20 CHAPTER 3 RESEARCH METHODOLOGY Chaigusi (2011) metioed that stock markets have differet characteristics, depedig o the ecoomies omie they are relateded to, ad, varyig from time to time, a umber of o-trivial tasks have to be dealt with whe developig Neural Networks for predictig exchages. It is ot easy task to desig artificial eural etwork model for a particular forecastig problem or a stock market idex movemet. Therefore, Modellig issues must be cosidered carefully because it affects the performace of a ANN. N. Oe critical factor is to determie the appropriate architecture, the umber of optimal hidde layers as well as the umber of hidde odes for each layer. Other etwork desig decisios ios iclude the selectio ecti of activatio fuctios s of the hidde ad output odes, the traiig algorithm, ad performace measures. The desig stage ivolves i this study to determie the iput (idepedet) ad output (depedet) et) layers through the hidde layers i the case where the output layer is kow to forecast future ure values. Output of the etwork was two patters 0 or 1 of stock price directio. The output layer of the etwork cosisted of oly oe euro that represets the directio of movemet. The umber of euros i the hidde layer was determied empirically. The determiatio of the formulatio betwee iput ad output layers is called learig ad through the learig process, model recogises the patters i the data ad produces estimatios.
21 From the literature, multi-layer feed-forward ANN with back-propagatio is the most commoly used architecture i this area. So, we use the three- layered feed-forward architecture (see Fig. 2). The etire data set covers the period from 03/01/2005 to 30/12/2010 for etwork traiig, while data from 03/01/2005 to 28/05/2014 is to test the predictive ability of the etwork. There are some steps as follow: ow: 12 idicators has to be calculated i excel ad the the results will be loaded to the etwork for traiig ad testig, The data will be loaded to the etwork ad the Normalizatio will take place ragig betwee -1, 1 so that the etwork will able to lear faster, traiig period will be i yearly because of avoidig too much of time cosumig. Traiig process will take place withi time frame (20 miutes), if the process caot reach the goal, ad the chagig its learig rate ad mometum met costat will be eeded. eded. Lookig oki for the best parameter a combiatio that ehace ce the best output ad save as et for testig step(forecastig) The testig process ca be coducted i the ew set of data to see how best the performace of the model The basic methodologies applied i this research are based o previous researches such as (Kim 2003, Mahmood Moei Aldi et al. 2012, Najeb
22 Masoud 2014,...) The performace evaluatio of the model ca be described below: 3.1 Statistical Performace Evaluatio of the Model I order to estimate the forecastig statistical i al performace of some methods or to compare several methods we should defie error fuctios. May previous research works had applied some of the followig forecast accuracy cura measures: Mea Error (ME), Mea Absolute Error ror (MAE), Mea Squared Error (MSE), Root Mea Squared Error (RMSE), Stadard Deviatio of Errors (SDE), Mea Percet Error (MPE) ad Mea Absolute Per cet Error (MAPE), etc. I our study we use four performace criteria ria amely mea absolute error (MAE), root mea square error (RMSE), mea absolute percetage error r r (MAPE) ad goodess of fit R 2. The backpropagatio learig algorithm was used to trai the three-layered feedforward ANN structure i this study were the most used error fuctios is as followig: owi The mea absolute error is a average age of the absolute errors rorsrs E = (P i - ), where P i ad are the actual (or observed) value ad predicted value, respectively. Lesser values of these measures show more correctly predicted outputs. This follows a log-stadig traditio of usig the ex-post facto perspective i examiig forecast error, where the error of a forecast is evaluated relative to what was subsequetly observed, typically a cesus based bechmark (Poo 2005). The most commoly used scale-depedet
23 summary measures of forecast accuracy are based o the distributios of absolute errors ( E ) or squared errors (E 2 ) observatios () is the sample volume. The mea absolute error is give by: Mea Absolute Error (MAE) = E i 1 / (i = 1, 2, ) (6) The MAE is ofte abbreviated as the MAD ( D for deviatio ). Both MSE ad RMSE are itegral compoets i statistical models (e.g., regressio). As such, they are atural measures to use i may forecast error evaluatios that use regressio-based ad statistical. The square root o of the mea squared error as follows: 2 Mea Square Error (MSE) = E i 1 / (i = 1, 2, ) 2 Root Mea Square Error (RMSE) = Sqrt E i 1 / (i = 1, 2, ) (7) If the above RMSE is very less sigificat, the predictio accuracy of the ANN model is very close to 100%. Sice percetage errors are ot idepedet, det, they are used to compare forecast performace across differet data sets of the area usig absolute percetage error give by APE = (P i - scale- )*100. Like the scale depedet measures, a positive value of APE is derived by takig its absolute value ( APE ) observatios (). This measure icludes: i1 MAPE = APE / (i = 1, 2, ) (8)
