The Proposed Mathematical Models for Decision- Making and Forecasting on Euro-Yen in Foreign Exchange Market

Transcription

1 Iranan Economc Revew, Vol.6, No.30, Fall 20 The Proposed Mahemacal Models for Decson- Makng and Forecasng on Euro-Yen n Foregn Exchange Marke Abdorrahman Haer Masoud Rabban Al Habbna Receved: 20/07/24 Acceped: 20/0/24 Absrac n hs paper wo approaches for radng and forecasng on Euro-Yen exchange raes are suggesed. In he frs approach hree decson- models are developed o maxmze prof of rades durng a Imakng specfc perod. Traders have hree opons o perform a rade a each marke me ha are: (a) Openng a buy rade, (b) Openng a sell rade and (c) Refusal of radng. These opons are consdered n he models by usng relaed decson varables. Resuls of hese models conform o qualave conens n leraure of foregn exchange marke and presen radng sraegy on he bass of he ndcaors o maxmze prof. The am of second approach s forecasng he drecon of exchange rae (ncrease or decrease) over a specfc perod on he bass of values of ndcaors n prevous me perod. In hs approach wo heursc models are developed o mnmze mean of errors of forecasng. Then mean of errors of developed models are compared wh four major classfcaon algorhms. Resuls show ha he proposed model has hgher accuracy n forecasng Keywords: Foregn Exchange Marke, Forecasng, Classfcaon Algorhms, Mean of Errors, Drecon of Exchange Rae, Prof Maxmzaon, EURJPY Exchange Rae. - Inroducon Inally an overvew of foregn exchange marke (Forex) s presened. In Forex marke, he raders exchange dfferen currences va Inerne. There are hree major orders for radng. Deparmen of Indusral Engneerng, College of Engneerng, Unversy of Tehran, Tehran, Iran, (Correspondng Auhor). Deparmen of Indusral Engneerng, College of Engneerng, Unversy of Tehran, Tehran, Iran. M.A. Suden, Faculy of Economcs, Unversy of Tehran, Tehran, Iran.

2 68/ The Proposed Mahemacal Models for Decson-Makng and Buy Order: Consder ha analyss expresses ha he EURJPY exchange rae wll ncrease soon. In hs condon, he rader reques Buy order. Sell Order: Consder ha analyss expresses ha he EURJPY exchange rae wll decrease soon. In hs condons, he rader reques Sell order. Close Order: Each opened rade mus be closed a a me. The suable me for rade closng depends o rader analyss. For example closng can be occurred when he rader s acquescen for rade prof. As well as, closng can be occurred when he rader s afrad of he rade loss. Volume: Volume s equal o amoun of money ha rader nves for radng n a me perod. There are four major exchange raes n each me perod. A me perod can be hourly, daly, weekly and ec. Exchange rae a he sar of a perod. Ths exchange rae s called Open. Maxmum value of exchange rae durng a perod. Ths exchange rae s called Hgh. Mnmum value of exchange rae durng a perod. Ths exchange rae s called Low. Exchange rae a he end of a perod. Ths exchange rae s called Close. In hs paper, he exchange rae a he openng me of a rade s called p o and he exchange rae a he closng me of a rade s called p c. If a buy rade s opened, he prof/loss of rade s equal o p c -p o -c. c s cos of each rade ha belongs o broker and s equal for buy or sell rades. I s necessary o menon ha c depends o volume of rade. Also f a sell rade s opened, he prof/loss of rade s equal o p o -p c -c. Moreover raders can assgn wo lms o her rades. These lms are called sop loss (SL) and ake prof

3 Haer, A. & A. Habbna, M. Rabban. /69 (TP). Afer rade openng f he loss of ha rade reaches o a specfc lm (SL), he broker auomacally close ha rade. Also f he prof of a rade reaches o a specfc lm (TP), he broker auomacally close ha rade. These lms are used for decreasng rade rsks. In Forex marke, prof and loss of each rade s saed on he bass of he Pp. Pp s a creron for exchange rae changes. For example consder ha EURJPY exchange rae changes from o In hs condon s sad ha EURJPY exchange rae ncreases one pp. If EURUSD exchange rae changes from.4595 o.4594, s sad ha EURUSD exchange rae decreases one pp. A whole one pp s equal o one un change n he las dg of exchange rae. There are wo general approaches for analyss and forecasng n Forex marke. The approaches are echncal and fundamenal. In echncal mehods, analyss and forecasng are performed on he bass of he exchange rae and echncal ndcaors such as movng average, RSI and ec. In fundamenal mehods, analyss and forecasng are performed on he bass of he mmense varables such as neres rae, unemploymen rae, GDP and ec. On he bass of hese nvesgaons forecasng abou ncrease or decrease of a currency versus oher currences s presened. Polcal evens and mmense decsons has affeced on he fundamenal analyss. 2- Leraure Revew In hs secon a revew abou some of he prevous researches abou exchange rae forecasng and decson-makng n foregn exchange marke s presened. By he aenon o paper approach, revewed papers are abou he echncal approach. J. Yao and Chew Lm Tan (2000) develop a neural nework for forecasng n Forex marke. Tme seres and movng average ndcaor are he npus of back propagaon neural nework. They presened forecasng abou Japanese yen, Brsh pound, Swzerland Frank and Ausralan dollar versus US dollar. A. Murel (2004) used of a chaoc movng model n physcs. He red o forecas rend of hree major currences versus US dollar. The model s esed on Ocober 2003 dae se. Fang-Me Tseng e al. (200) combned ARIMA (Auo Regressgn Inegraed Movng Average) n me sers and fuzzy regresson model o forecasng NT (New Tawanan) dollar versus US dollar. The model enables decson makers and raders o

