Extracting Trading Rules from the Multiple Classifiers and Technical Indicators in Stock Market

Transcription

1 Extractig Tradig Rules from the Multiple Classifiers ad Techical Idicators i Stock Market Kyoug-jae Kim ad Igoo Ha Graduate School of Maagemet, Korea Advaced Istitute of Sciece ad Techology Joh S. Chadler Departmet of Accoutacy, Uiversity of Illiois at Urbaa-Champaig Abstract This study iteds to mie reasoable tradig rules by classifyig the up/dow fluctuat directio of the price for Korea Stock Price Idex 200 (KOSPI 200) futures. This research cosists of two stages. The first stage is classifyig the fluctuat directio of the price for KOSPI 200 futures with several techical idicators usig artificial itelligece techiques. Ad the secod stage is miig the tradig rules to resolute coflict amog the outputs of the first stage usig the iductive learig. To verify the effectiveess of proposed approach, this study composes four comparable models ad performs statistical test. Experimetal results show that the classificatio performace of the proposed model outperforms that of other comparable models. I additio, the proposed model yields higher profit tha other comparable models ad buy-ad-hold strategy. Key words: Rule extractio, Coflict resolutio, Iductive learig, Artificial eural etwork, Case-based reasoig.

2 I. Itroductio It is kow that stock market shows a oliear patter. By this reaso, there may be some limitatios to aalyze the stock market with liear model. Therefore, artificial itelligece (AI) techiques are ofte used for the oliear patter aalysis such as stock market aalysis. Several studies show that artificial eural etwork ad case-based reasoig ca be applied to stock market predictios, but most of them have focused maily o predictio of spot market ad time series data (Ahmadi, 1990, Kamijo ad Taikawa, 1990, Kimoto et al., 1990, Yoo ad Swales, 1991). They also did ot bare outstadig predictio accuracy because tremedous oise ad o-statioarity of data. Korea lauched tradig i idex futures market (KOSPI 200) o May 1996, the more people became attracted to this market, because the ivestor ca avoid or reduce the risk of stock ivestmet via idex futures. The lack of the research o the idex futures market i Korea has ot met the people s iterest. By this reaso, this research iteds to classify the daily up/dow fluctuat directio of the futures price for Korea stock idex (KOSPI 200) to meet this recet surge of iterest. The classificatio methodologies employed i this research are the artificial eural etwork (ANN) ad case-based reasoig (CBR). Through the experimet, we ca get two outputs from each classifier. May cases of the two models idicate a cosistet sigal, but some cases produce a icosistet sigal betwee two models. Prior studies preseted several kids of esemble methods betwee the coflict of multiple classifiers (Macli ad Shavlik, 1995, Hase ad Salamo, 1990, Licol ad Skrzypek, 1990, Perroe ad Cooper, 1994, Rost ad Sader, 1993, Zhag et al., 1992, Wolpert, 1992). But most of them, the basic idea is to combie multiple eural etwork models, ot the heterogeeous classifiers. I additio, most of them focused o predictio or classificatio accuracy by combiig results of each classifier. Moreover, they did ot explai how these outputs

3 were produced. I this study, we try to resolute coflict betwee two outputs by tradig rules, ot to combie it. Tradig rules ca resolute these coflicts. ANN ad CBR, however, is ot a outstadig tool for rule geeratio. Therefore, we employ iductive learig to geerate the tradig rules. I this way, we ca take followig beefits. We ca resolute coflict betwee the outputs of multiple models. I additio, ivestors i the stock market ca get reasoable tradig rules. Fud maagers of tradig compay or cosultats of cosultig firm also ca modify this rule by addig their preferred factors i the aalysis of ivestmet. To verify the effectiveess of proposed approach, this study composes four comparable models ad performs statistical test. As to statistical test, we perform the McNemar test to examie whether the classificatio performace of proposed approach is sigificatly higher tha that of competitive approaches. I additio, we perform a simulatio of buyig ad sellig of stocks to verify the profitability of proposed approach. The rest of the paper is orgaized ito four sectios. The ext sectio reviews related prior researches. I the third sectio, we propose the research model ad execute experimets. I the fourth sectio, the results are verified ad discussed. I the followig sectio, the coclusios ad future research issues are preseted 2.1 AI Applicatios i Stock Market II. Prior Research Kimoto et al. (1990) ad Kamijo ad Taikawa (1990) used several learig algorithm ad predictio method for the Tokyo stock exchage prices idex (TOPIX) predictio system. Ahmadi (1990) was tried to test the Arbitrage pricig theory (APT) by ANN. Yoo ad Swales (1991) performed predictio usig mixed qualitative ad quatitative data. The architecture of eural etwork model was a four-layered etwork. Lee et al. (1989) developed the itelliget stock