24 The use of absolute values or squared values prevets egative ad positive errors from offsettig each other. All these features ad more make MATLAB a idispesable sabl tool for use i this work. Goodess of Fit (R 2 ) = E 2 (E 2 ) /( e ) (i= 1, 2, ) (9) i 1 where e i = p i - p i, is the forecast error values. p i, the actual values ad p i, deote the predicted values. The more R 2 correlatio relatio coefficiet gets closer to oe, the more the two data sets are correlated perfectly. As the aim of all of the predictio system models proposed i this study is to predict the directio of the stock price idex forecastig, the correlatio betwee ee the outputs do ot directly reflect the overall performace of the etwork. 3.2 Fiacial Performace Evaluatio of the Model I order to evaluate the fiacial al performace of the model, the correct rect predicted positios by the model have bee compared. Predictio performace is evaluated used i the formula to calculate the predictio accuracy cura cy (Kim 2003) ad is as follows: (i = 1,2,...) (10) Where R i the predictio result is for the i th tradig day is defied by:
25 PO i is the predicted output from the model for the i th tradig day, ad AO i is the actual output for the i th tradig day, the total predicted outputs. The error level was determied ed 5% ad it meas that those outputs with the error level less tha the defied value are cosidereded as correctly predicted values. 3.3 Research Data The research data used i this study is the directio io of chage i the daily Jakarta composite stock price idex (JKSE). This is composed o of closig price, the high price ad the low price of total price idex. The grad total umber of sample is 2,298 tradig days, from Jauary 3, 2005 to May 28, 2014. It is divided ito two sub-periods. First sub-periods of Jauary 3, 2005 to December 30, 2010 is i etwork traiig periods, its values are obtaied with differet fere combiatios of parameters ers for testig the models. The secod sub-period of Jauary 3, 2005 to May 28, 2014 is i sample period for testig predictio rate. The whole data i the statistical tistical populatio were employed i the aalysis alys ad this leads to o-selectio ectio of a specified samplig method. The umber of sample with icreasig directio is 1,303 while the umber of sample with decreasig directio is 995. That is, 57% of the all sample have a icreasig directio ad 43% of the all sample have a decreasig directio. The research data used i this study is the directio of daily closig price movemet i the JKSE. The umber of sample for each year is show i Table 1.
26 Table 1. The umber of sample i the etire data set Descriptio Year Total 05 06 07 08 09 10 11 12 13 14 May Icrease 136 144 151 123 141 140 137 135 131 62 1,300 (%) 56% 59% 60% 51% 58% 57% 55% 55% 55% 63% 57% Decrease 107 101 109 120 102 105 110 109 109 36 998 (%) 44% 41% 40% 49% 42% 43% 45% 45% 45% 37% 43% Total 243 245 250 243 243 245 247 244 4 240 98 2,298 Source: author calculatio, atio 2014 3.4 Data preparatio Some data ow a high amout i compariso with others ad this might lead to the excessive effect o predictio process which is a source of errors ad reductio of predictio ability of eural etworks. That s why the origial data should be ormalized i a rage of [l, h]. with regards to Mahmood Moei Aldi et al. (2012) ormalizig data is doe as follows: (i = 1,2,...) (11) Where: u = the ormalized data x i = the origial data x i,mi = the miimum value of the origial x i,max = the maximum value of the origial data
27 h i = upper boud of the ormalisig iterval ad l i = lower boud of the ormalisig iterval Max-mi ormalizatio plas a value u of x i i the rage (h i l i ) i.e. (-1.0; 1.0), i this case. As a value greater tha 0 represets a buy sigal while a value less tha 0 represets ets a sell sigal. (i = 1,2,3,...,) the umber of observatios. 3.5 Variable Calculatio Closig price, the high ad low price idex are coverted ito techical idicators. Techical idicators are used as iput variables ables i the costructio of predictio models to predict the positio of stock price movemets. I this research, 12 techical idicators has to be calculated i Excel ad the the etwork (Program ram matlab) ab) will read the results from excel spreadsheet. Traiig or learig data will be year o year, because if we combie data of may years to trai at oe time it meas the learig process is very log ad sometimes es may ot reach the goal. The research applied idicators are selected based o idicator selectio of differet groups ad also alog with the previous studies Kim (2003), Kumar & Themozhi (2006), Kara et al. (2011), Mahmood Moei Aldi et al. (2012), A. Victor Devadoss (2013) Table 2 demostrates the titles of twelve techical idicators ad their calculatio method separately.