4 70/ The Proposed Mahemacal Models for Decson-Makng and forecas he wors and he bes saus n fuure. Chakradhara Panda and V.Narasmhan (2007) used of feed forward neural nework o forecas Indan Rupee versus US dollar weekly exchange rae. Resuls show ha proposed model s beer han lnear regresson and random walk models. Vncen C.S Lee and Hsao Tshung Wong (2007) used neural nework o develop a rsk managemen model. Am of he model was forecasng drecon and value of exchange rae changes. Proposed model was a combned model and used of ANN (Arfcal neural nework) and fuzzy logc ools. Robero Bavera (2002) nvesgaed non relable markovan behavor of exchange rae. He used from ha o nference specal rules for dong successful rades. Crag Ells and Parck Wlson (2005) developed an negraed approach for forecasng foregn exchange rae. They used of random walk framework o forecasng drecon and value of exchange raes. They esmaed dfferen sascal crera such as mean, sandard devaon, p-value and ec. Pukhuanhong e al. (2007) examned random behavor hypohess n foregn exchange marke. The focus of hs research s on he fuure conracs. They used of regresson for deecng relaons among wo consecuve perods. Daa se ncludes exchange rae of Canadan dollar, Ausralan dollar, Japanese yen, Swzerland frank, Brsh pound and Euro versus US dollar. A he end a profable sraegy was presened. Gan e al. (995) used mul layered percepron (MLP) neural nework o forecasng exchange rae of Swzerland frank, Deusche Mark and Japanese yen versus US dollar. They examned wo models wh sngle and mulvarae me seres and compared hem wh random walk model. Oh, K.J. e al. (2005) by usng of non lnear programmng and neural nework developed a daly fnancal condon ndcaor (DFCI) for presenng me sgnals. Ther Proposed ndcaor had capably o creae a zone alarm regon for forecasng sochasc fnancal crss. A he end, he used of DFCI on Korean fnancal marke. Hau, H. e al. (2006) developed a balanced model among foregn exchange rae, prce sock and capal flow. Ther resuls show ha ne flow n foregn exchange marke has a posve correlaon wh value of currency un. Ther Resuls show ha forecasng on he daly, monhly and seasonal me horzons have accepable confdence. Ahmad, S.M. e al. (2007) by combnng he famous echncal ndcaors, developed a fuzzy ndcaor for presenng buy and sell sgnals n Forex and sock marke. Resuls of her

5 Haer, A. & A. Habbna, M. Rabban. /7 research show ha proposed ndcaor had hgher confdence han oher ndcaors. Me-Chh-Chen e al. (2007) by usng of movng average (MA), sochasc ndcaors (KD), movng average convergence dvergence (MACD), relave srengh ndex (RSI) and Wllams %R (WMS %R) developed a dynamc sock porfolo decson-makng asssance model o forecasng drecon of prce changes n Tawan sock marke. Thomas C. Shk. e al. (2007) compares RSI and movng average on sx currences. Terence Ta-Leung Chong and Wng-Kam Ng (2008) nvesgaed he benefcary effcacy of rules ha exraced from RSI and MACD n London sock marke. 3- Problem Defnon Ths paper ncludes wo man approaches ha nclude mahemacal decson-makng models. In frs approach a decson-makng model for radng n foregn exchange marke s developed. There are many ndcaors for analyss and decson-makng n Forex marke. Traders usually use ndcaors for decson-makng. RSI s an mporan ndcaor and s used n prevous researches frequenly. Some of hose are menoned n prevous secon. So n frs approach RSI s used for decson-makng abou raders. Relave-Srengh Index (RSI) s a useful and praccal ool for showng exchange raes swng. RSI compares Increased Quany of exchange rae or sock prce by Decreased Quany over a specfc perod and convers he quanes o a value beween 0 and 00. Am of proposed model s specfyng rules for radng o maxmze he prof over specfc me. Tme nerval s from begnnng of 2002 o he end of Tme perods are consdered daly. I s consdered ha a he sar of each day decson abou rades are made. A he sar of each day raders decde abou openng and closng rades on he bass of RSI value. For hs purpose hree models are developed. Then all models are solved by Branch and Bound (B-B) mehod wh Lngo 9.0 sofware. In second approach a heursc model for forecasng he drecon of exchange rae changes are presened. Drecon n each perod has wo saes. Consder ha exchange rae a he end of a day s greaer han exchange rae a he begnnng of ha day. In hs case s sad ha exchange rae s ncreased and value of drecon s equal o. Also consder ha exchange rae a he end of a day s less han exchange rae a he begnnng of ha