4 portfolio maagemet system (ISPMS). They are attempted to take advatage of optimizatio models ad expert systems, itegrated two models. Trippi ad DeSieo (1992) executed daily predictio of up ad dow directio of S&P 500 Idex Futures usig ANN. They performed composite rule geeratio procedure to geerate rules for combiig outputs of etworks. Duke ad Log (1993) also executed daily predictio of Germa Govermet Bod Futures usig feedforward backpropagatio eural etwork. Choi et al. (1995) also performed daily predictio of up/dow directio of S&P 500 Idex Futures. I summary, above three studies showed the availability of the artificial itelligece to predict future price for equity idex. However, they did ot obtai outstadig predictio accuracy. I additio, they did ot take variables specific to futures market like basis or ope iterest (OI) ito cosideratio i selectig iput variables. 2.2 Esemble Methods amog Multiple Classifiers Prior studies preseted several kids of esemble methods betwee classifiers. But most of them, the basic idea is combie multiple eural etwork models, ot the differet classifiers. The basic idea i combiig eural etworks is to trai a umber of etworks, ad the somehow use the collectio to icrease geeralizatio (Macli ad Shavlik, 1995). Hase ad Slamo (1990) used votig schemes, Licol ad Skrzypek (1990) ad Perroe ad Cooper (1994) used simple average scheme ad weighted average scheme respectively. Others used scheme for traiig combier (Rost ad Sader, 1993, Zhag et al., 1992, Wolpert, 1992). III. Research Model ad Experimets 3.1 Domai Kowledge based Categorical Preprocessig The Problem of aalyzig data usig statistical method or AI techiques is separable to tred

5 predictio ad patter classificatio problem. Tred predictio problem usually treated cotiuous sigle or multiple time series data as iput variable. It maily aims to capture temporal patters betwee the data o the time lag. The examples of tred predictio are stock price predictio, iterest rate predictio or ecoomic forecastig by regressio or time series aalysis (ARIMA etc.). However, patter classificatio problem such as bod ratig or credit evaluatio is usually uses multiple discrete or cotiuous data as iput variable. It chiefly aims to grasp the correlatio betwee the data o the same poit of time. Whe aalyzig the time series data usig ANN, cosiderig temporal patters betwee the data o the time lag is very importat. A temporal patter, however, ca be difficult to trai because the multi-layer perceptro has the risk of learig the uecessary radom correlatio ad oise, because it has a outstadig ability of fittig. Weiged et al. (1991) used weight-elimiatio, ad Jhee ad Lee (1993) used recurret eural etwork to prevet the overfittig problem. Moreover, time series predictio requires a log computatioal time because it uses a large umber of complex relatioships. Because of above reasos, this study icorporates the categorical approach based o domai kowledge for data preprocessig. Traditioal data preprocessig method geerally icludes liear scalig to [0,1] or [-1,1]. While the categorical preprocessig i this study mea categorizig cotiuous iput variables to some discrete categories. The categorical classificatio criteria are expert s kowledge. For example, market techicias usually regard below 25 of stochastic %K level as the sigal of a bear market, ad above 75 as the sigal of a bull market ad betwee 25 ad 75 as the sigal of a eutral market. The categorical approach ca covert cotiues time series data ito discrete ad symbolic oe for experimets. By this procedure, we ca perform patter classificatio i stock market

6 aalysis rather tha time series predictio. With patter classificatio problem, we ca overcome the limitatios of predictio problem. The categorical preprocessig brigs several advatages: This approach effectively filters the data ad traiig the classifier, ad ca extract the rules from the classifier easily. The superiority of this approach to traditioal preprocessig was justified by prior studies (Kim ad Ha, 1997, Kim ad Ha, 1998). Table 1 shows the examples of categorical classificatio criteria. Category Idicator Category 1 Category 2 Category 3 Stochastic %K below above 75 Mometum (-) 0 or (+) CCI (commodity chael idex) (-) 0 or (+) OSCP (price oscillator) (-) 0 or (+) PVI (positive volume idex) below MA5 of PVI above MA5 of PVI Stochastic Slow %D below above 75 RSI (relative stregth idex) below above 70 ROC (rate of chage) below or above 100 A/D Oscillator below or above 0.5 <Table 1> The examples of categorical classificatio criteria 3.2 Research Framework This study is composed of two phases. The Objective of the first phase is kowledge acquisitio usig machie learig. ANN ad CBR are two compoets of machie learig tool. Besides, categorical data preprocessig is preseted for ew preprocessig method. The secod phase is to resolve coflict betwee the outputs of ANN ad CBR whe both give icosistet sigals. By this procedure, this study ca geerate reasoable tradig rules from the multiple classifiers ad techical idicators i stock market. I this phase, the outputs of ANN ad CBR are