28 Table 2. Selected techical idicators ad their formulas No Name of idicators 1 A/D Oscillator 2 CCI Commodity odit Chael el idex 3 Larry William s (R%) Formulas Descriptio where C t is the closig price at time t, L t the low price at time t, H t the high price at time t (J. Chag et al. 1996) Where M t = (H t + C t + L t )/3, (S.B. Achelis, 199595 & J. Chag et al. 1996) (S.B. Achelis, 1995) 4 MACD MACD() t-1 +2/+1* (DIFF t - DIFF: EMA(12) t - (movig MACD() t-1 ) EMA(26) t, EMA is average expoetial movig covergece average, EMA(k) t : divergece) EMA(k) t-1 + α (C t - EMA(k) t-1 ), α smoothig ot factor: 2/(1 + k), k is time period of k day expoetial movig average (Gerald, 2005) 05) 5 Mometum where C t is the closig price at time t, the price day (J. Chag et al. 1996) 6 ROC Pricerate-of chage 7 RSI (Relative stregth idex) (J.J. Murphy, 1986) where Up t meas upwardprice chage ad Dw t meas dowward pricechage at time t. (S.B. Achelis, 1995)
29 No Name of Formulas idicators 8 Simple MA Descriptio It shows the average value of a security s price over a period of time. If the value of a security s price over a period of time. If the price moves above its MA, a buy sigal is geerated. If the price moves below its MA a sell sigal is geerated. (Mahmood Moei Aldi et al. 2012 & Najeb Masoud, 2014) 9 Stochastic (K %) where LL t ad HH t, mea lowest low ad highest high i the last t days, respectively. (S.B. Achelis, 1995) 10 Stochastic (D%) (S.B. Achelis, 1995) 11 Stochastic slow (D%) 12 WMA (E. GiEord, 1995) Mahmood Moei Aldi et al. (2012), Najeb Masoud (2014) Notes: I this study the origial data were ormalized i a rage of [-1,1].
30 Table 3. Defied Variables Code A/D Oscillator CCI Commodity Chael idex Larry William s iam s (R%) MACD (movig average covergece divergece) Mometum Defiitios Accumulatio/distributio cumu oscillator. It is a mometum idicator that associates chages i price It measures the variatio atio of a security s price from its statistical tical mea It is a mometum idicator icator that measures overbought/ oversold levelsels Movig average covergece divergece It measures the amout that a security s price has chaged over a give time spa ROC chage RSI Price-rate-of It displays the differece betwee the curret r price ad the price days ago Relative stregth idex. It is a price followig a oscillator that rages from 0 to 100. A method for aalysig alys RSI is to look for divergece ece i which the security is makig a ew high. Simple MA Stochastic (K %) Simple 10-day movig average It compares where a security s price closed relative to its price rage over a give time period Stochastic (D%) Movig average of %K Stochastic slow Movig average of %D. (D%) WMA Weighted 10-day movig average Source: Kim K. (2003), Kara et al. (2011), Mahmood Moei Aldi et al. (2012), Najeb Masoud (2014)