Title: Stock Market Prediction Using Artificial Neural Networks

Transcription

1 Ttle: Stock Market Predcton Usng Artfcal Neural Networks Authors: Brgul Egel, Asst. Prof. Bogazc Unversty, Hsar Kampus 34342, Istanbul, Turkey Meltem Ozturan, Assoc. Prof. Bogazc Unversty, Hsar Kampus 34342, Istanbul, T u r k e y ozturanm@boun.edu.tr Bertan Badur, Asst. Prof. Bogazc Unversty, Hsar Kampus 34342, Istanbul, Turkey badur@boun.edu.tr Abstract Predcton of stock market returns s an mportant ssue n fnance. Artfcal neural networks have been used n stock market predcton durng the last decade. Studes were performed for the predcton of stock ndex values as well as daly drecton of change n the ndex. In some applcatons t has been specfed that artfcal neural networks have lmtatons for learnng the data patterns or that they may perform nconsstently and unpredctable because of the complex fnancal data used. In Turkey artfcal neural networks are mostly used n predctng fnancal falures. There has been no specfc research for predcton of Turksh stock market values. The am of ths paper s to use artfcal neural networks to predct Istanbul Stock Exchange (ISE) market ndex value. Prelmnary research performed on Turksh stock market has suggested that the nputs to the system may be taken as: prevous day s ndex value, prevous day s TL/USD exchange rate, prevous day s overnght nterest rate and 5 dummy varables each representng the workng days of the week. After the nputs have been determned, the data have been gathered for the perod of July 1, 2001 through February 28, 2003 from the Central Bank o f R e p u b l c o f T u r k e y. Tranng set s determned to nclude about 90% of the data set and the rest 10% wll be used for testng purposes. Network archtecture s determned to be Mult Layer Perceptron and Generalzed Feed Forward networks. Tranng and testng s performed usng these two network archtectures. However, subsystems are consdered, whch had dfferent number of hdden layers (1, 2 and 4) for a mean-squared error value of The results are then compared wth the results of movng averages for 5 and 10- day perods, whch showed that artfcal neural networks have better performances than movng averages. Keywords: Artfcal neural networks; Stock exchange ndex value; Predcton 1

2 Stock Market Predcton Usng Artfcal Neural Networks Brgul Egel, Meltem Ozturan, Bertan Badur Department of Management Informaton Systems, Bogazc Unversty, Istanbul, Turkey Abstract Predcton of stock market returns s an mportant ssue n fnance. Artfcal neural networks have been used n stock market predcton durng the last decade. Studes were performed for the predcton of stock ndex values as well as daly drecton of change n the ndex. In some applcatons t has been specfed that artfcal neural networks have lmtatons for learnng the data patterns or that they may perform nconsstently and unpredctable because of the complex fnancal data used. In Turkey artfcal neural networks are mostly used n predctng fnancal falures. There has been no specfc research for predcton of Turksh stock market values. The am of ths paper s to use artfcal neural networks to predct Istanbul Stock Exchange (ISE) market ndex value. Prelmnary research performed on Turksh stock market has suggested that the nputs to the system may be taken as: prevous day s ndex value, prevous day s TL/USD exchange rate, prevous day s overnght nterest rate and 5 dummy varables each rep resentng the workng days of the week. After the nputs have been determned, the data have been gathered for the perod of July 1, 2001 through February 28, 2003 from the Central Bank o f R e p u b l c o f T u r k e y. Tranng set s determned to nclude about 90% of the data set and the rest 10% wll be used for testng purposes. Network archtecture s determned to be Mult Layer Perceptron and Generalzed Feed Forward networks. Tranng and testng s performed usng these two network archtectures. However, subsystems are consdered, whch had dfferent number of hdden layers (1, 2 and 4) wth a mean-squared error value of The results are then compared wth the results of movng averages for 5 and 10-day perods, whch showed that artfcal neural networks have better performances than movng averages. Keywords: Artfcal neural networks; Stock exchange ndex value; Predcton 2