7 used as oe of the techical idicators like CCI, RSI etc. The research framework of this study is show i Figure 1. Kowledge acquisitio Rule extractio Machie learig Coflict resolutio ANN CBR Iductive Learig Categorical preprocessig Techical idicator Other factors Techical idicator Database <Figure 1> The research framework 3.3 Research Data ad Experimets Research data The research data used i this research is futures price for KOSPI 200 from May 1996 through November Futures are the stadard forms that decide the quatity ad price i the certified market (tradig place) at certai future poit of time (delivery date). Geeral fuctios of futures market are supplyig iformatio about future price of commodities, fuctio of speculatio ad hedgig (Kolb ad Hamada, 1988). Beig differet from the spot market, futures market does ot have cotiuity of price data. That is because futures market has price data by cotract. So, i futures market aalysis, earest cotract data method is maily used ad icorporated i this research. May previous stock market aalyses have used techical or fudametal idicator. I

8 geeral, fudametal idicators are mostly used for log-term tred aalysis while techical idicators are for short-term patter aalysis. I this research, we use the techical idicators as iput variables. Iitial available variables are techical idicators such as PVI (positive volume idex), Stochastic %K, Stochastic %D, Stochastic Slow %D, Basis, Ope iterest, Mometum, ROC (rate of chage), LW%R (Larry William s %R), A/D Oscillator (accumulatio / distributio oscillator), ADL (Accumulatio / distributio Lie), Disparity 5days, CCI (commodity chael idex), OSCP (price oscillator) ad RSI (relative stregth idex). The descriptio ad formula of techical idicators are preseted i Appedix. Previous researches usually used the statistical method such as correlatio test, factor aalysis, stepwise regressio aalysis etc. This study uses stepwise regressio aalysis ad geetic algorithms (GA) for iput variable selectio. I the first place, this study screes the cadidate for iput variables by stepwise regressio aalysis ad selects appropriate variables. The GA is executed for selected variables from regressio aalysis. GA is performed by NeuralWorks Predict (NeuralWare, Ic., 1995). The crossover probabilities ad probability of mutatio assumed to be 0.7 ad 0.05 respectively. I additio, we use two kids of AI techiques; oe is ANN ad the other is CBR. Cosequetly, fial iput variables for each AI techiques are summarized at Table 2. GA selects these variable sets, because each set reveals the best evaluatio values respectively. ANN CBR Stochastic %K, Mometum, CCI, OSCP, PVI Stochastic Slow %D, RSI, ROC, A/D Oscillator, PVI <Table 2> Iput variables for ANN ad CBR Experimets Phase I: Kowledge Acquisitio

9 I Phase I, experimets are implemeted by NeuralWorks Predict (NeuralWare, Ic., 1995) for ANN modelig ad KATE 5.02 (AckoSoft, 1996) for CBR modelig. The backpropagatio algorithm ad sigmoid fuctio are used i ANN. Learig rate ad mometum is 0.1 respectively ad iitial weight is 0.3. The 10% of data for testig, 20% for holdout, ad 70% for traiig mutually ad exclusively used i order to avoid overfittig. Ad 50,000 learig evets sice miimum average error of test set are permitted. I experimets for CBR, this study uses earesteighbor method as case retrieval algorithm ad employs the Euclidea distace as a measure of similarity. We use cross-validatio method to solve isufficiecy problem i the umber of data ad to geeralize the experimetal results. The cross-validatio error rate estimator is a almost ubiased estimator of the true error rate of a classifier (Weiss ad Kulikowski, 1991). I this study, first we classifyig the mutually exclusive five sets which is composed of 30 of all 150 data respectively. The it uses four sets for traiig ad testig ad the other oe set for holdout. We repeated this procedure for five times. Fially, we compose data set of 600 data for traiig ad testig ad 150 data for validatig Phase II: Coflict Resolutio through Rule Extractio As the results of Phase I, we get the two experimetal outputs by ANN ad CBR for each case. If above two outcomes give the same sigals, the ivestors follow that. If above two, however, do ot give same sigals, ivestors may be come ito a coflict. Moreover, some ivestors may wish the model cosider the idividual preferred factors of decisio makig about ivestmet, for example raifall, specific techical idicator, climate etc. Because the model selects its iput variables through the structured way, such as statistical test or heuristic search, these factors caot be reflected i the model etirely. I this study, we use the iductive learig to cosider the user-

