An Improved Model for Stock Price Prediction using Market Experts Opinion

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1 An Improved Model for Stock Prce Predcton usng Market Experts Opnon Adeby, Ayodele. A. Department of Computer and Informaton Scences, Covenant Unversty, Ota, Ngera Ayo, Charles K Department of Computer and Informaton Scences, Covenant Unversty, Ota, Ngera ckayome@yahoo.com Otokt, Sunday O Department of Busness Studes, Covenant Unversty, Ota, Ngera dr_atok@yahoo.com ABSTRACT Several research efforts had been done to forecast stock prce based on techncal ndcators whch rely purely on hstorcal stock prce data. Nevertheless, ther performance s not always satsfactory. However, there are other nfluental factors whch can affect the drecton of stock market whch form the bass of market experts opnon such as nterest rate, nflaton rate, foregn exchange rate, busness sector, management calber, government polcy and poltcal effects among others. In ths paper, the effect of usng market experts opnon n addton to the use of techncal and fundamental ndcators for stock prce predcton s examned. Input varables extracted from these hybrd ndcators are fed nto a fuzzy-neural network for mproved accuracy of stock prce predcton. The emprcal results obtaned wth publshed stock data shows that the proposed model can be effectve to mprovng accuracy of stock prce predcton. Keywords: Artfcal Neural Networks, Fuzzy Logc, Techncal and Fundamental Indcators, Market Experts Opnon. 1. Introducton Stock prce predcton has always been a subect of nterest for most nvestors and professonal analysts. Nevertheless, fndng the best tme to buy or sell has remaned a very dffcult task because there are numerous factors that may nfluence stock prces [1, 2, 3]. Several research efforts have been carred out to predct the market n order to make proft usng dfferent technques wth dfferent results. Artfcal neural networks (ANNs) and fuzzy logc (FL) are two of the key technologes that have receved growng attenton n solvng real world, nonlnear, tme varant problems. The need to solve hghly nonlnear, tme varant problems has been on the ncrease as many of today s applcatons have nonlnear and uncertan behavour whch changes wth tme lke stock market [4, 5]. The several dstngushng features of ANNs make them attractve and wdely used for forecastng task n the doman of 28

2 busness, economc, and fnance applcatons. Frst, artfcal neural networks are data-drven self-adaptve methods n that there are few a pror assumptons made about the models for problems under study. Second, artfcal neural networks can generalze after learnng the data presented to them and correctly nfer unseen part of the populaton. Thrd, ANNs are unversal approxmators n that t has been shown that a network can approxmate any contnuous functon to any desred accuracy. Fnally, ANNs are strong n solvng nonlnear problems. Tradtonal technques to tme seres predctons, such as the Box-Jenkns or Autoregressve Integrated Movng Average (ARIMA) assume that the tme seres under study are generated from lnear processes whch s napproprate because real world systems are often nonlnear [6, 7, 8]. A revew of prevous studes on stock prce forecastng shows that the use of techncal ndcators wth ANN model s prevalent. In recent tme, hybrd models have been effectvely engaged n stock prce predcton. Examples n lterature where techncal ndcators have been used nclude the followng: n [9, 10, 11, 12, 13, 14] techncal ndcators wth ANNs model was used to forecast stock prce. Other works that had appled ANN models wth techncal ndces to stock prce predctons wth varyng fndngs are n [15, 16, 17, 18, 19, 20, 21, 22, 23]. Smlarly, n [8, 24, 25, 26] hybrd ANN wth techncal ndcators was used and ther fndngs showed that ANN combned wth other technques exhbt effectvely mproved forecastng accuracy of stock prce predcton. However, O Connor and Maddem n [18] used fundamental ndcators wth ANN and ther fndngs 29 revealed that ANN has forecast ablty n stock market because t has better return than overall stock market. From the above lterature revew, t s obvous that techncal ndcators wth ANN model had been wdely used, whle there are only few cases of the use of fundamental ndcators. Ths paper contrasts prevous approaches by combnng techncal ndcators, fundamental ndcators and experts opnon to mprove stock prce predcton usng fuzzy-neural archtecture. The techncal analyss varables are the core stock market ndces such as current stock prce, openng prce, closng prce, volume, hghest prce and lowest prce etc. Fundamental ndcators are the company performance ndces such as prce per annual earnng, return on asset, return on common equty, book value, fnancal status of the company, etc. whle the experts opnon are other nfluental factors such as nterest rate, nflaton rate, foregn exchange rate, busness sector, management calber, government polcy and poltcal factors among others. Hence, the novelty of ths work stems from the use of hybrd parameters for mprovng stock market predcton. The rest of the paper s organzed as follows. Secton 2 presents a revew of basc concepts and modelng technques used n ths study. Secton 3 descrbes the proposed hybrd model. Secton 4 also descrbes the research methodology used. The mplementaton s presented n secton 5, whle secton 6 dscussed the results obtaned. The paper s concluded n secton 7.