3 1. Introducton Predcton of stock market returns s an mportant ssue n fnance. Nowadays artfcal neural networks (ANNs) have been popularly appled to fnance problems such as stock exchange ndex predcton, bankruptcy predcton and corporate bond classfcaton. An ANN model s a computer model whose archtecture essentally mmcs the learnng capablty of the human bran. The processng elements of an ANN resemble the bologcal structure of neurons and the nternal operaton of a human bran. Many smple nterconnected lnear or nonlnear computatonal elements are operatng n parallel processng at multple layers. In some applcatons t has been specfed that ANNs have lmtatons for learnng the data patterns. They may perform nconsstently and unpredctable because of the complex fnancal data used. Sometmes data s so volumnous that learnng patterns may not work. Contnuous and large volume of data needs to be checked for redundancy and the data sze should be decreased for the algorthm to work n a shorter tme and gve more generalzed solutons [1]. Artfcal neural networks have been used n stock market predcton durng the last decade. One of the frst projects was by Kmoto and frends [2] who had used ANN for the predcton of Tokyo stock exchange ndex. Mzuno and frends [3] appled ANN agan to Tokyo stock exchange to predct buyng and sellng sgnals wth an overall predcton rate of 63%. Sexton and frends [4] concluded n 1998 that use of momentum and start of learnng at random ponts may solve the problems that may occur n tranng process. Phua and frends [5] appled neural network wth genetc algorthm to the stock exchange market of Sngapore and predcted the market drecton wth an accuracy of 81%. In Turkey ANNs are mostly used n predctng fnancal falures [6]. There has been no specfc research for predcton of Turksh stock market values. The am of ths paper s to use ANNs to forecast Istanbul Stock Exchange (ISE) market ndex values. 2. Artfcal Neural Network Approach Machne learnng approach s appealng for artfcal ntellgence snce t s based on the prncple of learnng from tranng and experence. Connectonst models, such as ANNs, are well suted for machne learnng where connecton weghts are adjusted to mprove the performance of a network. An ANN s a network of nodes connected wth drected arcs each wth a numercal weght, w, j, specfyng the strength of the connecton (Fgure - 1). These weghts ndcate the nfluence of prevous node, u j, on the next node, u, where p o s tve weghts represent renforcement; negatve weghts represent nhbton [7]. Generally the ntal connecton weghts are randomly selected. Feed -forward networks were frst studed by Rosenblatt [8]. Input layer s composed of a set of nputs that feed nput patterns to the network. Followng the nput layer there wll be at least one or more ntermedate layers, often called hdden layers. Hdden layers wll then be followed by an output layer, where the results can be acheved (Fgure-2). In feed - forward networks all connectons are undrectonal. 3

4 Fgure-1. Connecton weght between nodes. Fgure hdden layers network wth n nputs and 1 output. Mult Layer Perceptron (MLP) networks are layered feed -forward networks typcally traned wth statc backpropagaton. These networks, also known as backpropagaton networks, are manly used for applcatons requrng statc pattern classfcaton [9]. The backpropagaton algorthm selects a tranng example, makes a forward and a backward pass, and then repeats untl algorthm converges satsfyng a pre -specfed mean squared error value. The man advantage of MLP networks s ther ease of use and approxmaton of any nput/output map. The man dsadvantage s that they tran slowly and requre lots of tranng data. Generalzed feed -forward (GFF) networks are a generalzaton of the MLP networks where connectons can jump over one or more layers, but these networks often solve problems much more effcently [9] Tranng Algorthm Tranng s the process by whch the free parameters of the networks (.e. the weghts ) get optmal values. Supervsed learnng models, that are used for MLP and GFF networks, tran certan output nodes to respond to certan nput patterns and the changes n connecton weghts, due to learnng, cause those same nodes to respond to more general 4