6 72/ The Proposed Mahemacal Models for Decson-Makng and day. In hs case s sad ha exchange rae s decreased and value of drecon s equal o 0. Drecon of exchange rae changes s forecased on he bass of EMA (exponenal movng average) and RSI. EMA s weghed average exchange rae of prevous days. EMA s a useful ndcaor ha assgns graer weghs o he laes daa o respond faser o changes. In whole of hs paper daa of exchange rae of Euro versus Yen ha s showed wh EURJPY s used. 3-- Models for Maxmzng Prof In hs secon hree models for maxmzng prof are presened. I s necessary o menon ha he models are developed by he auhors and don adoped from oher references Model () In hs case, s consdered ha each opened rade s closed a he sar of laer day. Indeed he duraon of each rade s one day. So raders have hree opons a sar of each day: Openng a buy rade Openng a sell rade Refusal of radng Traders decde on he bass of he RSI values a he sar of each day. For hs purpose RSI values are poroned o en equal nervals. I varable s defned for specfyng he nerval of RSI. Table shows I and RSI values.

7 Haer, A. & A. Habbna, M. Rabban. /73 RSI I [0,0] [0,20] 2 Table : RSI Indcaor and I Values [20,30] [30,40] [40,50] [50,60] [60,70] [70,80] [80,90] 9 [90,00] 0 Parameers: P : EURJPY exchange rae a he sar of -h day CT: he cos of each rade I, : Value of I varable a he sar of -h day T: Se of days n consdered perod J : Se of days ha a he sar of hem, I s equal o ( 0) Decson Varables: 0, : Suppose ha I s equal o. If 0, = ndcaes don performng rade and f 0, =0 ndcaes performng rade., : Suppose ha I s equal o. If, = ndcaes performng buy rade and f, =0 ndcaes don performng buy rade. 2, : Suppose ha I s equal o. If 2, = ndcaes performng sell rade and f =0 ndcaes don performng sell rade. 2, Objecve Funcon: = 0 = 0 Max = ( P + = + ( = + ) P CT), P P CT 2, j J j j j j J j (-) Objecve funcon s maxmzng he prof of rades n consdered perod. Frs erm of objecve funcon expresses prof (loss) of buy rades and second erm expresses prof (loss) of sell rades. Each of wo erms ncludes cos of rades. Consran: 0, + 2 =,, 0 (-2) Consran (-2) expresses ha n each day, only one of he buy, sell or refusal s gven.

8 74/ The Proposed Mahemacal Models for Decson-Makng and Model (2) In model () duraon of each rade was one day. Bu n model (2) duraon of each rade can be more han one day. Indeed n hs model here s no any consran abou duraon of rades. In hs model parameers are defned smlar o model (). In follow decson varables of model (2) are defned. Decson Varables: Theses varable are bnary and ndcaes dong an acon () or no dong an acon (0). 0,, : Open a buy rade (when here sn an opened rade) when I s equal o 0, 2, : Open a sell rade (when here sn an opened rade) when I s equal o 0, 3, : Refusal o radng (when here sn an opened rade) when I s equal o,, : Hold an opened buy rade when I s equal o, 2, : Close an opened buy rade when I s equal o, 3, : Close an opened buy rade and openng a sell rade when I s equal o 2,, : Hold an opened sell rade when I s equal o 2, 2, : Close an opened sell rade when I s equal o 2, 3, : Close an opened sell rade and openng a buy rade when I s equal o N 0, : If here sn any opened rade N 0, s equal o and oherwse s equal o 0. N, : If here s an opened buy rade N, s equal o and oherwse s equal o 0. N 2, : If here s an opened sell rade N, s equal o and oherwse s equal o 0.

9 Haer, A. & A. Habbna, M. Rabban. /75 Objecve Funcon: = 0 = 0 Max = [ N 0, j ( CT( 0,, 0,2, ))] j J + = = j J [ N, j (( P j+ P j )(,, ) CT(,3, ))] = 0 + = j J [ N 2, j (( P j P j+ )( 2,, ) CT( 2,3, ))] (2-) Objecve funcon ndcaes he prof/loss of rades n whole of perod. Dependng on ha each of he N, j N, j N 2, j 0 varables s equal o, he respecve erm s acvaed. Each erm ncludes prof/loss of rades and cos of rade openng. Frs erm calculaes cos of rade openng when here sn any opened rade. Second erm calculaes prof/loss of opened buy rades and cos of sell rade openng. Thrd erm calculaes prof/loss of opened sell rades and cos of buy rade openng. Consrans: 0,, + 0,2, + 0,3, =,,,2,,3, = 2,, 2,2, 2,3, = εj 0 (2-2) εj 0 (2-3) εj 0 (2-4) N N + N T (2-5) 0, +, 2, = N, = N, N, (,2,,,3,, ) N 0, ( 0,,, ) + + N 2, = N 2, N 2, ( 2,,, 2,2,, ) N 0, ( + 0,2,, + ) εj 0 (2-6) εj 0 (2-7) Consran (2-2) expresses ha f ehre s no any opened rade, only one of he buy, sell or refusal decsons s made.