3 2. Overvew of Artfcal Neural Networks and Fuzzy Logc In ths secton, the basc concepts and modelng approaches of artfcal neural networks (ANNs) and fuzzy logc models for tme seres predcton are brefly revewed. 2.1 ANNs approach to Tme Seres modelng One of the sgnfcant advantages of the ANN models over other classes of nonlnear models s that ANNs are unversal approxmators that can approxmate a large class of functons wth hgh degree of accuracy. Ther power comes from parallel processng of the nformaton from data. No pror assumpton of the model form s requred n the model buldng process rather the network model s largely a functon of the characterstcs of the data [6]. One of the ANN models that s wdely used n tme seres forecastng s backprogaton neural network (BPNN) model. The man reason s that t provdes an effcent way to manage the networks error functon wth respect to the weghts adustment and hence mnmzes the dscrepancy between real data and the output of the network model. For tme seres forecastng, the relatonshp between the output (y t ) and the nputs ( yt 1, yt 2,..., yt p ) has the followng mathematcal representaton: q p yt = w0 + w. g w0 + w. yt 1 + εt = 1 = 1 (1) where, w ( = 0,1,2,..., p, = 1,2,..., q) and w ( = 0,1,2,..., q) are model parameter often called connecton weghts; p s the number of nput nodes; and q s the number hdden nodes. The actvaton functon can take several forms. The most wdely used actvaton functon for output layer s the lnear functon. The logstc and hyperbolc functons are often used as the hdden layer transfer functon that are shown n equatons (2) and (3), respectvely. 1 Sg( x) =, 1+ exp( x) (2) 1 exp( 2x) Tanh( x) = (3) 1+ exp( 2x) Hence, the ANN model of (1), performs a nonlnear functonal mappng from past observatons to the future value y t,.e. yt = f ( yt 1,..., yt p, w) + ε t, (4) where, w s a vector of all parameters and f(.) s a functon determned by the network structure and connecton weghts [6]. 2.2 Fuzzy logc One way to represent nexact data and knowledge, closer to human-lke thnkng, s to use fuzzy rules nstead of exact rules when representng knowledge. Fuzzy systems are rule-based expert systems based on fuzzy rules and fuzzy nference. Fuzzy rules represent n a straghtforward way commonsense knowledge and sklls, or knowledge that s subectve, ambguous, vague, or contradctory. Ths knowledge mght have come from many dfferent sources. Commonsense knowledge may have been acqured from long-term experence, from the experence of many people, over many years [28]. A fuzzy logc system conssts of three man blocks: fuzzfcaton, nference mechansm, and defuzzfcaton. These 30

