Optimization of Backtesting Techniques in Automated High Frequency Trading Systems Using the d-Backtest PS Method

Computational Economics volume 56, pages975–1054(2020)Cite this article

Abstract

Trading strategies intended for high frequency trading in Forex markets are executed by cutting-edge automated trading systems. Such systems implement algorithmic trading strategies and are configured with predefined optimized parameters in order to generate entry and exit orders and execute trades on trading platforms. Three high-frequency automated trading systems were developed in the current research, using the MACD (oscillator), the SMA (moving average) and the PIVOT points (price crossover) technical indicators. The systems traded on hourly time frames, employing historical data of closing prices and the parameter optimization for each system was done using the d-Backtest PS method over weekly periods. With this work we intend to extend the methods of parameter selection for automated trading systems in high frequency trading. Through this research and the interpretation and evaluation of its results, we conclude that backtesting parameters’ optimization, especially through the d-Backtest PS method, is much more profitable than the default values of the parameters and that the optimization of parameters yields the highest profits through the implementation of restrictive relationships among them. It is also observed that the selection of the most profitable parameters of a trading system can be unrestricted, rendering the validation of the minor divergence occurring among slightly varying prices redundant. Meanwhile, other conclusions that can be drawn are that the most profitable classification system employed by the d-Backtest PS method is calibrated by means of two validation periods and that the most efficient profitability ratio between historical data period and validation period is 6:1 (in- and out-of-the-sample ratio).

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Acknowledgements

We would like to thank COSMOS4U for providing the nessesary infrastructure for this research. We would also like to thank the anonymous reviewers for their valuable comments on our work. This research has been co-financed by the European Union and Greek national funds through the Operational Program Competitiveness, Entrepreneurship and Innovation, under the call RESEARCH—CREATE—INNOVATE (project code:T1EDK-02342).

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  1. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, 67100, Greece

    D. Th. Vezeris, C. J. Schinas & V. A. Bizergianidou

  2. COSMOS4U, Xanthi, 67100, Greece

    Th. S. Kyrgos & I. P. Karkanis

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  1. D. Th. Vezeris
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Appendices

Appendix 1

PIVOT

Returns by implementing the PIVOT system, with fixed previous week BT period optimization parameters and dynamic optimization parameters.

Symbol Avg(PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27)
FOREX returns of a classic PIVOT(24) trading system
AUDUSD 39.33 869 0 54 40.91 25.11 10.78 − 57.39 796.95 − 681.54 − 7575.23 132
EURUSD 49.88 1096.14 0 66 50 12.14 9.36 − 2.3 742.18 − 528.39 − 303.61 132
GBPUSD 57.52 1640.5 0 60 45.45 4.1 0 − 9.26 821.14 − 527.68 − 1222.03 132
USDCAD 27.32 657.83 0 61 46.21 12.61 0 − 27.23 382.35 − 412.54 − 3594.05 132
USDJPY 46.89 1079.61 0 53 40.15 16.18 7.38 − 21.49 884.46 − 1131.38 − 2836.09 132
XAUUSD 76.3 3063 0 58 43.94 6.63 11.09 − 41.85 931.7 − 621.74 − 5524.23 132
figurea
Symbol Avg(PF) Max(PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27)
FOREX returns of an adaptive AdPIVOT (x w-1 ) trading system, using previous week’s best BT period for parameters’ optimization
AUDUSD 88.53 1372.13 0 57 43.18 6.54 4.87 − 26.88 767.83 − 587.16 − 3548.62 132
EURUSD 92.74 1656.81 0 62 46.97 4.56 8.54 − 15.39 701.14 − 716.47 − 2031.48 132
GBPUSD 116.21 2391.03 0 51 38.64 9.13 0 − 35.56 761.81 − 525.54 − 4693.53 132
USDCAD 92.03 1371.1 0 63 47.73 5.8 0 − 25.6 548.04 − 525.78 − 3379.71 132
USDJPY 101.69 1603.95 0 55 41.67 17.77 7.38 − 34.61 1104.06 − 1276.02 − 4568.46 132
XAUUSD 236.51 3063 0 62 46.97 4.67 9.39 11.96 989.6 − 867.49 1578.17 132
figureb
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (Sharpe Ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum s(Profit) Weeks (2016.02.28–2017.08.27)
FOREX returns of an adaptive AdPIVOT (x dyn ) trading system, using d-Backtest PS method for parameters’ optimization
AUDUSD wa vp > 2 82.49 1372.13 0 59 44.7 25.11 4.87 − 21.11 767.83 − 580.75 − 2786.13 132
EURUSD ea 56.81 1647.81 0 62 46.97 4.56 8.37 − 14.8 592.85 − 689.62 − 1954.23 132
GBPUSD avg vp > 2 150.1 2513.98 0 57 43.18 9.13 0 − 16.22 1457.53 − 525.54 − 2141.05 132
USDCAD avg ccbt vp > 2 121.04 1237.6 0 67 50.76 12.61 0 1.63 494.64 − 525.78 214.77 132
USDJPY ea vp > 2 116.74 1603.95 0 61 46.21 15.38 7.38 − 16.85 1104.06 − 1162.57 − 2224.66 132
XAUUSD wa ccbt vp > 2 276.15 3173.82 0 63 47.73 1.91 11.09 23.09 1078.76 − 867.49 3048.04 132
figurec

SMA

Forex returns of theSMA trading system, utilizing fixed parameters for previous week BT period optimization and dynamic optimization parameters.

