Automatic Tuning for FOREX Trading System Using Fuzzy Time Series


 Raymond Fields
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1 utomatic Tuig for FOREX Tradig System Usig Fuzzy Time Series Kraimo Maeesilp ad Pitihate Soorasa bstract Efficiecy of the automatic currecy tradig system is time depedet due to usig fixed parameters which are most effective i specific period of time This paper presets a method of optimizig automatic currecy tradig system by adustig its time variat parameters usig fuzzy timeseries forecastig to predict the tred of parameters Improved predictio for two sets of time series forecastig with fuzzy relatios is also illustrated Idex Terms Fuzzy timeseries, forecast, foreig exchage, FOREX I INTRODUCTION Ivestmet i currecy marets have progressed sigificatly The curret ivestmet products are developed to be the automatic tradig systems which are becomig more popular Research o the fiacial forecasts ofte predicts merely o how much the prices would icrease or decrease [1], [] This iformatio is ot sufficiet to be employed for automatic tradig system Because it does ot eve wat to ow that the price will icrease or decrease but acquires to ow the time for opepositio ad closed positio [3], which typically uses a techical idicator to decide various ope ad closed positio by settig some parameter values for decisio maig[4] However, the efficiecy of automatic tradig system is sesitive to some owcharacteristics of the maret This paper presets a algorithm to determie parameters of a automated tradig system to esure more efficiet i all aspects of the maret The proposed algorithm uses fuzzy time series to chage parameters rather tha predict direct exchage rate tred The results were compared to the results of the system whe the parameters are costat at most profitable durig the experimet The test will be carried out usig the period from May 3, 010 to July 6, 010 The exchage rate of the EUROUS$ by the profits ad losses will be based o total umber of Pips durig the experimet Sice we have two timeseries i cosideratio, i this paper, we proposed a fuzzy time series methods modified from Che's method [5] usig the vector to assist the forecasted output process Mauscript received pril 9, 01; revised May 4, 01 Kraimo Maeesilp is with the School of Computer Egieerig Faculty of Egieerig, Kig Mogut s Istitute of Techology Ladrabag, Ladrabag, Bago, Thailad Pitihate Soorasa is with the School of Computer Egieerig ad Iformatio Sciece, Faculty of Egieerig, Kig Mogut s Istitute of Techology Ladrabag, Ladrabag, Bago, Thailad II TEMPLTE MODEL OF N UTOMTIC TRDING SYSTEM To mae the test clear ad simple, the automatic tradig system is adopted from the experimetal wor usig Relative Stregth Idex RSI) [6] as the idicator i the decisio to ope the order to buy / sell i the maret This is because RSI is very simple to uderstad ad is oe of the high probability tredig patters i FOREX maret [7] However, the system is protected from the ope order to prevet the opeig by the fault sigals This system has two parameters They are RSI Up ad RSI Dow The RSI Up is the value that determies whe RSI is higher tha the settig values I this case, the system will ope order "sell" I cotrary, the RSI Dow is the value that determies whe the RSI is lower tha the settig value; this will ope the order buy Every order cofiguratio taes profit at 10 Pips ad is cofigured Stop loss at 100 Pips I a certai period of time the system cosiders order at most oe order ad waits util the old order is clear out by Tae Profit or Stop Loss before it opes ew order The operatio procedure of the system is preseted as the flow chart i Fig 1 Fig 1 Flow chart of a automatic tradig system Upo testig, we limit RSI Up ragig i betwee ad RSI Dow ragig i from the price data from May 3, 010 to July 6, 010 based o EUROUS$ currecy exchage rates The procedure of the test is as follows: First, we use exchage rate for the first 0 days to fid profit ad loss by usig every value of the RSI Up ad RSI Dow, ad the repeat the same actio by recalculatig for every 5 days for 8 times Fially we plot the results as show i Fig to H 560