4 components of fuzzy logc system are brefly descrbed below [29] Fuzzfcaton Fuzzfcaton s a mappng from the observed numercal nput space to the fuzzy sets defned n the correspondng unverse of dscourse. The fuzzfer maps a numercal value denoted by x = ( x1, x2,..., x m ) nto fuzzy sets represented by membershp functons n U. The Gaussan functons, denoted by µ ( ) as expressed n equaton (5). A x 2 1 x b µ = ( x ) a exp (5) A 2 c where1 m refers to the varable () from m consdered nput varables; 1 consders the membershp n functon among all n membershp functons consdered for varable (); a defnes the maxmum of each Gaussan functon, here a = 1.0; b s the center of the Gaussan functon; and shape wdth. c defnes ts Inference Mechansm Inference mechansm s the fuzzy logc reasonng process that determnes the outputs correspondng to the fuzzfed nputs. The fuzzy rule-based s composed by IF-THEN rules lke R (l) ( l) ( l) : IF (x 1 s A 1 and x 2 s A 2 (l) (l) and x m s A m ) THEN ( y s w ), where: R (l) s the lth rule wth 1 l c determnng the total number of rules; x 1, x2,..., xm and y are, respectvely, the nput and output system varable; (l) A are the antecedent lngustc terms n rule 31 (l) wth 1 m beng the number (l ) antecedent varables; and w s the rule concluson for that type of rules, a real number usually called fuzzy sngleton. The concluson, a numercal value can be consdered as a pre-defuzzfed output that helps to accelerate the nference process. The reasonng process combnes all rule (l ) contrbutons w usng the centrod defuzzfcaton formula n a weghted form, as ndcated n equaton (6). The equaton maps nput process states x ) to ( the value resultng from nference functon Y ( x ). Y ( x ) = m c l = 1 = 1 c l = 1 = µ ( l ) ( x ) A w µ x ( l ) ( A ) 1 m ( l ) (6) Defuzzfcaton Bascally, defuzzfcaton maps output fuzzy set defned over an output unverse of dscourse to crsp outputs. The common defuzzfcaton strateges are the max crteron method, the mean of maxmum method and the center of area method. 3. The proposed hybrd model In ths paper, a hybrd predctve model based on techncal, fundamental ndcators and experts opnon usng fuzzy neural archtecture s proposed. The am s to yeld more accurate results n stock prce predcton. Based on the dea behnd techncal analyss of nvestment tradng, t s assumed that the behavour of stock market n the future could be predcted wth prevous nformaton gven n the hstory [30]. Therefore, there exsts a functon n equaton (7) p t + 1) = f ( p,..., p ; x,..., x ; y,..., y ;...) (7) ( t k t t 1 t t m t

5 where p s the stock prce, x and y are the other nfluence factors such as daly hghest prce, daly lowest prce, experts opnon etc. In the frst phase, fuzzy logc s used to convert the nput qualtatve data of experts opnon lngustc varables nto fuzzy values express n the range of [0, 1] usng lnear membershp functon. The three lngustc propertes that was used are low, medum and hgh. The dependent varable crterons are based on [1, 10]. Fuzzy set low ranges from 1 to 4, fuzzy set medum ranges from 3 to 7 and fuzzy set hgh ranges from 6 to 10 and ther membershp expresson are shown n equaton (8), (9) and (10) respectvely. µ 1 1 low ( x) = x (8) 3 3 µ 1 3 medum ( x) = x (9) 4 4 µ 1 3 hgh ( x) = x (10) 4 2 In second phase, an artfcal neural network s used n order to model the nonlnear data. Thus, q p yt = w0 + w. g w0 + w. yt 1 + ε t (11) = 1 = 1 where, w ( = 0,1,2,..., p, = 1,2,..., q) and w ( = 0,1,2,..., q) are model parameter often called connecton weghts; p s the number of nput nodes; and q s the number hdden nodes. The study used three-layer (one hdden layer) multlayer perceptron models (a feedforward neural network model) traned wth backpropagaton algorthm. The actvaton functon that was used s sgmod functon. The fgure 1 depcts the fuzzy-neural archtecture used n ths study. Quanttatve Data Fuzzy Interface Input Neural Networks Decson Output Qualtatve Data Learnng Algorthm Neural outputs Fg.1: Proposed Fuzzy-Neural Archtecture for Stock Predcton In ths paper three dfferent models for the emprcal nvestgaton and valdaton of the proposed model was used as ndcated n table 4. The frst model used ANN only. The nputs to the ANN model are purely techncal analyss varables of hstorcal stock data. The second and thrd models are hybrd models that combned artfcal neural networks and fuzzy logc. The nputs of second model are techncal and fundamental analyss varables only whle the nputs to the thrd model combned both the techncal and fundamental varables wth the market experts opnon 32