Symbol Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (Sharpe ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27)
FOREX returns of a classic SMA(200,5) trading system
AUDUSD 90.97 1372.13 0 46 34.85 1.58 9.24 − 75.84 767.83 − 661.65 − 10010.36 132
EURUSD 150.29 1656.81 0 54 40.91 4.45 8.36 − 27.46 596.09 − 527.55 − 3625.08 132
GBPUSD 214.19 2391.03 0 54 40.91 0.96 7.07 − 22.53 857.99 − 542.53 − 2973.82 132
USDCAD 149.25 1371.1 0 62 46.97 2.27 10.13 − 19.67 548.04 − 591.54 − 2596.38 132
USDJPY 185.43 1822.4 0 59 44.7 1.52 6.61 7.23 728.56 − 494.31 954.91 132
XAUUSD 370.84 3169.06 0 66 50 5.35 2.79 10.18 1077.14 − 712.77 1343.2 132
figured
Symbol Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (Sharpe Ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27)
FOREX returns of an adaptive AdSMA (x w-1 ,y w-1 ) trading system, using previous week’s best BT period for parameters’ optimization
AUDUSD 58.05 1372.13 0 56 42.42 1.91 4.87 − 54.79 787.84 − 648.98 − 7231.83 132
EURUSD 88.48 1656.81 0 49 37.12 4.56 8.54 − 47.9 596.09 − 550.55 − 6322.86 132
GBPUSD 142.29 2513.98 0 55 41.67 4.41 7.87 − 29.16 1457.53 − 622.19 − 3848.67 132
USDCAD 96.57 1124.05 0 59 44.7 3.72 7.36 − 38.46 449.22 − 690.66 − 5076.77 132
USDJPY 111.04 1603.95 0 58 43.94 17.84 7.38 − 26.62 702.99 − 1276.02 − 3514.02 132
XAUUSD 260.48 3169.06 0 59 44.7 1.29 2.79 − 18.04 1077.14 − 885.03 − 2381.71 132
figuree
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (Sharpe Ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27)
FOREX returns of an adaptive AdSMA (x dyn ,y dyn ) trading system, using d-Backtest PS method for parameters’ optimization
AUDUSD ea ccbt vp > 2 68.83 1372.13 0 56 42.42 3.84 9.24 − 26.3 767.83 − 568.92 − 3471.09 132
EURUSD ea vp > 1 103.58 1656.81 0 62 46.97 2.74 8.54 − 15.35 596.09 − 511.75 − 2026.57 132
GBPUSD avg 149.59 2513.98 0 57 43.18 1.7 8.13 − 17.75 1457.53 − 509.9 − 2342.72 132
USDCAD avg vp > 2 120.45 1237.6 0 62 46.97 5.8 7.36 − 13.68 494.64 − 690.66 − 1805.62 132
USDJPY avg vp > 1 123.57 1603.95 0 55 41.67 17.77 7.38 − 9.94 735.11 − 1162.57 − 1311.94 132
XAUUSD wa vp > 1 232.11 3061.57 0 62 46.97 1.59 2.79 − 18.59 987.86 − 812.79 − 2453.65 132
figuref

Appendix 2

AdMACD

In this appendix we expand on the returns of the AdMACD trading system, by implementing various restrictions among parameters and we display their profitability results.

fast <>slow

Symbol Condition Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (Sharpe Ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Max profit Best profit among condition Sum profit of all assets
AUDUSD fast <>slow 48.16 1102.1 0 38 48.1 14.24 3.33 9.53 925.74 − 687.76 752.9 79 1   
EURUSD fast <>slow 30.62 827.64 0 30 38 2.56 7.1 − 33.1 343.37 − 907.64 − 2614.7 79    
GBPUSD fast <>slow 89.57 2423 0 40 50.6 3.89 9.59 9.43 726.61 − 1162.7 745.12 79    
USDCAD fast <>slow 50.89 745.23 0 47 59.5 16.25 4.01 29.5 679.18 − 383.78 2330.42 79 1   
USDJPY fast <>slow 61.03 2201 0 38 48.1 2.49 0.58 − 8.95 352.08 − 330.35 − 706.89 79    
XAUUSD fast <>slow 93.58 1347.9 0 42 53.2 3.44 6.08 5.91 644.12 − 963.49 466.74 79   2 973.6
figureg

fast < slow

Symbol Condition Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (Sharpe Ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Max profit Best profit among condition Sum profit of all assets
AUDUSD fast < slow 67.82 1102.1 0 33 41.8 14.24 4.8 − 39.32 572.57 − 581.15 − 3106.6 79    
EURUSD fast < slow 31.19 827.64 0 32 40.5 2.56 7.1 − 26.72 504.17 − 907.64 − 2110.7 79    
GBPUSD fast < slow 87.73 2423 0 45 57 3.89 4.67 24.66 726.61 − 1162.7 1948.3 79    
USDCAD fast < slow 54.82 745.23 0 48 60.8 16.25 3.19 9.46 439.1 − 511.54 747.28 79    
USDJPY fast < slow 82.84 2201 0 40 50.6 3.1 0.53 − 6.15 352.08 − 330.35 − 486.11 79    
XAUUSD fast < slow 88.99 1347.9 0 44 55.7 1.55 9.45 29.61 644.12 − 952.6 2339.29 79   0 − 668.5
figureh

fast < slow & signal < fast

Symbol Condition Avg(PF) max(PF) min(PF) PF > 1 % PF > 1 Max (Sharpe Ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Max profit Best profit among condition Sum profit of all assets
AUDUSD fast < slow & signal < fast 67.79 1102.1 0 32 40.5 14.24 4.8 − 39.99 572.57 − 581.15 − 3159 79    
EURUSD fast < slow & signal < fast 31.32 827.64 0 32 40.5 2.56 7.1 − 27.76 558.86 − 907.64 − 2193 79    
GBPUSD fast < slow & signal < fast 87.62 2423 0 44 55.7 3.89 8.49 25.96 726.61 − 1162.7 2051.08 79 1   
USDCAD fast < slow & signal < fast 54.8 745.23 0 48 60.8 16.25 3.19 5.31 439.1 − 511.54 419.23 79    
USDJPY fast < slow & signal < fast 82.86 2201 0 40 50.6 3.1 0.53 − 5.43 352.08 − 330.35 − 428.75 79    
XAUUSD fast < slow & signal < fast 89.21 1347.9 0 46 58.2 1.55 9.45 34.41 644.12 − 952.6 2718.43 79 1 2 − 591.99
figurei

fast < slow < (fast x 4)