10 76/ The Proposed Mahemacal Models for Decson-Makng and Consran (2-3) expresses ha f here s an opened buy rade, only one of he hold, close or close buy rade and open sell rade decsons s made. Consran (2-4) expresses ha f ehre an opened sell rade, only one of he hold, close or close sell rade and open sbuy rade decson s made. Consran (2-5) expresses ha n each day here s a mos one buy or sell opened rade. Ths consran s logcal. For example consder a buy rade s opened and a he sar of a laer day rader feels ha he exchange rae wll decrease. In hs case he can open a sell rade. So sn logcal ha he buy rade s remaned n opened saus. So rader should close buy rade and open a sell rade. Smlar descrpon can be presened abou condon ha a sell rade s opened. Consrans (2-7) and (2-7) updae N, + and N values on he bass of 2, + he N and N values and decson ha was made n prevous day. I s, 2, obvous ha N 0, value s aaned from consran (4) for each day Model (3) In hs procedure an addonal aspec of rades s consdered. In foregn exchange marke, raders can assgn wo lms o her rades. These lms are called sop loss (SL) and ake prof (TP). Afer rade openng f he loss of ha rade reaches o a specfc lm (SL), he broker auomacally close ha rade. As well as f he prof of a rade reaches o a specfc lm (TP), he broker auomacally close ha rade. In hs secon, rade lms (SL and TP) s consdered n proposed model and a new model on he bass of rade lms s developed. In model (3) hree addonal parameers are added. Parameers: TP: Take prof lm SL: Sop loss lm Noe ha values of TP and SL wll express on he bass of Pp. Decson Varables: L : Amoun of prof/loss of a rade a he sar of -h day V, W, X, A, B, F : Bnary varables ha s used n consrans Oher decson varables are smlar o model (2).

11 Haer, A. & A. Habbna, M. Rabban. /77 Objecve funcon n model (3) s smlar equal o model (2). Consrans of model (3) are as follows: Consrans: 0,, 0,2, 0,3, =,,,2,,3, = 2,, 2,2, 2,3, = εj 0 (3-) εj 0 (3-2) εj 0 (3-3) N N + N T (3-4) 0, +, 2, = L N ) L + ( N )( P P ) + ( N )( P P ) (3-5) + = ( 0, +, + + 2, + + L SL + M * (3-6) V L + M * W TP (3-7) F M * X (3-8) + V + W + M * A (3-9) B X 0 + M * (3-0) A B (3-) N, = ( F ) *( N, N, (,2,,3, ) N 0, ( 0,, )) (3-2) N 2, = ( F )*( N 2, N 2, ( 2,, 2,2, ) N 0, ( 0,2, )) + εj (3-3) εj Consrans (3-) o (3-4) are smlar o consrans of model (2). Consran (3-5) expresses ha he prof/loss of a rade equals o prof/loss of he rade a he sar of he prevous day plus o dfferenaon beween exchange rae a he sar of (+)-h day and -h day. L + depends o he L and he rade ha are s opened a he sar of (+)-h day as follows: If a buy rade a he sar of day (+) s opened, hen he N,+ s equal o. So on he bass of he consran (3-4) N 0,+ and N 2,+ are

12 78/ The Proposed Mahemacal Models for Decson-Makng and equal o 0. Therefore on consran (3-7) saes ha L+ = L + ( P + P ). If a sell rade a he sar of (+)-h day s opened, hen he N 2,+ s equal o. So on he bass of he consran (3-4) N 0,+ and N,+ are equal o 0. Therefore consran (3-7) saes ha L + = L + ( P P + ) If here sn any opened rade a he sar of (+)-h day, hen he N 0,+ s equal o. So on he bass of he consran (3-4) N,+ and N 2,+ are equal o 0. Therefore consran (3-7) saes ha L + = 0 The above descrpons show ha he consran (3-5) calculaes he prof/loss of each rade correcly. Consrans (3-6) o (3-) ensure ha f L s equal or less han SL or L s equal or greaer han TP, he opened rade a he sar of day s closed. If L SL hen consran (3-6) gves ha V =0. Also f L TP hen consran (3-7) gves ha W =0. If L SL or L TP hen V +W. In hs case consran (3-9) gves ha A =0. Then Consran () gves ha B =0. Afer ha consran (3-0) gves ha X =0. Then consran (3-8) gves ha F. Noe ha F s a bnary varable. So F =. Consrans (3-2) and (3-3) express ha f he F s equal o hen he opened rade s closed. Because f F = hen (-F ) =0. So N, and N 2, are equal o 0. So a he begnnng of - h day, N 0, s equal o. So a he begnnng of (+)-h day here sn any opened rade Models for Mnmzng Mean of Forecasng Errors In prevous secon npu daa was RSI value a he sar of each day and objecve funcon was prof. Three models were developed for ha purpose. In hs secon wo models are developed for forecasng abou drecon of exchange rae n a day. In hs secon models wh below specfcaons are developed. Objecve funcon s mnmzng error of forecasng. RSI and anoher useful ndcaor are consdered. Indcaor values for some prevous days are consdered.