6 varables. The fundamental varables consst of fnancal ratos such as P/E, ROA, and ROE. P/E s equal to the market prce per share of stock dvded by the earnng per share. The ROA measures a frm s performance n usng the asset to generate ncome. ROE measures the rate of return earned on the common stockholders nvestment. The experts opnon consst of nflaton rate (I), management qualty (M), government polcy (G) and poltcal factors (T) etc. For the hybrdzed approach 20 nput varables was dentfed and used to tran the network comprsng both techncal, fundamental varables, and experts opnon varables as ndcated n model 3 of table 4. Table 4: The Input and Output Parameters of the Models used n ths Study Model Technque Input Output 1 ANN O -1,O -2,H -1,H -2,L -1,L -2,C -1,C -2,V -1,V -2 y(t+1) 2 FL+ ANN O -1,O -2,H -1,H -2,L -1,L -2,C -1,C -2,V -1,V -2,P -1,P -2,R - y(t+1) 1,R -2,E -1,E -2 3 FL+ ANN O -1,O -2,H -1,H -2,L -1,L -2,C -1,C -2,V -1,V -2,P -1,P -2,R - 1,R -2,E -1,E -2,M -1, I -2,G -1,T -2, y(t+1) Table 5: Descrpton of Input Varables used n ths study Techncal Analyss Varables Fundamental and Expert Opnon Varables O -1 the openng prce of day -1 P -1 the prce per annual earnng of year -1 O -2 the openng prce of day -2 P -2 the prce per annual earnng of year -2 H -1 the daly hgh prce of day -1 R -1 return on asset of tradng year -1 H -2 the daly hgh prce of day -2 R -2 return on asset of tradng year -2 L -1 the daly low prce of day -1 E -1 return on equty of tradng year -1 L -2 the daly low prce of day -2 E -2 return on equty of tradng year -2 C -1 the closng prce of day -1 M -1 management qualty as at tradng day -1 C -1 the closng prce of day -2 I -1 nflaton rate as at tradng day -1 V -1 the tradng volume of day -1 G -1 government polcy as at tradng day -1 V -2 the tradng volume of day -2 T -1 poltcal effect as at tradng day Methodology The central obectve of ths paper s to mprove the accuracy of stock prce predcton by the combnaton of techncal ndcators (quanttatve data), fundamental ndcators and market experts opnon (qualtatve data) usng fuzzy neural archtecture. In order to acheve ths am the followng steps were carred out as descrbed n the subsecton below. 4.1 Data Collecton and Pre-processng Data selecton and pre-processng are crucal step n any modelng effort. In 33

7 order to generalze the new predctve model, dfferent dataset of hstorcal stock prces from dfferent companes were collected from Ngera Stock Exchange (NSE) except the fnancal ndces whch are obtaned from publshed annual report and expert s opnon. The stock data are dvded nto two sets: the tranng and testng data whch are scaled to the range of (0, 1) usng mn-max normalzaton equaton (9). x xmn xn = (12) x x where n max mn x s the real-world stock value, x s the scaled nput value of the realworld stock value x and xmn and xmax are the mnmum and maxmum values of the unscaled dataset. The network predcted values, whch are n the range (0, 1), are transformed to real-world values wth the followng equaton: x = x ( x x x (13) n max mn ) + mn 4.2 Input Varables The basc nput data ncludes: raw data such as the daly open, hgh, low and close prces, and tradng volumes of NSE whch formed the techncal varables n table 1. Table 2 conssts of fundamental varables whle the market expert opnon varables are lsted n table 3. Table 1: Stock Varables (Techncal Indcators) Table 2: Stock Varables (Fundamental Indcators) Table 3: Possble Stock Prce Influence Factors (Experts Opnon) Varable Descrpton M I G T Varable O C V H L Varable P/E ROA ROE Descrpton Openng prce of a stock for a specfc tradng day Closng prce of a stock for a specfc tradng day Stock transactons volume (Buy/Sell) Hghest stock prce wthn a specfed tme nterval (day, month etc.) Lowest stock prce wthn a specfed tme nterval (day, month etc.) Descrpton Prce per annual earnng Return on Asset Return on Common Equty Management Qualty Inflaton Rate Government Polcy Poltcal Effects 5. Implementaton For the mplementaton of the dfferent models, we expermented wth the dfferent neural network model 34