Symbol Condition Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Max profit Best profit among condition Sum profit of all assets
AUDUSD fast < slow < (fast x4) 33.63 1102.1 0 27 34.2 14.24 4.8 − 80.65 572.57 − 581.15 − 6371.4    
EURUSD fast < slow < (fast x4) 31.3 528.21 0 31 39.2 3.35 7.1 − 18.72 504.17 − 680.76 − 1479.2    
GBPUSD fast < slow < (fast x4) 87.45 2423 0 37 46.8 3.28 9.59 − 14.78 726.61 − 1162.7 − 1167.4    
USDCAD fast < slow < (fast x4) 46.04 745.23 0 47 59.5 2.66 3.19 17.45 583.28 − 381.73 1378.18    
USDJPY fast < slow < (fast x4) 32.84 816 0 38 48.1 28.72 0.53 − 5.07 317.79 − 330.35 − 400.16    
XAUUSD fast < slow < (fast x4) 45.51 1172.3 0 42 53.2 1.55 9.45 15.4 644.12 − 992.5 1216.83   0 − 6823.15
figurej

fast < slow < (fast x 4) & signal < fast

Symbol Condition Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (Sharpe Ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Max profit Best profit among condition Sum profit of all assets
AUDUSD fast < slow < (fast x4) & signal ≤ fast 33.65 1102.1 0 27 34.2 14.24 4.8 − 78.1 572.57 − 581.15 − 6170.3 79    
EURUSD fast < slow < (fast x4) & signal ≤ fast 31.66 528.21 0 32 40.5 3.35 7.1 − 18.28 558.86 − 680.76 − 1443.8 79 1   
GBPUSD fast < slow < (fast x4) & signal ≤ fast 90.14 2423 0 37 46.8 3.28 4.55 − 17.52 726.61 − 1162.7 − 1384.1 79    
USDCAD fast < slow < (fast x4) & signal ≤ fast 46.02 745.23 0 47 59.5 2.66 3.19 13.97 583.28 − 417.93 1103.72 79    
USDJPY fast < slow < (fast x4) & signal ≤ fast 32.85 816 0 38 48.1 28.72 0.53 − 5.15 317.79 − 330.35 − 406.91 79    
XAUUSD fast < slow < (fast x4) & signal ≤ fast 45.73 1172.3 0 45 57 1.55 9.45 20.42 644.12 − 992.5 1613.57 79   1 − 6687.8
figurek

(fast x 2) < slow

Symbol Condition Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (Sharpe Ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Max Profit Best profit among condition Sum profit of all assets
AUDUSD (fast x2) < slow 32.57 1102.1 0 28 35.4 14.24 4.8 − 49.18 925.74 − 637.36 − 3885.6 79    
EURUSD (fast x2) < slow 16.16 475.81 0 36 45.6 2.35 9.22 − 24.77 634.47 − 907.64 − 1956.5 79    
GBPUSD (fast x2) < slow 45.08 984 0 33 41.8 2.53 6.33 − 45.57 550.48 − 1199.1 − 3600.1 79    
USDCAD (fast x2) < slow 31.03 745.23 0 45 57 2.9 7.67 27.32 703.42 − 357.84 2157.9 79    
USDJPY (fast x2) < slow 100.2 2201 0 35 44.3 4.35 0.58 − 7.99 450.7 − 332.53 − 631.29 79    
XAUUSD (fast x2) < slow 128.7 3156.9 0 42 53.2 1.63 6.08 − 1.51 946.77 − 1171.4 − 119.47 79   0 − 8035.09
figurel

(fast x 2) < slow & signal < fast

Symbol Condition Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (Sharpe Ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Max profit Best profit among condition Sum profit of all assets
AUDUSD (fast x2) < slow) & signal ≤ fast 63.07 1102.1 0 32 40.5 11.85 4.8 − 43.29 572.57 − 581.15 − 3420.2 79    
EURUSD (fast x2) < slow) & signal ≤ fast 31.69 827.64 0 34 43 2.56 7.1 − 35.4 304.71 − 907.64 − 2796.5 79    
GBPUSD (fast x2) < slow) & signal ≤ fast 100.6 2423 0 39 49.4 3.89 6.33 15.89 726.61 − 1179.2 1255.4 79    
USDCAD (fast x2) < slow) & signal ≤ fast 50.79 745.23 0 48 60.8 16.25 3.19 12.22 439.1 − 511.54 965.65 79    
USDJPY (fast x2) < slow) & signal ≤ fast 79.91 2201 0 38 48.1 3.1 0.53 − 4.73 352.08 − 342.86 − 373.67 79    
XAUUSD (fast x2) < slow) & signal ≤ fast 91.68 1347.9 0 45 57 1.54 9.45 30.34 637.3 − 952.6 2397.11 79   0 − 1972.18
figurem

(fast x 2) < slow < (fast x 4)

Symbol Condition Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (Sharpe Ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Max profit Best profit among condition Sum profit of all assets
AUDUSD (fast x2) < slow < (fast x4) 28.97 1102.1 0 28 35.4 11.85 4.8 − 83.24 572.57 − 581.15 − 6576.1 79    
EURUSD (fast x2) < slow < (fast x4) 25.18 475.81 0 34 43 2.56 7.1 − 19.81 363.55 − 612.75 − 1565.2 79    
GBPUSD (fast x2) < slow < (fast x4) 88.03 2423 0 33 41.8 3.28 9.59 − 21.86 726.61 − 1179.2 − 1727.3 79    
USDCAD (fast x2) < slow < (fast x4) 42.14 745.23 0 47 59.5 2.66 3.19 19.4 583.28 − 381.73 1532.41 79    
USDJPY (fast x2) < slow < (fast x4) 32.34 816 0 38 48.1 28.72 0.53 − 2.75 317.79 − 293.61 − 217.51 79    
XAUUSD (fast x2) < slow < (fast x4) 47.02 1172.3 0 43 54.4 1.55 9.45 17.74 644.12 − 992.5 1401.53 79   0 − 7152.07
figuren