5 classes of patterns. In these models nput layer unts dstrbute nput sgnals to the network. Connecton weghts modfy the sgnals that pass through t. Hdden layers and output layer contan a vector of processng elements wth an actvaton functon. Usually the Sgmod functon s used as the actvaton functon. Every unt u computes ts new actvaton u as a functon of the weghted sum of the n p u t s t o u n t u ( u j ) from drectly connected cells. Therefore, the output of each processng unt for the forward pass wll be defned as: S = n j = 0 w u, j * j (1) u = f S ) where ( 1 f ( x ) = (2) 1 x ( + e ) The backward pass s the error back -propagaton and adjustment of weghts. Gradent descent approach wth a constant step length, also referred to as learnng rate, s used to tran the network. Ths method mnmzes the sum of squared errors of the system untl a gven mnmum or stop at a gven number of epochs, where epoch s the term specfyng the number of teratons to be done over the tranng set. The error s mult-dmensonal and may contan many local mnma. A momentum term may be added to avod gettng stuck n local mnma or slow convergence. The output of each processng unt for the backward pass s defned as: ( S ) = u ( u ) f * 1 (3) Weghts are then updated by the formula where ε s the mean squared error and ρ s t h e step sze: ε δ = (4) S w *, j = w, j + ρδ u j (5) After t he tranng process s completed, the network wth specfed weghts can be used for testng a set of data dfferent than those used for tranng. The results acheved can then be used for generalzaton of the approxmaton of the network. 3. M o d e l n g of Stock Market Index Value Forecastng of stock exchange market ndex values s an mportant ssue n fnancal sector. The objectve of ths paper s to llustrate that the ANNs can effectvely be used to predct the Istanbul Stock Exchange (ISE) ndex values usng prevous day s ndex value, prevous day s TL/USD exchange rate, prevous day s overnght nterest rate and 5 dummy varables each representng the workng days of the week. Supervsed learnng models have been utlzed n whch certan output nodes were traned to respond to certan 5

6 nput patterns and the changes n connecton weghts due to learnng caused those same nodes to respond to more general classes of patterns System Model In ths study the followng nput varables were consdered to ultmately affect the stock exchange market ndex value. Prevous day s ISE Natonal 100 ndex value (accordng to closng prce) (ISE_PREV) Prevous day s TL/USD exchange rate (average of buyng and sellng values) (TL_USD_PREV) Prevous day s Smple Interest Rate Weghted Average Overnght (ON_PREV) Dummy varable 1 representng Monday (wll be 1 when the day s Monday, else 0) (M) Dummy varable 2 representng Tuesday (T) Dummy varable 3 representng Wednesday (W) Dummy varable 4 representng Thursday (TH) Dummy varable 5 representng Frday (F) Consderng the nput varables, the followng system model was consdered for the predcton stock exchange market ndex value: f = f (ISE_PREV, T L_USD_PREV, ON_PREV, M, T, W, TH, F) ISE 3.2. Data Sets Expermental data were gathered drectly from the Central Bank of Republc of Turkey for a perod of 417 days startng from July 2, 2001 to February 28, From ths data set, the frst 376 cases (about 90%) were taken as tranng and 41 as testng examples Network Parameters For the system model descrbed before, two dfferent ANN models (MLP and GFF) were appled wth dfferent number of hdden layers (HL = 1, 2, 4) for mnmum mean squared error value of 0.003, for the data set. Thus, 6 dfferent ANN models have been used Tranng Results In ths study, 6 ANN models were appled to the system model, usng an ANN software package. ANN models performances can be measured by the coeffcent of determnaton (R 2 ) or the mean relatve percentage error. Ths coeffcent of determnaton s a measure of the accuracy of predcton of the traned network models. Hgher R 2 values ndcate better predcton. The mean relatve percentage erro r may also be used to measure the accuracy of predcton through representng the degree of scatter. For each predcton model, Eq.6 was utlzed to calculate the relatve error for each case n the testng set. Then, the calculated values were averaged and factored by 100 to express n percentages. ( f ISE ) ( f ISE ) actual ( f ISE ) actual predcted (6) 6