8 confguratons to determne the best performance n each of the model usng Matlab Neural Network Tools Box verson 7. The algorthm of the ANN experment s shown n fgure 2 below. Tranng data and testng data was carefully selected and the varous outcomes of the dfferent network structure models mplemented wth Matlab Neural Network Tools Box verson 7. In tranng the network model, the test data were not used. It was traned for 3,000 epochs for each tranng set. The output of neural network model was analysed by comparng the predcted values wth the actual values over a sample perod. For the output of the proposed model to be consdered useful for tradng decson support, overall ht rate of level of accuracy should be consderably hgh enough to be acceptable. The emprcal results are presented n the next secton. (1) Defne the output (2) Choose the approprate network archtecture and algorthm. Multlayer perceptron model traned wth backpropagaton algorthm was prmarly chosen. (3) Determne the nput data and preprocess f necessary. (4) Choose approprate learnng functon. (5) Choose the approprate network structure. (6) Perform the tranng and testng for each cycle. (7) If the network produce acceptable results for all cycles, perform step 8 else perform step 5 to try other approprate network structures else perform step 4 to try wth other learnng algorthm else perform step 3 to add or remove from nput set. Otherwse, go back to step 2 to try dfferent neural 35 network archtecture. (8) Fnsh - record the results. Fgure 2: Algorthm for ANN predctve model. 6. Results and Dscusson After several experments wth dfferent network archtectures, the network predctve model that gave the most accurate daly stock prce predcton n model 1 was Ths model was created wth artfcal neural networks. The data used was purely techncal analyss varables whch are quanttatve n nature. The nput varables to the model consst of ten techncal varables. For model 2 that combned techncal and fundamental analyss varables usng fuzzy neural approach. The network predctve model that gave the best accurate daly stock prce predcton was The proposed hybrd model (model 3), whch combned the quanttatve and qualtatve data of techncal, fundamental and experts opnon respectvely usng fuzzy neural approach. The best-ftted network that gave the best forecastng accuracy wth test data s composed of twenty nputs, twentysx hdden and one output neurons The results presented n table 6 were the fndngs from testng perod (out of sample test data) over dfferent models. Smlarly, fgure 3-5 llustrates the correlaton of the level accuracy among dfferent models. From the emprcal results, the forecastng accuracy level of model 1`compared wth model 2 are qute mpressve. However, the performance of model 2 was better than model 1 n the level of accuracy on many occasons from the dfferent test data. From the fgure 5, t s obvous that model 3 s the best of all the three predctve models. There s a great

9 mprovement n terms of forecastng accuracy n comparson to results of model 1 and 2. The stock prce predcton accuracy of the proposed model that combned techncal, fundamental ndcators and experts opnon to create a predctve model was the best. Hence, the proposed predctve model can be used successfully as decson-support n real-lfe tradng n a way that wll enhance the proftng of nvestors or traders for daly tradng. Table 6: Sample of Emprcal Results of Daly Stock Prce Predcton usng dfferent model Sample Actual Predcted Values Perod Value Model 1 Model 2 Model 3 12/10/ /11/ /12/ /15/ /16/ /17/ /18/ /19/ /22/ /23/ /24/ /26/ /29/ /30/ of stock prce predcton wth varyng results. In ths paper, an mproved predctve model for stock prce predcton based on experts opnon wth techncal and fundamental ndces usng fuzzy-neural archtecture s presented. The emprcal results confrmed superor performance of the proposed model to mprove forecastng accuracy of stock prce over the conventonal approach of usng ANN model wth techncal ndcators. Therefore, the proposed predctve model has the potental to enhance the qualty of decson makng of nvestors n the stock market by offerng more accurate stock predcton. In future work, the crtcal mpact of specfc experts opnon varables on qualty of stock prce predcton wll be examned. Stock Prces /10/2008 Predctve Model Aganst Actual Stock Prces 12/12/ /14/2008 Fgure 3: Model 1 12/16/ /18/ /20/ /22/ /24/2008 Sample Perod Actual 12/26/ /28/2008 Predcted 12/30/ Concluson Techncal ndces had been wdely used n forecastng stock prces wth artfcal neural networks. Nevertheless, ther performance s not always satsfactory. Also, n recent tmes, hybrd models that combne ANNs and other ntellgent technques wth techncal ndces had been engaged n order to mprove accuracy level 36 Stock Prces Predctve Model Aganst Actual Stock Prces /10/ /12/ /14/2008 Fgure 4: Model 2 12/16/ /18/ /20/ /22/ /24/2008 Sample perod Actual 12/26/ /28/2008 Predcted 12/30/2008

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