(fast x 2) < slow < (fast x 4) & signal < fast

Symbol Condition Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (Sharpe Ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Max profit Best profit among condition Sum profit of all assets
AUDUSD (fast x2) < slow < (fast x4) & signal ≤ fast 28.98 1102.1 0 29 36.7 11.85 4.8 − 76.32 572.57 − 581.15 − 6029.3 79    
EURUSD (fast x2) < slow < (fast x4) & signal ≤ fast 25.32 475.81 0 34 43 2.56 7.1 − 31.63 394.37 − 612.75 − 2498.7 79    
GBPUSD (fast x2) < slow < (fast x4) & signal ≤ fast 103.2 2423 0 35 44.3 3.28 4.55 − 17.55 726.61 − 1179.2 − 1386.6 79    
USDCAD (fast x2) < slow < (fast x4) & signal ≤ fast 38.64 745.23 0 47 59.5 2.66 3.19 18.48 583.28 − 417.93 1459.88 79    
USDJPY (fast x2) < slow < (fast x4) & signal ≤ fast 32.35 816 0 39 49.4 28.72 0.53 − 0.04 317.79 − 293.61 − 3.12 79 1   
XAUUSD (fast x2) < slow < (fast x4) & signal ≤ fast 48.23 1172.3 0 44 55.7 1.54 9.45 22.04 637.3 − 992.5 1741.29 79   1 − 6716.56
figureo

SMA

x ≥ 5 & y ≥ 2

Symbol Condition Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27) Max profit Best profit among condition Sum profit of all assets
AUDUSD x ≥ 5 & y ≥ 2 63.69 1372.1 0 50 37.9 1.91 9.24 − 56.47 767.83 − 568.92 − 7453.97 132    
EURUSD x ≥ 5 & y ≥ 2 91.77 1656.8 0 61 46.2 2.74 9.57 − 30.15 596.09 − 550.55 − 3980.18 132    
GBPUSD x ≥ 5 & y ≥ 2 130.5 2514 0 59 44.7 6.01 8.13 − 19.24 1457.5 − 622.19 − 2539.39 132    
USDCAD x ≥ 5 & y ≥ 2 119.1 1237.6 0 59 44.7 5.8 7.36 − 23.02 494.64 − 690.66 − 3038.14 132 1   
USDJPY x ≥ 5 & y ≥ 2 100.8 1604 0 53 40.2 8.71 9.27 − 33.12 735.11 − 1276 − 4371.7 132    
XAUUSD x ≥ 5 & y ≥ 2 261 3169.1 0 55 41.7 1.29 2.79 − 35.7 1077.1 − 812.79 − 4711.74 132 1 2 − 26095.12
figurep

x > y

Symbol Condition Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27) Max profit Best profit among condition Sum profit of all assets
AUDUSD x > y 63.69 1372.1 0 50 37.9 1.91 9.24 − 56.47 767.83 − 568.92 − 7453.97 132    
EURUSD x > y 91.77 1656.8 0 61 46.2 2.74 9.57 − 30.15 596.09 − 550.55 − 3980.18 132    
GBPUSD x > y 130.5 2514 0 59 44.7 6.01 8.13 − 19.24 1457.5 − 622.19 − 2539.39 132    
USDCAD x > y 119.1 1237.6 0 59 44.7 5.8 7.36 − 23.02 494.64 − 690.66 − 3038.14 132 1   
USDJPY x > y 100.8 1604 0 53 40.2 8.71 9.27 − 33.12 735.11 − 1276 − 4371.7 132    
XAUUSD x > y 261 3169.1 0 55 41.7 1.29 2.79 − 35.7 1077.1 − 812.79 − 4711.74 132 1 2 − 26095.12
figureq

y ≥ x

Symbol Condition Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27) Max profit Best profit among condition Sum profit of all assets
AUDUSD x < y 54.79 1372.1 0 52 39.4 25.11 9.24 − 39.27 787.71 − 514.05 − 5183.86 132 1   
EURUSD x < y 62.86 1606.1 0 63 47.7 2.74 9.36 − 10.81 728.35 − 485.73 − 1427.47 132 1   
GBPUSD x < y 73.98 1325.4 0 55 41.7 8.14 8.95 − 19.2 821.14 − 511.15 − 2534.71 132 1   
USDCAD x < y 60.9 1237.6 0 60 45.5 12.61 7.97 − 26.38 494.64 − 690.66 − 3481.57 132    
USDJPY x < y 50.18 992.7 0 60 45.5 20.65 7.38 − 7.93 961.26 − 1162.6 − 1046.2 132 1   
XAUUSD x < y 81.44 1836.1 0 45 34.1 1.69 2.79 − 78.66 717.52 − 867.92 − 10383.5 132   4 − 24057.27
figurer

PIVOT

Symbol Condition Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (Sharpe Ratio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27) Max profit Best profit among condition Sum profit of all assets
AUDUSD f ≥ 4 80.99 1372.1 0 61 46.2 6.54 9.24 − 25.47 767.83 − 580.75 − 3361.7 132 1   
EURUSD f ≥ 5 116.7 1656.8 0 56 42.4 4.56 8.54 − 34.01 597.12 − 716.47 − 4489.4 132    
GBPUSD f ≥ 6 145.5 2514 0 56 42.4 9.13 0 − 19.39 1457.5 − 525.54 − 2559.5 132    
USDCAD f ≥ 7 121.2 1237.6 0 67 50.8 12.61 0 0.84 494.64 − 525.78 110.59 132 1   
USDJPY f ≥ 8 90.58 1604 0 52 39.4 20.94 7.38 − 39.46 1104.1 − 1276 − 5209 132    
XAUUSD f ≥ 9 274.2 3173.8 0 58 43.9 1.91 9.39 9.07 1078.8 − 867.49 1197.77 132   2 − 14311.3
figures

Appendix 3

figuret
figureu
figurev
figurew

Appendix 4

AdMACD

The following table displays the returns of the implementation of the AdMACD trading system in detail, while sorting procedure involves 24 d-Backtest PS methods.