2 B C D system to be fixed RSI) Fig 4 shows compoets of the adaptive RSI automatic tradig system for which the parameter forecastig service usig fuzzy time series to forecast the ext values of RSI Up ad RSI Dow ad sedig ew parameters to the automatic tradig applicatio The ew parameter is fed to update decisio cotrol of the automatic tradig system This research uses Meta Trader 4 Platform [8], which has a fuctio called the Expert dvisor i supportig the automatic tradig system The advatage of this system is that the two subsystems wor separately betwee the forecastig service ad the tradig system I doig so, if some error occurs, the subsystem will ot be detrimetal to the overall system E F Fig 4 Compoets of adaptive RSI automatic tradig system G H Fig Profit ad loss for the first 0 daysperiod recalculatig by shiftig the data for every 5 days ccordig to the experimetal results, although we use the same parameters, profit / loss ca tur aroud differetly depedig o time period i cosideratio For example, Fig a, if we set RSI Dow lower tha 0, the results are positive at all values of RSI Up ad the system will gets most profitable with RSI Up i rage This meas that the tred of exchage rate is bearish I this case, the system should be a opesell order strategy rather tha a buy order oe However, if the system parameter is set as the same values show i period of Fig e, the system will get more loss This is because the exchage rate i this period is bullish The graph shows RSI Up ad RSI Dow which get most profits ragig i ad The strategy should be opebuy order rather tha sell order Moreover, if the system is set RSI Up ragig i ad is set RSI Dow to 0, it ca get the most profit as show i Fig a Nevertheless, the same period yields the great loss i Fig e III FORECST PRMETERS WITH FUZZY TIME SERIES I the previous sectio, if the system has bee adusted the parameters to the optimal oes, performace of the system should be sigificatly ehaced doptig this cocept, this paper uses fuzzy timeseries [9], [10] to forecast the tred of parameter chages RSI Up, RSI Dow) to gai the profit We hypothesize that expectatio of RSI Up ad RSI Dow of the series at two sets are related, ad are parameters of the system This paper proposes a predictio usig two sets of time series with correlatio The cocept is modified from Che's Method [5] usig vector cocept to solve the problem The procedures are as follows: Defie Scope Uiverse Of Discourse U o Sets of Time Series, Divided Them to J ad K ito Equal Parts The boudary of RSI Up is ad the boudary of RSI Dow is Hece, the member of U is ragig i betwee splittig ito 10 equal part Similarly, the member of U is betwee from 60 to 90 ad splits ito 10 equal parts B Defie Membership Fuctio of U ad U after that, Fuzzify Historical Data by the Membership Fuctios Sice ad is divided ito 10 equal parts, the fuzzy membership fuctio ca be defied as show i Fig 5 Fig 3 Profit  loss of all RSI values throughout the experimet Fig 3 depicts profit ad loss whe we exted period to all data startig from May 3, 010 to July 6, 010 The result is a system with the most profit at RSI Up ad RSI Dow about 61 ad 0, which will use these costats for compariso the Fig 5 Membership fuctios of U ad U 561
3 Utilizig historical data to fid the RSI Up ad RSI Dow i the most profitable exchage rate usig a 3day period ad the shift the data to recalculate by employig the same test method for all data RSI Dow has the same multiple maximum profits We select a value that is the shortest distace from the last state ad the fuzzify data by membership fuctio The result is show i Table I TBLE I: RSI UP, RSI DOWN OF THE MOST PROFIT ND FUZZIFIED RESULTS C Fid Fuzzy Relatioship From State Relatio Usig Fuzzified Results This time series cotai sets of relatios The fuzzy relatios are exteded to defie each value of ad Therefore the fuzzy relatios ca be defied as, Determiatio of the relatioship ca be doe by fidig a state with ad correspodig to, of ccordig to, Table 1, the values ad of the ext state are filled i the relatio table ad are the updated value ad of, Repeat the same step util all, state relatio table for time series of all Table II are well defied Next, is show i D Calculate Forecast Output Table from Next State Relatio Table Based o 3 Rules with dapted From Che's Method [4] as Follows 1) If, ) has oly oe member of fuzzy relatioship which is, p q ), the the midpoits of is p m ad midpoits p of is m respectively Forecasted output of, ) q q is m, m ) p q ) If, ) members of relatioship are 1, 1),, ),, ),, p, ad the umber of 3 3 q ) members is Midpoits of,,,, are 1 3 p m,, m, m, m 1 3 m,, m, m, m 1 3, ) is p q ad midpoits of,,,, are 1 3 p respectively Forecasted output of [ m m m m ] [ m m m m p ] 3 1 q, 3 1 3) If, ) is ot a member of fuzzy relatioship, the the midpoit of is m ad the midpoit of is output of, ) is m, m ) m Forecasted TBLE II: NEXT STTE RELTION TBLE Usig these procedures summarized i Table II, the forecasted results ca be writte i Table III To predict RSI Up, RSI Dow i the ext period, we examie the RSI Up, RSI Dow by matchig to the Profit Max i the curret period, correspodig to the same rage We the tae the output at the positio value of, ad as the expectatio values 56