13 Haer, A. & A. Habbna, M. Rabban. /79 In hs secon wo ndcaors are used for forecasng drecon n each day. These ndcaors are exponenal movng average (EMA) and RSI. Goal of hs secon s developng a heursc mehod for daly drecon forecasng on he bass of values of number of ndcaors n prevous days. The consdered ndcaors are EMA and RSI. For each day, values of ndcaors a he sar of ha day and 5 prevous days are consdered. Daa se of hs secon ncludes EURJPY daly exchange rae n 2006, 2007 and 2008 years. Daa se s dvded n o wo secons. Frs secon ha ncludes 2006, 2007 and frs sx monhs of 2008 s used for ranng. Nex secon ha ncludes second sx monhs of 2008 s used for model esng Model (4) For drecon forecasng a heursc approach s offered. Frs a lnear expresson (funcon) of ndcaors s defned. Then on he bass of he value of funcon, drecon of exchange rae n fuure day s forecased. If value of he funcon s less han or equal o a specfc value (Tha s called L), forecased value of drecon s 0 (0 ndcaes ha exchange rae n ha day wll decrease). Also f value of he funcon s greaer han L, forecased value of drecon s ( ndcaes ha exchange rae n ha day wll ncrease). Parameers: EMA - : Value of exponenal movng average a he sar of (-)-h day (0 I 5) RSI - : Value of RSI a he sar of (-)-h day (0 I 5) D : Drecon of exchange rae n -h day. 0 ndcaes ha exchange rae a -h day s decreased. ndcaes ha exchange rae a -h day s ncreased. L: Consans value ha specfes forecased drecon on he bass of he F T: Number of days ha are used for ranng (In daa se ha s seleced, T s equal o 630) Decson varables: F : lnear funcon of ndcaors

14 80/ The Proposed Mahemacal Models for Decson-Makng and PD : Forecased drecon of daly exchange rae n -h day. A - : Coeffcen of EMA - n F B - : Coeffcen of RSI - n F y, z : Bnary varables ha are used n consrans H: A varable ha s used n consrans Objecve Funcon: T = = Mn = ( PD D ) T (4-) / The goal s mnmzng error of forecasng. If forecased drecon s equal o acual drecon, PD D s equal o 0. Also f forecased drecon sn equal o acual drecon, PD D s equal o. Dvdng he whole expresson by T s resuled n aanng mean of errors. For objecve funcon lnearzaon a varable ha s called H s defned and wo consrans are added o se of consrans. So he objecve funcon s defned as below: Mn = H (4-2) Consrans: = 5 = 0 = 5 F = ( A EMA + B RSI ) / 32 T (4-3) My = 0 F L + T (4-4) F + Mz L T (4-5) PD = T (4-6) y y z = T (4-7) + H T = = ( ( PD D ) ) T T (4-8) / T = = H ( ( D PD )) T T (4-9) /

15 Haer, A. & A. Habbna, M. Rabban. /8 Consran (4-3) calculaes lnear funcon F on he bass of he EMA and RSI a sar of -h day and ffeen prevous days. F uses 32 expressons. So he whole expresson s dvded on 32. Consran (4-4) and (4-5) Compare F and L. If F s less han or equal o L, y s equal o 0. So on he bass of he consdered approach forecased value of drecon s mus be equal o 0. Consran (4-6) ses forecased value of drecon equal o 0. Also f F s greaer han L, z s equal o 0. So on he bass of he consdered approach forecased value of drecon mus be equal o. Consran (4-7) resuls n y s equal o. Consran (4-6) ses forecased value of drecon equal o. Consrans (4-8) and (4-9) resul n ha H varable s equal o ( T = = PD D ) T. / Model (5) Model (4) s solved by branch and bound approach wh Lngo 9.0 sofware. Opmal soluon resuls n ha objecve funcon s equal o 0. Tha ndcaes ha he model specfes A and B coeffcens o adjus F wh L and drecon of exchange raes. Indeed model specfes A and B so ha n each day wh drecon 0, F s less han or equal o L. Also A and B s specfed so ha n each day wh drecon, F s greaer han L. Unforunaely resuls of applyng coeffcens on esng daa se are no accepable. Mean of errors on esng daa se more han 50%. Ths condon s smlar o a usual problem ha can occur durng ranng and esng a neural nework. The problem s memorzng. Memorzng occurs when a neural nework consders whole relaons beween npus and oupus and res o cover all deal of relaons. So he bul nework doesn have generaly propery o adjus wh new daa se. In hs condon accuracy of model on ranng daa se s much greaer han accuracy of model on esng daa se (Danel T. Larose (2005)). For reducng hs problem a heursc approach can be appled. Tranng daa se s dvded o wo secons. A consran s added o model o ensure ha dfference beween mean of errors of wo secons s no greaer han a specfc lm. Indeed n hs approach, values of A - and B - are aaned o mnmzng error of forecasng on frs secon of ranng daa se. The oher problem agans generaly ha can occurs s model basng o forecasng one value much more han he oher values. For example n our