W1 Nm W2 Nm W3 Nm W4 Nm W5 Nm W6 Nm Final sorting Nm
avg 1 avg 20 avg 22 avg 22 avg 19 avg 14 avg 98
avg vp > 1 6 avg vp > 1 24 avg vp > 1 17 avg vp > 1 12 avg vp > 1 22 avg vp > 1 12 avg vp > 1 93
avg vp > 2 9 avg vp > 2 22 avg vp > 2 6 avg vp > 2 23 avg vp > 2 10 avg vp > 2 4 avg vp > 2 74
avg ccbt 24 avg ccbt 23 avg ccbt 13 avg ccbt 18 avg ccbt 4 avg ccbt 8 avg ccbt 90
avg ccbt vp > 1 22 avg ccbt vp > 1 19 avg ccbt vp > 1 15 avg ccbt vp > 1 21 avg ccbt vp > 1 13 avg ccbt vp > 1 9 avg ccbt vp > 1 99
avg ccbt vp > 2 4 avg ccbt vp > 2 16 avg ccbt vp > 2 8 avg ccbt vp > 2 20 avg ccbt vp > 2 2 avg ccbt vp > 2 5 avg ccbt vp > 2 55
ea 19 ea 10 ea 19 ea 13 ea 6 ea 24 ea 91
ea vp > 1 16 ea vp > 1 15 ea vp > 1 14 ea vp > 1 2 ea vp > 1 21 ea vp > 1 22 ea vp > 1 90
ea vp > 2 14 ea vp > 2 8 ea vp > 2 7 ea vp > 2 9 ea vp > 2 17 ea vp > 2 18 ea vp > 2 73
ea ccbt 12 ea ccbt 4 ea ccbt 23 ea ccbt 3 ea ccbt 15 ea ccbt 19 ea ccbt 76
ea ccbt vp > 1 7 ea ccbt vp > 1 7 ea ccbt vp > 1 21 ea ccbt vp > 1 1 ea ccbt vp > 1 23 ea ccbt vp > 1 13 ea ccbt vp > 1 72
ea ccbt vp > 2 5 ea ccbt vp > 2 3 ea ccbt vp > 2 12 ea ccbt vp > 2 8 ea ccbt vp > 2 20 ea ccbt vp > 2 11 ea ccbt vp > 2 59
pf 17 pf 9 pf 4 pf 16 pf 16 pf 20 pf 82
pf vp > 1 2 pf vp > 1 21 pf vp > 1 2 pf vp > 1 17 pf vp > 1 24 pf vp > 1 15 pf vp > 1 81
pf vp > 2 18 pf vp > 2 11 pf vp > 2 1 pf vp > 2 24 pf vp > 2 8 pf vp > 2 6 pf vp > 2 68
pf ccbt 10 pf ccbt 18 pf ccbt 3 pf ccbt 19 pf ccbt 11 pf ccbt 3 pf ccbt 64
pf ccbt vp > 1 8 pf ccbt vp > 1 13 pf ccbt vp > 1 5 pf ccbt vp > 1 14 pf ccbt vp > 1 14 pf ccbt vp > 1 2 pf ccbt vp > 1 56
pf ccbt vp > 2 13 pf ccbt vp > 2 5 pf ccbt vp > 2 10 pf ccbt vp > 2 5 pf ccbt vp > 2 9 pf ccbt vp > 2 1 pf ccbt vp > 2 43
wa 23 wa 12 wa 11 wa 11 wa 1 wa 23 wa 81
wa vp > 1 21 wa vp > 1 17 wa vp > 1 16 wa vp > 1 10 wa vp > 1 5 wa vp > 1 21 wa vp > 1 90
wa vp > 2 20 wa vp > 2 14 wa vp > 2 20 wa vp > 2 15 wa vp > 2 7 wa vp > 2 17 wa vp > 2 93
wa ccbt 15 wa ccbt 6 wa ccbt 24 wa ccbt 7 wa ccbt 12 wa ccbt 16 wa ccbt 80
wa ccbt vp > 1 11 wa ccbt vp > 1 2 wa ccbt vp > 1 18 wa ccbt vp > 1 6 wa ccbt vp > 1 18 wa ccbt vp > 1 10 wa ccbt vp > 1 65
wa ccbt vp > 2 3 wa ccbt vp > 2 1 wa ccbt vp > 2 9 wa ccbt vp > 2 4 wa ccbt vp > 2 3 wa ccbt vp > 2 7 wa ccbt vp > 2 27

Sorted by means of frequency of profitability occurrence they are on display as follows:

Final sum of sorting Points Normalized
avg ccbt vp > 1 99 55.00
avg 98 54.44
avg vp > 1 93 51.67
wa vp > 2 93 51.67
ea 91 50.56
avg ccbt 90 50.00
ea vp > 1 90 50.00
wa vp > 1 90 50.00
pf 82 45.56
pf vp > 1 81 45.00
wa 81 45.00
wa ccbt 80 44.44
ea ccbt 76 42.22
avg vp > 2 74 41.11
ea vp > 2 73 40.56
ea ccbt vp > 1 72 40.00
pf vp > 2 68 37.78
wa ccbt vp > 1 65 36.11
pf ccbt 64 35.56
ea ccbt vp > 2 59 32.78
pf ccbt vp > 1 56 31.11
avg ccbt vp > 2 55 30.56
pf ccbt vp > 2 43 23.89
wa ccbt vp > 2 27 15.00

AdPIVOT

The following tables expand on returns obtained through the implementation of the AdPIVOT trading system, while sorting procedure involves 24 d-Backtest PS methods.