10 preferred factors ad to resolute coflict amog the outputs of model ad above factors. I this way, we ca take followig beefits. We ca resolute coflict amog the output of each model ad userpreferred factors. I additio, fud maagers i the Securities compay or cosultats at cosultig firm ca modify this rule by addig their preferred factors i the aalysis for ivestmet. Moreover, ivestors i the stock market ca get reasoable tradig rules i ivestmet. The coflict resolutio rule is as follows. If the output of CBR ad the output of ANN give the same sigal The follow this sigal Else adapt the solutio by the rules from the iductive learig As to the iductio method, ID3 is used. ID3 is a simple decisio tree learig algorithm developed by Quila (1986) ad the most frequetly used method amog the iductive algorithms. We use KATE 5.02 (AckoSoft, 1996) to implemet the ID3 model. After the experimets, several rules geerated from each validatio set. We validate these rules ad adapt the solutios usig coflict resolutio algorithm. By this procedure, We ca get reasoable tradig rules. Figure 2 is the example of geerated tradig rules by ID3. <Figure 2> The example of the geerated rules by ID3 IV. Results To verify the effectiveess of proposed approach, this study composes four comparable models

11 ad performs statistical test. Model_A uses ie techical idicators as iput variables for iductive learig. These idicators are selected as iput variables for ANN ad CBR modelig through GA. Model_B icludes three techical idicators, which are ot selected ANN ad CBR modelig. All idicators used for Model_A ad Model_B are icluded i Model_C. Amog the idicators, ie idicators are used as iput variables of ANN ad CBR modelig. Model_D employs output values of ANN ad CBR, ad three techical idicators, which are ot used for ANN ad CBR modelig. Iput variables for each model are summarized i Table 3. Iput variables Stochastic %K, Stochastic Slow %D, Mometum, ROC, RSI, PVI, AD Oscillator, Model_A CCI, OSCP Model_B Disparity5, Stochastic %D, Larry William s %R Stochastic %K, Stochastic Slow %D, Mometum, ROC, RSI, PVI, AD Oscillator, Model_C CCI, OSCP, Disparity5, Stochastic %D, Larry William s %R Model_D Output values of ANN ad CBR, Disparity5, Stochastic %D, Larry William s %R <Table 3> Iput variables for each model Table 4 describes the average classificatio accuracy for each competitive model. The classificatio accuracy of Model_D is 77.33% ad Model_A ad Model_C is 69.33% ad 68.00%, respectively. I additio, Model_B is 58.00%. O the average, Model_D outperforms the other models by about 9~19% of classificatio accuracy. Set 1 Set 2 Set 3 Set 4 Set 5 Average Model_A Model_B Model_C Model_D <Table 4> Average classificatio accuracy (hit ratio, %) As to statistical test, we employ the McNemar tests to examie whether the classificatio performace of proposed approach is sigificatly higher tha that of competitive approaches. The

12 results show that Model_D performs sigificatly better tha Model_B ad Model_C at the 1% sigificace level ad Model_A at the 5% sigificace level. Therefore, we ca coclude that our proposed approach outperforms other competitive approaches with statistical sigificace. Table 5 is the results of statistical test. Model_A Model_B Model_C Model_A Model_B Model_C Model_D (0.010)*** - a (0.250) (0.029)** <Table 5> Chi-square value (P value) from McNemar test - a (0.027)** (0.000)*** - a (0.004)*** a. Biomial distributio used. * sigificat at the 10% level ** sigificat at the 5% level ***sigificat at the 1% level We also perform a simulatio of buyig ad sellig of stocks to verify the profitability of proposed approach. Buyig ad sellig is simulated uder followig assumptios. If geerated rule idicates bullish market, all available moey is used to buy stocks at a time. Ad we hold it util the rule produces the sigal of bearish market. If geerated rule idicates bearish market, all stocks are sold at a time. Total amouts of the tradig simulatio ad retur o ivestmet (ROI) are summarized i Table 6 ad Figure 3. Tradig Strategy Total amout (ROI) (assume iitial ivestmet of 1,000,000 wo) Followig Buy-ad-hold strategy 760,510 wo (-23.9%) Followig the rules of Model_A 1,278,039 wo (27.8%) Followig the rules of Model_B 986,678 wo (-1.3%) Followig the rules of Model_C 1,246,296 wo (24.6%) Followig the rules of Model_D 1,409,400 wo (40.9%) <Table 6> Total amout ad ROI of buyig ad sellig simulatios