16 82/ The Proposed Mahemacal Models for Decson-Makng and case, a model maybe based o forecas mos of drecons equal o 0 or equal o. A consran s added o model agans hs problem. Parameers: Mos of parameers are smlar o model (4). Some new parameers are defned as below: T : Number of days of frs secon of ranng daa se. (T s seleced equal o 580) Gap: Upper lm of dfference beween mean of errors of wo secon of ranng se Gap2: Upper lm of dfference beween mean of errors of days of second secon of ranng se ha predced drecon s equal o 0 and days of second secon of ranng se ha predced drecon s equal o Decson Varables: Decson varables are smlar o model (4). Some new consrans are defned as below: H, H 2, H 3 : Three varables ha are used n consrans Objecve Funcon: T = = Mn = ( PD D ) / T (5-) Objecve funcon s mnmzng mean of errors of frs secon of ranng daa se. Consrans: Mos of consrans are smlar o model (4). Also wo below consrans are added o model. = T = T (( PD D ) / T ) (( PD D ) /( T T )) Gap (5-2) = = T

17 Haer, A. & A. Habbna, M. Rabban. /83 T y T = T = T z Gap2 (5-3) Consran (5-2) ensures ha dfference beween mean of errors of wo secons of ranng daa se s no greaer han a specfc lm (Tha s called Gap). Also consran (5-3) ensures ha dfference among number of days ha forecased value s equal o 0 and number of days ha forecased value s equal o, s no greaer han a specfc lm (Tha s called Gap2). For objecve and consrans lnearzaon hree varables ha are called H, H 2 and H 3 are defned. Then objecve funcon and consrans are changed as below: Objecve Funcon: Mn = H / T (5-4) Consrans: T H ( ( PD D ) ) T (5-5) = = T H ( ( D PD )) T (5-6) = = T T H ( y z ) (5-7) 2 = T = T T T H 2 ( z y ) (5-8) H H = T = T 3 ( H / T ) ( H /( T T )) 3 ( H /( T T )) ( H / T (5-9) ) (5-0) H 3 Gap (5-) H 2 Gap2 (5-2)

18 84/ The Proposed Mahemacal Models for Decson-Makng and I s assumed ha Gap s equal o 0. (0%). Because 0% dfference among accuracy on ranng daa se and esng daa se s accepable. Noe ha s known ha n average number of days wh drecon 0 and number of days wh drecon s approxmaely equal. So s logcal ha number of days ha forecasng s saed ha exchange rae wll ncrease s equal o number of days ha forecasng s saed ha exchange rae wll decrease. So Gap2 s should be seleced as low as possble. Bu for values lower han 0.46 he model s nfeasble. So Gap2 s se equal o Average value of EMA and RSI s equal approxmaely o 05. So L s defned equal o numbers ha are near o 05. Model s run for L=80, 90, 00, 0, 20. Inally model s run on ranng daa se. Then aaned values of A - and B - are used on esng daa se. 4- Compuaonal Resuls and Dscusson In hs secon resuls of solvng models are presened. 4-- Resuls of Model () Model () s solved. Global opmal soluon s found. The objecve value s Values of decson varables are show n able 2. Table 2: Decson Varable Values n Global Soluon for Model () Decson Decson Decson Value Value varable varable varable Value 0, 0, 0 2, 0,2 0,2 0 2,2 0,3 0,3 2,3 0 0,4 0,4 2,4 0 0,5 0,5 2,5 0 0,6 0,6 2,6 0 0,7,7 0 2,7 0 0,8 0,8 0 2,8 0,9 0,9 0 2,9 0,0 0,0 0 2,0 Noe ha he maxmum value for RSI ndcaor n daa se s equal o 9 and he mnmum value s equal o 3. So values of 0,,,, 2,, 0,2,,2, 2,2, 0,0,,0 and 2,0 doesn affec objecve funcon value. So dscusson and analyss s performed on oher decson varables. In leraure of Forex marke much analyss s expressed. Rober D. Edwards and John Magee n (200) saed ha RSI value lower han 30 s an