W1 Points W2 Points W3 Points W4 Points W5 Points W6 Points Final sorting Points
avg 1 avg 2 avg 5 avg 2 avg 3 avg 10 avg 23
avg vp > 1 9 avg vp > 1 7 avg vp > 1 7 avg vp > 1 15 avg vp > 1 5 avg vp > 1 7 avg vp > 1 50
avg vp > 2 19 avg vp > 2 12 avg vp > 2 6 avg vp > 2 21 avg vp > 2 12 avg vp > 2 12 avg vp > 2 82
avg ccbt 18 avg ccbt 9 avg ccbt 2 avg ccbt 9 avg ccbt 2 avg ccbt 2 avg ccbt 42
avg ccbt vp > 1 21 avg ccbt vp > 1 14 avg ccbt vp > 1 1 avg ccbt vp > 1 13 avg ccbt vp > 1 11 avg ccbt vp > 1 3 avg ccbt vp > 1 63
avg ccbt vp > 2 22 avg ccbt vp > 2 21 avg ccbt vp > 2 3 avg ccbt vp > 2 20 avg ccbt vp > 2 15 avg ccbt vp > 2 15 avg ccbt vp > 2 96
ea 6 ea 1 ea 11 ea 1 ea 13 ea 21 ea 53
ea vp > 1 4 ea vp > 1 8 ea vp > 1 20 ea vp > 1 14 ea vp > 1 14 ea vp > 1 24 ea vp > 1 84
ea vp > 2 14 ea vp > 2 5 ea vp > 2 22 ea vp > 2 18 ea vp > 2 21 ea vp > 2 20 ea vp > 2 100
ea ccbt 16 ea ccbt 6 ea ccbt 24 ea ccbt 6 ea ccbt 9 ea ccbt 5 ea ccbt 66
ea ccbt vp > 1 11 ea ccbt vp > 1 15 ea ccbt vp > 1 23 ea ccbt vp > 1 16 ea ccbt vp > 1 19 ea ccbt vp > 1 14 ea ccbt vp > 1 98
ea ccbt vp > 2 20 ea ccbt vp > 2 19 ea ccbt vp > 2 12 ea ccbt vp > 2 12 ea ccbt vp > 2 17 ea ccbt vp > 2 17 ea ccbt vp > 2 97
pf 3 pf 3 pf 17 pf 5 pf 24 pf 11 pf 63
pf vp > 1 7 pf vp > 1 13 pf vp > 1 19 pf vp > 1 11 pf vp > 1 23 pf vp > 1 9 pf vp > 1 82
pf vp > 2 8 pf vp > 2 17 pf vp > 2 21 pf vp > 2 23 pf vp > 2 16 pf vp > 2 16 pf vp > 2 101
pf ccbt 17 pf ccbt 22 pf ccbt 18 pf ccbt 3 pf ccbt 4 pf ccbt 8 pf ccbt 72
pf ccbt vp > 1 10 pf ccbt vp > 1 24 pf ccbt vp > 1 13 pf ccbt vp > 1 8 pf ccbt vp > 1 1 pf ccbt vp > 1 18 pf ccbt vp > 1 74
pf ccbt vp > 2 12 pf ccbt vp > 2 23 pf ccbt vp > 2 8 pf ccbt vp > 2 17 pf ccbt vp > 2 10 pf ccbt vp > 2 23 pf ccbt vp > 2 93
wa 2 wa 4 wa 10 wa 4 wa 18 wa 22 wa 60
wa vp > 1 5 wa vp > 1 20 wa vp > 1 14 wa vp > 1 22 wa vp > 1 20 wa vp > 1 19 wa vp > 1 100
wa vp > 2 13 wa vp > 2 10 wa vp > 2 15 wa vp > 2 24 wa vp > 2 22 wa vp > 2 13 wa vp > 2 97
wa ccbt 23 wa ccbt 11 wa ccbt 16 wa ccbt 19 wa ccbt 6 wa ccbt 1 wa ccbt 76
wa ccbt vp > 1 15 wa ccbt vp > 1 16 wa ccbt vp > 1 9 wa ccbt vp > 1 7 wa ccbt vp > 1 8 wa ccbt vp > 1 4 wa ccbt vp > 1 59
wa ccbt vp > 2 24 wa ccbt vp > 2 18 wa ccbt vp > 2 4 wa ccbt vp > 2 10 wa ccbt vp > 2 7 wa ccbt vp > 2 6 wa ccbt vp > 2 69

Sorted by means of frequency of profitability occurrence they are on display as follows:

PIVOT final sorting Points Normalized
pf vp > 2 101 56.11
ea vp > 2 100 55.56
wa vp > 1 100 55.56
ea ccbt vp > 1 98 54.44
ea ccbt vp > 2 97 53.89
wa vp > 2 97 53.89
avg ccbt vp > 2 96 53.33
pf ccbt vp > 2 93 51.67
ea vp > 1 84 46.67
avg vp > 2 82 45.56
pf vp > 1 82 45.56
wa ccbt 76 42.22
pf ccbt vp > 1 74 41.11
pf ccbt 72 40.00
wa ccbt vp > 2 69 38.33
ea ccbt 66 36.67
avg ccbt vp > 1 63 35.00
pf 63 35.00
wa 60 33.33
wa ccbt vp > 1 59 32.78
ea 53 29.44
avg vp > 1 50 27.78
avg ccbt 42 23.33
avg 23 12.78

AdSMA

The following tables display detailed returns’ data emerging through the implementation of the AdSMA trading system, while sorting procedure involves 24 d-Backtest PS methods.