13 \1,500,000 \1,400,000 Amouts \1,300,000 \1,200,000 \1,100,000 \1,000,000 \900,000 \800,000 Model_A Model_B Model_C Model_D Buy&Hold \700, Cases <Figure 3>Performace of simulatios While the uderlyig idex decreased about 24% durig the period, we ca yield the high level of profit usig the proposed approach. I additio, our proposed approach yields higher profit tha other competitive approaches, such as Model_A, Model_B, Model_C, ad buy-ad-hold strategy. These results demostrate that proposed approach is promisig methods for extractig profitable tradig rules. V. Coclusio ad Future Research Issues This study suggests that the outputs of ANN ad CBR ca be proper substitutes for techical idicators. This study also proposes iductive learig ca be a tool of resolvig coflict betwee multiple classifiers. Iductive learig ca effectively resolve the coflict betwee the icosistet output values of ANN ad CBR model ad ca provide reasoable ad profitable tradig rules to ivestors i stock market. Followig issues are further research eeded.

14 Additioal classifiers such as geetic algorithm ad fuzzy eural etwork ca be the cadidates for base classifier. I this study, oly two classifiers are used as base classifier, but additioal classifier ca provide syergistic effect to the itegrated system. Appedix: Techical idicator Name Descriptio Formula The Positive Volume Idex (PVI) focuses Ct Ct 1 PVI o days whe the volume icreased from PVI t 1 + ( PVI t 1) the previous day. Ct 1 The Stochastic Oscillator compares where Ct L Stochastic %K a security s price closed relative to its price 100 rage over a give time period. H L The Stochastic Oscillator compares where 1 a security s price closed relative to its price Stochastic %D %K t i rage over a give time period. It is a i= 0 movig average of %K. The Stochastic Oscillator compares where 1 Stochastic a security s price closed relative to its price %Dt i Slow %D rage over a give time period. It is a i= 0 movig average of %D. Basis Ope Iterest Mometum ROC Larry William s %R A/D Oscillator Disparity 5days The basis is the curret spot price of a particular commodity mius the price of a particular futures cotract for the same commodity. The basis ca be used to predict future spot prices of the commodities that uderlie the futures cotract. Ope Iterest is the umber of ope cotracts of a give futures cotract. A ope cotract ca be a log or short cotract that has ot bee exercised, closed out, or allowed to expire. The Mometum idicator measures the amout that a security s price has chaged over a give time spa. The Price Rate-of-Chage (ROC) idicator displays the differece betwee the curret price ad the price x periods ago. Larry William s %R is a mometum idicator that measures overbought/oversold levels. The A/D Oscillator measures the accumulatio ad distributio of market power. It meas relative stregth of bullish ad bearish market. The Disparity meas the distace of curret spot price ad movig average. Curret spot price Futures price H H N/A C t C t 4 C C t t Ct L H t H t Ct MA 100 Ct L t 100

15 CCI The Commodity Chael Idex (CCI) measures the variatio of a security s price from its statistical mea. High value of CCI idicates prices are uusually high compared to average prices ad low value of CCI idicates that prices are uusually low. MA MA 5 10 MA RSI The RSI is price followig oscillator that rages from 0 to 100. The RSI usually tops above 70 ad bottoms below i = 0 1 i = 0 Up Dw t i t i <Table A> Techical idicators (Kolb ad Hamada, 1988, Achelis, 1995) Note) C: Closig price, L: Low price, H: High price, Volume: Tradig volumes ( H ) t + Lt + Ct MA: Movig average of price, M t : D t : i= 1 M t i+ 1 SM t 3, SM t : i= 1 M t i+ 1, Up: Upward price chage, Dw: Dowward price chage Referece Achelis, S. B., Techical Aalysis from A to Z, Probus Publishig, AckoSoft, CaseCraft TM : The KATE TM Toolbox for reasoig from Cases, Ahmadi, H., Testability of the arbitrage pricig theory by eural etworks., Proceedigs of the Iteratioal Coferece o Neural Networks, 1990, pp Choi, J. H., Lee, M. K., ad Rhee, M. W., Tradig S&P 500 stock idex futures usig a eural etwork., The Third Aual Iteratioal Coferece o Artificial Itelligece Applicatios

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