19 Haer, A. & A. Habbna, M. Rabban. /85 ndcaon o ha exchange rae places on boom and s a sgnal for exchange rae ncrease. So n hs case a good opporuny for buy rade s occurred. Also hey saed ha RSI values hgher han 70 s an ndcaon o ha exchange rae places on op and s a sgnal for exchange rae decrease. So n hs case a good opporuny for sell rade s occurred. For nvesgae wo menoned hypoheses RSI values n [0, 30] and [70,00] nervals are consdered. Noe ha RSI values hgher han 70 s equvalen o ha I, s equal o 8 or 9 or 0. Also RSI values lower han 30 s equvalen o ha I, s equal o or 2 or 3. So an analyss s performed on decson varables ha her I values are equal o, 2, 3, 4, 5 or 6. On he bass of daa n Table 2, hese resuls are aaned:,3 s equal o. Ths saes ha when RSI s n [20, 30], openng a buy rade s an opmal decson. 2,8 s equal o. Ths saes ha when RSI s n [70, 80], openng a sell rade s an opmal decson. 2,9 s equal o. Ths saes ha when RSI s n [80, 90], openng a sell rade s an opmal decson. These resuls are equvalen o analyss ha s sad by Rober D.Edwards, John Magee. (200). In oher words, resuls of model confrm analyss ha s sad n leraure abou RSI Resuls of Model (2) Model (2) s solved. Local opmal soluon s found. The value of objecve funcon s equal o I s noable ha upper objecve bound of objecve funcon (prof) s aaned equal o So he local opmal soluon s a global soluon for model (2). Opmal value of objecve funcon for model (2) s much greaer han of objecve funcon for model (). I shows ha consran relaxaon abou rade duraon resuls n ncrease prof of rades. Values of decson varables are show n able 3.

20 86/ The Proposed Mahemacal Models for Decson-Makng and Table 3: Decson Varable Values n Global Soluon for Model (2) Decson Varable 0,, 0,,2 0,,3 0,,4 0,,5 0,,6 0,,7 0,,8 0,,9 0,,0 Value Decson Varable 0,2, 0,2,2 0,2,3 0,2,4 0,2,5 0,2,6 0,2,7 0,2,8 0,2,9 0,2,0 Value Decson Varable 0,3, 0,3,2 0,3,3 0,3,4 0,3,5 0,3,6 0,3,7 0,3,8 0,3,9 0,3,0 Value Decson Varable,,,,2,,3,,4,,5,,6,,7,,8,,9,,0 Value Decson Varable,2,,2,2,2,3,2,4,2,5,2,6,2,7,2,8,2,9,2,0 Value Decson Varable,3,,3,2,3,3,3,4,3,5,3,6,3,7,3,8,3,9,3,0 Value Decson Varable 2,, 2,,2 2,,3 2,,4 2,,5 2,,6 2,,7 2,,8 2,,9 2,,0 Value Decson Varable 2,2, 2,2,2 2,2,3 2,2,4 2,2,5 2,2,6 2,2,7 2,2,8 2,2,9 2,2,0 Value Decson Varable 2,3, 2,3,2 2,3,3 2,3,4 2,3,5 2,3,6 2,3,7 2,3,8 2,3,9 2,3,0 Value Smlar o model () decson varables ha are relaed o RSI values n [70, 00] and [0, 30] nervals are consdered. The decson varables nvesgaon shows hese resuls: 0,,3 s equal o. Ths saes ha when RSI s n [20, 30] and here sn an opened rade, openng a buy rade s an opmal decson. 0,2,8 s equal o. Ths saes ha when RSI s n [70, 80] and here sn an opened rade, openng a sell rade s an opmal decson.,,3 s equal o. Ths saes ha when RSI s n [20, 30] and a buy rade s opened, holdng opened buy rade s an opmal decson.,2,9 s equal o. Ths saes ha when RSI s n [80, 90] and a buy rade s opened, closng opened buy rade s an opmal decson. 2,,9 s equal o. Ths saes ha when RSI s n [80, 90] and a sell rade s opened, holdng sell rade s an opmal decson. 2,2,3 s equal o. Ths saes ha when RSI s n [80, 90] and a sell rade s opened, closng opened sell rade s an opmal decson. The menoned resuls sae ha when RSI s above 70, s probable ha exchange rae wll decrease soon. So openng a sell rade s opmal decson. Also resuls show ha when RSI s below 30, s probable ha exchange

21 Haer, A. & A. Habbna, M. Rabban. /87 rae wll ncreased soon. So openng a buy rade s opmal decson. These resuls are equvalen o analyss ha s sad by Rober D.Edwards, John Magee. (200). In oher words, resuls of solved model confrm analyss ha s sad n leraure abou RSI Resuls of Model (3) Model (3) s run o aanng opmal values for SL and TP. Afer 3 hour runnng wh Lngo 9.0 sofware, he model ddn reach o a local or global soluon. Bu he upper objecve bound of objecve funcon (prof) s aaned equal o Afer ha he model s solved for dfferen values for SL and TP. Table 4 shows resuls for some SL and TP values. Noe ha because SL shows loss of rades, SL s saed wh negave numbers. Table 4: Values of profs for dfferen values for TP and SL Sraegy Index TP SL Objecve funcon Noe ha for all en proposed sraeges Lngo reached o local opmal. Bu n all sraeges upper objecve bound s equal o bes objecve (local objecve). So he local opmal s global opmal. The resuls of model show ha here sn much dfferen n objecve funcon among dfferen values for SL and TP. Also he maxmum value of objecve funcon s and near o upper bound (37.05). Also resuls show ha he model () wh 46.7 for objecve funcon and model (2) wh 82.3 for objecve funcon have hgher performance relave o model (3). So usng of TP and SL has a negave effec on prof.