4 TBLE III: FORECSTED OUTPUT TBLE s we have see, the predictios of RSI Up ad RSI Dow are agreed as i the same directio with the actual data But there are still some errors We will measure errors by usig root mea squared errors show i equatio 1) RMSE i1 ctualrsi ForecastRSI i From the measured values, the RMSE of RSI Up is located at 4583 ad RMSE of RSI Dow at 788 errors may be reduced if we exted the time series or addig more data i 1) IV EXPERIMENTL RESULTS The experimet is desiged to aim for two parts: First part is experimet for estimatio of appropriate RSI Up ad RSI Dow for the ext steps This result will be compared to actual time series that eables to determie the predictio ability Secod part is the experimet o adustig RSI Up ad RSI Dow for the automatic tradig system The result of secod part will be compared to the automatic tradig system with fixed parameters at most profit for all periods I the experimet, we use the exchage rate of Euro US$ EURUSD) i the period from May 3, 010 to July 6, 010 Fig 6 shows the results obtaied from the first part whe the actual data ad predicted data are plotted i compariso Fig 6 Forecast outputs compared to actual values Fig 7 shows the results from the secod part usig the RSI Up ad RSI Dow predictio to cotrol the opeig order of the system The results are compared with those of fixed RSI at the maximum profit s ca be see, the graph of adaptive RSI has cotiuously icreased earig profits, while that of the fixed RSI yields icreased earig profit at first ad the turs aroud to be a decrease oe as time goes by This is because the maret tred has bee chaged Fig 7 Compariso o the growth profit betwee fixed RSI ad dyamic RSI usig fuzzy time series V CONCLUSIONS Followig the proposed ivestmet algorithm usig fuzzy time series, the results show that the adustmet parameters of the proposed automatic tradig system ca actually icrease the profits of the system Eve though there is small error i the forecast accuracy of some parameters, but the results are better tha those usig the fixed parameters 563
5 Because the slope of the curve of the profit to parameter is ot high, the small error of the estimatio has ot much affected to the performace s a result, it is oly little dimiished a profit, but it does ot cause the loss evetually This study cosiders oly the coditios of order opeig, which is oly oe factor i causig the profits Nevertheless, i some extesio, a more practical automatic tradig system has other factors For example, coditios of order closig ad order maagemet are those ifluet factors to be cosidered I spite of existece of a more complicated system, a simple oe is show i this paper to iitiate ad first validate the effectiveess of the proposed method The more complex system as metioed will be suited for future wor REFERENCES [1] K Chi, F P Fu, ad W G Che, modified model of fuzzy time series for forecastig exchage rates, Iteratioal Worshop o Educatio Techology ad Computer Sciece, vol 3, o, pp 4043, 010 [] Y Leu, C P Lee, ad Y Z Jou, distacebased fuzzy time series model for exchage rates forecastig, Expert Systems with pplicatios, vol36, pp , 009 [3] T Stridsma, Tradig systems that wor: buildig ad evaluatig effective tradig systems, New Yor: McGrawHill, 000, pp [4] P J Kaufma, New tradig systems ad methods, 3 rd ed, New Jersey: Joh Wiley adsos, 005, pp [5] S M Che, Forecastig erollmets based o fuzzy time series, Fuzzy Sets ad Systems, vol 81, o3, pp , 1996 [6] J Murphy, Techical aalysis of the fiacial marets, New Yor: Pretice Hall, 1986, pp 556 [7] E Posi, FOREX Patters ad Probabilities: tradig strategies for tredig ad rageboud marets, New Jersey: Joh Wiley adsos, 007, pp [8] Meta Quotes Software 000) MQL4 Referece [Olie] vailable: [9] Q Sog ad BS Chissom, Forecastig erollmets with fuzzy time series Part I, Fuzzy Sets ad Systems, vol 54, o1, pp19, 1993 [10] Q Sog ad BS Chissom, Forecastig erollmets with fuzzy time series Part II, Fuzzy Sets ad Systems, vol 6, o1, pp18, 1994 Kraimo Maeesilp was bor i Thailad He received a BId ad MEg from Kig Mogut s Istitute of Techology Ladrabag His research iterests iclude Fiacial Iformatio Behavior, oliear forecastig ad utomatic Tradig System He is worig toward his Doctoral degree at the school of Computer Egieerig Faculty of Egieerig, Kig Mogut s Istitute of Techology Ladrabag, Ladrabag, Bago, Thailad Pitihate Soorasa was bor i Thailad He is curretly ssociate Professor of Electrical Egieerig at the School of Computer Egieerig ad Iformatio Sciece, Faculty of Egieerig, Kig Mogut s Istitute of Techology Ladrabag, Ladrabag, Bago, Thailad His research iterests iclude IT oliear systems ad computeraided cotrol He received a BEd Hos) ad MSc i Physics from Sriahariwirot Uiver sity, a MS from George Washigto Uiversity199) ad a PhD from the Uiversity of Housto1996), both i Electrical Egieerig 564
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