7 Table-1 shows the ANN models wth the R 2 values of the 3 MLP and 3 GFF network models appled to system model. Number of A N N M o d e l H d d e n L a y e r s M L P G F F Table-1 Coeffcent of determnatons (R 2 ) for ANN models 3.5. Comparson wth Movng Averages The ANN performances can be compared wth Movng Averages (MA) approach. The movng average s the average of lagged ndex values over a specfed past perod (5 and 10 days n ths study). The mean relatve percentage errors were calculated as for 5 days and 0.03 for 10 days. Table-2 shows all models wth mean relatve percentage errors. Model Mean Relatve Percentage Error (%) MLP - 1 H d d e n L a y e r 1.62 MLP - 2 Hdden Layers 1.65 MLP - 4 Hdden Layers 1.70 GFF - 1 Hdden Layer 1.59 GFF - 2 Hdden Layers 1.65 GFF - 4 Hdden Layers 1.71 MA - 5 days 2.17 MA - 10 days 3.03 Table-2 Mean relatve percentage errors for all models 4. E v aluaton The accuracy of the predcton for each ANN model has been compared by the coeffcent of determnaton. The effcency of ANN models vared wth the number of hdden layers. For both MLP and GFF network models, the hghest accuraces are obtane d wth 1 hdden layer. The mean relatve percentage errors calculated for all models verfed that the ANN models were superor to the MA model. 7

8 5. Concluson Ths study was amed at fndng the best model for the predcton of Istanbul Stock Exchan ge market ndex values. Total of 8 sets of predctons, that result from the applcaton of 6 ANN models and two MA were performed. Results were compared usng the coeffcents of determnaton for ANN models and usng mean relatve percentage errors for a ll of the models. Based on the fndngs of ths study t can be concluded that: 1. The predcton models based on ANNs were more accurate than the ones based on MAs. 2. Among the ANN models, GFF network model was found to be more approprate for the predcton. Acknowledgement Authors would lke to thank Bogazc Unversty Research Fund for supportng the project 03N301. R e f e r e n c e s [1] Dash, M. and Lu, H. (1997), Feature selecton methods for classfcatons, Intellgent Data Analyss: An Internatonal Journal 1(3), [2] Kmoto, T., Asakawa, K., Yoda, M., and Takeoka, M. (1990), Stock market predcton system wth modular neural network, n Proceedngs of the Internatonal Jont Conference on Neural Networks, 1-6. [3] Mzuno, H., Kosaka, M., Yajma, H. and Komoda N. (1998), Applcaton of Neural Network to Techncal Analyss of Stock Market Predcton, Studes n Informatc and Control, Vol.7, No.3, pp [4] Sexton, R. S., R. E. Dorsey And J. D. Johnson (1998), Toward global optmzaton of neural networks: A comparson of the genetc algorthm and backpropagaton, Decson Support Systems 22, [5] Phua, P.K.H. Mng, D., Ln, W. (2000), Neural Network Wth Genetc Algorthms For Stocks Predcton, Ffth Conference of the Assocaton of Asan-Pacfc Operatons Research Socetes, 5th - 7th July, Sngapore. [6] Yldz, B. (2001), Use of Artfcal Neural Networks n Predcton of Fnancal Falures (Turksh), Journal of IMKB, Vol.5, No.17. [ 7 ] Gallant SI. Neural network learnng and e xpert systems. MIT Press, Cambrdge, [ 8 ] Rosenblatt F. Prncples of neurodynamcs: perceptrons and the theory of bran mechansms. Spartan Press, Washngton, DC, [ 9 ] Rumelhart DE, Hnton GE, Wllams RJ. Learnng nternal representatons by error propagaton. Parallel Dstrbuted Processng: Exploratons n the Mcrostructures of Cognton. Rumelhart DE., McClelland, J.L. (eds.), 1: MIT Press, Cambrdge,