = O,.... 4) is the unknown coefficients for the variables. The parameter x denotes the average value of the price movements over the past ten days, which is defined as x= e - e - The parameter y denotes the maximum difference in the price over past five days, which is defined as 10 (2) y = max(ek 4, e 3)ek 2>ek l>ek) k 4 k 3 k 2, ek l k min(e,e,e >e ) (3)

4 740 DataMining where max and min denote the maximum and the minimum values of the stock price, respectively. The parameter z denotes the difference between the prices on a day and the preceding day, which is defined as z = ek ek l (4) The parameter nhz denotes the difference between the prices of the Nikkei Stock Average on a day and the preceding day, which is defined as nh.z = NsA~ _ NsAk 1 (5) where NSAk denotes the Nikkei Stock Average at the day k. The parameter kz denotes the difference between the currency exchange rate of JPY against US Dollar on a day and the preceding day, which is defined as kz = (CERk CERk-l) X P (6) where C ER denotes the currency exchange rate at the day k. Besides, P = 100 is the magnification factor of the currency exchange rate against the stock price. The side-constraint for the coefficient ga is specified as: where gl and g. denote lower and upper bounds for gi, respectively. Besides, there exists the movement limit for the stock price. The price movement limit is specified as lek+l ekl < eml (8) where enl denotes the price movement limit, which is specified as JPY. 2.2 Genetic algorithm The flow of the genetic algorithm employed in this study is briefly shown in Fig.2. Population is constructed by N individuals. Each individual has the chromosome by the concept of real-coded genetic algorithm. The individuals of initial population are defined randomly. Selection operation selects two individuals according to their fitness function values and crossover operation generates new individuals from them. Values of genes of the chromosome are changed randomly by mutation operation Definition of chromosome The unknown coefficient ga is considered as genes of chromosome. According to the concept of real-coded genetic algorithm, a chromosome is defend as the series of the unknown coefficient gi as follows (9)

5 DataMining 741 Figure 3: BLX-a mutation operation Fitness function Fitness function of the individual i is defined from the predicted real stock prices as and the (lo) where (ek)r~al and eh denote the real and the predicted stock prices on the day k. Besides, the summation is taken for all days in the learning process Selection The roulette selection operation is employed in this study. This operation selects the individual from the population with the probability which is proportional to the fitness values of the individuals. The selection probability of the individual i is defined as (11) where the denominator means the summation of the fitness function values of the individuals.

6 7 42 DataMining Table 1: Simulation parameters (Learning process) Price movement limit e~l = JPY Bounds for parameter gl = 10.0, glj = 10.0 Learning period 100 days Prediction period 100 days Number of agents N = 200 Crossover rate Pc = 1.0 Crossover parameter a = 0.5 Mutation rate P nut = 0.05 Number of simulation times Crossover After selecting two individuals as the parents on the selection operation, new individuals (children) are generated from blend crossover (BLX-a) operation[9]. Firstly, the interval between two points that centain the two parents is determined. The interval is equally extended on either side determined by the user-specified parameter a. Two points containing children are generated as values selected randomly on the extended interval (Fig.3). This operation is performed for each genes. Crossover operation is performed until PC x N individuals are replaced with new ones. The parameter pc denotes the crossover rate taken as a value between zero to one Mutation The mutation operation changes the value of a gene with probability Pmut. The new value of the gene is randomly selected with the limits of the sideconstraint (Eq. (7)). 3 Numerical examples Prediction of the stock price of Toyota motor company from January 1 to October is considered as a numerical example. nitial population is constructed by some agents with randomly specified strategy for predicting the stock price. The parameters in the learning process are shown in Table 1. Besides, the simulation results are average value of one thousand runs. Real and predicted stock prices on the learning process are compared in Fig.4. A solid and a broken lines denote histories of the real and the predicted prices, respectively. The history of the predicted price is shown as the average value of predicted ones of all agents. Figure 5 shows the comparison of histories of moving averages over past 50 days of the real

7 vatamuung ) v.- : G Day 100 Figure 4: Real and predicted stock prices (Learning process) ~ w , = 5oooz.. m... -.,......, ; > , : & > , ; EEGl... Z Day Figure 5: Moving average for past 50 days (Learning process) and the predicted prices. This figure shows that the difference between the predicted price slightly approach to the real price as the learning process goes. The reason why the deviation between the real and the predicted

8 7 44 Data Mining - - Predicted price by best individual :. :! Day Figure 6: Real and predicted stock prices (Prediction process) ;... ;.,.. : : :~.>: { 4BO0 - : :;.- : Predicted price by best individual Day Figure 7: Moving average for past 50 days (Prediction process) prices is relatively large is the predicted price is estimated from the prices by all agents. Figure 6 shows the comparison of real and predicted stock prices on the

9 Data Mining 745 prediction process. A solid and a chain lines respectively denote histories of the real price and the price predicted by best agent in the learning process. A broken line denotes the history of the average value of the price predicted by all agents. Histories of the moving average of these prices are compared in Fig. 7. The history of the average price is different from that of the real price. However, the history of the price predicted by the best agent is relatively similar to that of the real price. 4 Conclusion This paper describes the prediction scheme of the stock price using multiagent system. Each agent has the strategy to predict the stock price from technical and fundamental view-points. The simulation process is composed of the learning and the prediction processes. Firstly, the strategies are specified randomly and then, agents improve their strategies during the learning process. After the learning process, the prediction process starts. Prediction of stock price of Toyota motor company is considered as an example. During the learning process, the average value of the prices predicted by the agents get close to the real stock price. Therefore, in the prediction process, the strategies are applied for predicting more erratically fluctuating stock price than in learning process. Unfortunately, the performance of the prediction strategy dose not reach the satisfactory settlement. One of main causes maybe that number of parameters is too small. Besides, Now, we are planning the improvement of the prediction strategy still more. References [1] W. P. Hamilton. The Stock Market Barometer. Harper & Brothers Publications, [2] J. E. Granville. A Strategy of Daily Stock Market timing for Maximum Profit. Pentice-Hall, [3] R. D. Edwards and J. Magee. Technical Analysis of Stock Trends. John Magee, [4] E. J. Elton and N. J. Gruber. Modern Portfolio Theory and nvestment Analysis. John Wiley & Sons, [5] D. J. Luenberger. nvestment Science. Oxxford University Press, [6] L. Davis. Handbook of Genetic Algorithms. Van Nostrand Reinhold, 1 edition, 1991.

10 746 Data Mining [7] D. E. Goldberg. Genetic Algorithms in Search, Optimization and Machine Learning. Addison Wesley, 1 edition, [8] K. Deb. iwulti-objectiue Optimization using Evolutionary Algorithms. John Wiley & Sons, [9] L. J. Eshelman and J. D. Schaefer. Real-coded genetic algorithms and interval schemata. n L. D. Whitley, editor, Foundation of Genetic Algorithms.2, pp Morgan Kaufmann Publications, 1992.