# Automatic Tuning for FOREX Trading System Using Fuzzy Time Series

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3 Utilizig historical data to fid the RSI Up ad RSI Dow i the most profitable exchage rate usig a 3-day 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

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