22 88/ The Proposed Mahemacal Models for Decson-Makng and 4-4- Resuls of Model (4) and Model (5) Mean of errors of model (4) s hgh. On he bass of heursc approach ha s descrpon s sad n secon, model (5) s developed o solve he lacks of model (4). So n hs secon resuls of model (5) are repored. Then four srong classfcaon algorhms are used for forecasng he drecon on he bass of ndcaors. So n classfcaon algorhms, EMA - and RSI - (0 I 5) are npu felds and Targe feld s D. Table 5 shows resuls of proposed model and four classfcaon algorhms. For use of classfcaon algorhms SPSS Clemenne. sofware s used. Table 5: Comparson of Proposed Model (5) wh four Classfcaon Algorhms Mehods Classfcaon algorhms Proposed model for dfferen values of L C5.0 CART QUEST CHAID L= 80 L= 90 L= 00 L= 0 L= 20 Mean of errors on ranng 40.98% 3.96% % % % % % % daa se Mean of errors on 54.96% esng daa 49.62% % 43.5% % 43.5% % % se Table 5 shows ha values of objecve funcon (Mean of errors on ranng daa se) for proposed model s equal o lower bound of objecve funcon for L = 80, 00, 0, 20. So n hose cases, opmal soluon s global soluon. Also for L=90, value of objecve funcon s approxmaely equal o lower bound of objecve funcon (42.000%). Noe ha Ques algorhm ddn produce any classfcaon algorhm and s showed wh dash lne n able 9. Resuls show ha for all values for L, mean of errors of proposed model s less han all of four srong classfcaon algorhms. Table 6 shows mean of errors ha obaned from neural neworks. The neural nework model s run for dfferen values for nodes n hdden layer. N= o N=20.

23 Haer, A. & A. Habbna, M. Rabban. /89 Table 6: Mean of Errors n Neural Neworks Model N Mean of Errors on Mean of Errors on Tranng daa Se Tesng daa Se Average Concluson Ths paper had wo major secons. Frs hree models were presened. Goal of he models was maxmzng prof of rades over a consdered perod. In hose models decson-makng was performed on he bass of he RSI value a he sar of each day. Resuls of he models ndcaed ha usng Take Prof and Sop Loss parameers don ncrease prof of rades. Also resuls showed ha when RSI value s n [70, 00], usually he opmal decson s performng a sell rade. Also he resuls showed ha when RSI value s n [0, 30], he opmal decson usually s ssung a buy rade. In second secon a heursc model for forecasng he drecon (ncrease or decrease) of exchange rae n a day was presened. Then by usng of a heursc approach he accuracy of proposed model was ncreased. The accuracy of forecasng for proposed model was beer han he accuracy of four man classfcaon algorhms. The noveles of hs research are: Developng mahemacal decson-makng models for radng n foregn exchange marke Resuls of developed models conform o qualave conens n leraure of Forex abou sgnals of RSI ndcaor

24 90/ The Proposed Mahemacal Models for Decson-Makng and Presen a heursc mehod for forecasng he drecon of exchange rae n a day Presen a heursc approach for reducng error of forecasng he drecon of exchange rae Accuracy of proposed models s more han four major classfcaon algorhms A he end an offer for fuure research s presened. Forecasng he value of exchange rae changes and forecasng of exchange rae a he end of day can be a subjec for anoher research. References - Ahmad, S.M., El Gayar, N., Abd Elazm, H.Y. (2007), A fuzzy engne model for fnancal marke forecasng, WSEAS Transacons on Informaon Scence and Applcaons, Volume 4, Issue 2, pp Chakradhara Panda and V. Narasmhan (2007), Forecasng exchange rae beer wh arfcal neural nework, Journal of Polcy Modelng, Volume 29, Issue 2, pp Chong, T.T.-L., Ng, W.-K. (2008), Techncal analyss and he London sock exchange: Tesng he MACD and RSI rules usng he FT30, Appled Economcs Leers, Volume 5, Issue 4, pp Crag Ells, Parck Wlson (2005), A sochasc approach o modelng he USD/AUD exchange rae, Inernaonal Journal of Manageral Fnance, Volume, No., pp Danel T. Larose. (2005), Dscoverng knowledge n daa, John Wley & Sons Inc. 6- Fang-Me Tseng, Gwo-Hshung Tzeng, Hsao-Cheng Yu and Benjamn J. C. Yuan (200), Fuzzy ARIMA model for forecasng he foregn exchange marke, Fuzzy Ses and Sysems, Volume 8, Issue, pp Gan, Woon-Seng, Ng, Kah-Hwa (995), Mulvarae FOREX forecasng usng arfcal neural neworks, IEEE Inernaonal Conference on Neural Neworks- Conference Proceedngs, Volume 2, pp Hau, H., Rey, H. (2006), Exchange raes, equy prces, and capal flows, Revew of Fnancal Sudes, Volume 9, Issue SPEC. ISS., pp

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