W1 Points W2 Points W3 Points W4 Points W5 Points W6 Points Final sorting Points
avg 9 avg 4 avg 2 avg 18 avg 18 avg 7 avg 58
avg vp > 1 7 avg vp > 1 8 avg vp > 1 3 avg vp > 1 15 avg vp > 1 10 avg vp > 1 2 avg vp > 1 45
avg vp > 2 12 avg vp > 2 2 avg vp > 2 1 avg vp > 2 17 avg vp > 2 11 avg vp > 2 4 avg vp > 2 47
avg ccbt 11 avg ccbt 5 avg ccbt 5 avg ccbt 10 avg ccbt 1 avg ccbt 1 avg ccbt 33
avg ccbt vp > 1 3 avg ccbt vp > 1 3 avg ccbt vp > 1 12 avg ccbt vp > 1 11 avg ccbt vp > 1 7 avg ccbt vp > 1 14 avg ccbt vp > 1 50
avg ccbt vp > 2 15 avg ccbt vp > 2 1 avg ccbt vp > 2 11 avg ccbt vp > 2 16 avg ccbt vp > 2 16 avg ccbt vp > 2 19 avg ccbt vp > 2 78
ea 22 ea 6 ea 6 ea 12 ea 3 ea 20 ea 69
ea vp > 1 21 ea vp > 1 15 ea vp > 1 21 ea vp > 1 1 ea vp > 1 8 ea vp > 1 15 ea vp > 1 81
ea vp > 2 8 ea vp > 2 23 ea vp > 2 22 ea vp > 2 7 ea vp > 2 12 ea vp > 2 13 ea vp > 2 85
ea ccbt 14 ea ccbt 24 ea ccbt 23 ea ccbt 2 ea ccbt 2 ea ccbt 12 ea ccbt 77
ea ccbt vp > 1 19 ea ccbt vp > 1 22 ea ccbt vp > 1 24 ea ccbt vp > 1 5 ea ccbt vp > 1 17 ea ccbt vp > 1 3 ea ccbt vp > 1 90
ea ccbt vp > 2 24 ea ccbt vp > 2 16 ea ccbt vp > 2 20 ea ccbt vp > 2 14 ea ccbt vp > 2 15 ea ccbt vp > 2 11 ea ccbt vp > 2 100
pf 2 pf 14 pf 7 pf 23 pf 4 pf 21 pf 71
pf vp > 1 4 pf vp > 1 12 pf vp > 1 18 pf vp > 1 22 pf vp > 1 14 pf vp > 1 24 pf vp > 1 94
pf vp > 2 10 pf vp > 2 19 pf vp > 2 10 pf vp > 2 21 pf vp > 2 19 pf vp > 2 17 pf vp > 2 96
pf ccbt 5 pf ccbt 7 pf ccbt 19 pf ccbt 19 pf ccbt 13 pf ccbt 6 pf ccbt 69
pf ccbt vp > 1 1 pf ccbt vp > 1 10 pf ccbt vp > 1 9 pf ccbt vp > 1 20 pf ccbt vp > 1 20 pf ccbt vp > 1 22 pf ccbt vp > 1 82
pf ccbt vp > 2 6 pf ccbt vp > 2 9 pf ccbt vp > 2 14 pf ccbt vp > 2 24 pf ccbt vp > 2 24 pf ccbt vp > 2 23 pf ccbt vp > 2 100
wa 20 wa 11 wa 4 wa 13 wa 5 wa 16 wa 69
wa vp > 1 23 wa vp > 1 18 wa vp > 1 8 wa vp > 1 4 wa vp > 1 9 wa vp > 1 8 wa vp > 1 70
wa vp > 2 13 wa vp > 2 20 wa vp > 2 13 wa vp > 2 9 wa vp > 2 21 wa vp > 2 10 wa vp > 2 86
wa ccbt 16 wa ccbt 21 wa ccbt 16 wa ccbt 3 wa ccbt 6 wa ccbt 9 wa ccbt 71
wa ccbt vp > 1 18 wa ccbt vp > 1 17 wa ccbt vp > 1 17 wa ccbt vp > 1 6 wa ccbt vp > 1 23 wa ccbt vp > 1 5 wa ccbt vp > 1 86
wa ccbt vp > 2 17 wa ccbt vp > 2 13 wa ccbt vp > 2 15 wa ccbt vp > 2 8 wa ccbt vp > 2 22 wa ccbt vp > 2 18 wa ccbt vp > 2 93

Sorted by means of frequency of profitability occurrence they are on display as follows:

SMA final sorting Points Normalized
ea ccbt vp > 2 100 55.56
pf ccbt vp > 2 100 55.56
pf vp > 2 96 53.33
pf vp > 1 94 52.22
wa ccbt vp > 2 93 51.67
ea ccbt vp > 1 90 50.00
wa vp > 2 86 47.78
wa ccbt vp > 1 86 47.78
ea vp > 2 85 47.22
pf ccbt vp > 1 82 45.56
ea vp > 1 81 45.00
avg ccbt vp > 2 78 43.33
ea ccbt 77 42.78
pf 71 39.44
wa ccbt 71 39.44
wa vp > 1 70 38.89
ea 69 38.33
pf ccbt 69 38.33
wa 69 38.33
avg 58 32.22
avg ccbt vp > 1 50 27.78
avg vp > 2 47 26.11
avg vp > 1 45 25.00
avg ccbt 33 18.33

Appendix 5

AdMACD

The following tables expand on returns emerging through the implementation of the AdMACD trading system for the six verification periods.

Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 52.48 1102.1 0 39 49.37 12.83 2.74 19.02 880.29 − 595.59 3002.72 79 W1
EURUSD wa vp > 2 33.33 827.64 0 33 41.77 2.76 9.22 − 24.11 614.5 − 907.64 − 404.61 79 W1
GBPUSD wa vp > 2 67.64 1620.5 0 37 46.84 3.89 9.11 − 18.07 544 − 1427.82 72.83 79 W1
USDCAD wa vp > 2 41.35 745.23 0 47 59.49 16.25 5.17 9.06 425.13 − 390.44 2215.48 79 W1
USDJPY wa vp > 2 73.97 2201 0 33 41.77 2.88 0.58 − 17.08 352.08 − 330.35 150.51 79 W1
XAUUSD wa vp > 2 104.39 1347.91 0 43 54.43 3.44 6.08 3.65 644.12 − 1628.75 1788.27 79 W1
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 41.63 1102.1 0 29 36.71 12.83 2.74 − 50.74 583.92 − 687.76 − 2508.76 79 W2
EURUSD wa vp > 2 25.64 539.93 0 36 45.57 3.64 7.1 8.07 388.03 − 907.64 2137.39 79 W2
GBPUSD wa vp > 2 47.33 1086.09 0 36 45.57 3.89 7.86 − 36.49 538.69 − 1162.67 − 1382.73 79 W2
USDCAD wa vp > 2 51.87 745.23 0 44 55.7 2.9 4.44 20.27 652.42 − 383.78 3101.02 79 W2
USDJPY wa vp > 2 71.98 2201 0 41 51.9 4.9 0.49 0.22 280.76 − 238.59 1517.33 79 W2
XAUUSD wa vp > 2 81.9 1347.91 0 38 48.1 4.71 6.08 − 22.54 644.12 − 1628.75 − 280.29 79 W2
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 46.68 1102.1 0 36 45.57 12.83 4.8 − 25.47 630.36 − 687.76 − 512.36 79 W3
EURUSD wa vp > 2 17.29 513.08 0 33 41.77 2.35 9.44 − 17.68 614.5 − 907.64 103.5 79 W3
GBPUSD wa vp > 2 75.29 1620.5 0 41 51.9 3.89 6.33 0.59 550.48 − 1170.99 1546.71 79 W3
USDCAD wa vp > 2 53.32 764.37 0 44 55.7 2.9 4.44 8.9 652.42 − 383.78 2202.78 79 W3
USDJPY wa vp > 2 81.69 2201 0 41 51.9 4.9 0.61 − 5.3 352.08 − 266.49 1081.51 79 W3
XAUUSD wa vp > 2 54.26 1439.91 0 36 45.57 4.71 6.08 − 24.1 644.12 − 1241.43 − 403.99 79 W3
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 36.95 1102.1 0 35 44.3 12.83 4.8 − 19.76 630.36 − 499.21 − 61.13 79 W4
EURUSD wa vp > 2 19.94 827.64 0 40 50.63 2.35 6.69 − 13.61 385.11 − 907.64 424.84 79 W4
GBPUSD wa vp > 2 44.09 1620.5 0 36 45.57 2.22 9.78 − 45.25 527.15 − 1502.01 − 2075.13 79 W4
USDCAD wa vp > 2 48.71 745.23 0 42 53.16 2.9 5.06 14.18 679.18 − 396.48 2620.25 79 W4
USDJPY wa vp > 2 81.27 2201 0 38 48.1 8.4 0.61 − 4.76 391.13 − 342.86 1124.34 79 W4
XAUUSD wa vp > 2 70.68 1347.91 0 37 46.84 4.71 6.08 − 19.65 644.12 − 1241.43 − 52.47 79 W4
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 17.66 883.11 0 32 40.51 12.83 4.89 − 35.61 880.29 − 499.21 − 313.5 79 W5
EURUSD wa vp > 2 11.42 539.93 0 36 45.57 3.64 6.86 − 13.79 634.47 − 907.64 410.23 79 W5
GBPUSD wa vp > 2 60.2 1620.5 0 38 48.1 3.28 9.78 − 12.83 538.69 − 1162.67 486.78 79 W5
USDCAD wa vp > 2 59.45 764.37 0 43 54.43 2.56 5.06 31.09 679.18 − 314.82 3955.84 79 W5
USDJPY wa vp > 2 87.76 2201 0 42 53.16 3.39 0.61 − 2.96 352.08 − 342.86 1265.88 79 W5
XAUUSD wa vp > 2 87.11 1347.91 0 40 50.63 1.63 6.08 − 17.13 644.12 − 952.6 146.75 79 W5
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 34.55 1102.1 0 31 39.24 12.83 4.8 − 39.28 925.74 − 637.36 − 1603.44 79 W6
EURUSD wa vp > 2 13.38 492.93 0 32 40.51 3.18 7.52 − 38.3 634.47 − 907.64 − 1525.33 79 W6
GBPUSD wa vp > 2 56.26 1620.5 0 36 45.57 2.53 9.18 − 15.15 538.69 − 1162.67 302.76 79 W6
USDCAD wa vp > 2 58.93 764.37 0 43 54.43 2.9 5.06 26.64 703.42 − 357.84 3604.71 79 W6
USDJPY wa vp > 2 57.48 990 0 32 40.51 4.35 0.61 − 0.87 450.7 − 332.53 1431.17 79 W6
XAUUSD wa vp > 2 79.96 1439.91 0 44 55.7 1.63 6.08 16.45 644.12 − 952.6 2799.81 79 W6

AdPIVOT

The following tables expand on returns emerging through the implementation of the AdPIVOT trading system for the six verification periods.

Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 82.49 1372.13 0 59 44.7 25.11 4.87 − 21.11 767.83 − 580.75 − 2786.13 132 1 week
EURUSD wa vp > 2 88.4 1656.81 0 59 44.7 4.56 8.54 − 34.26 597.12 − 689.62 − 4522.64 132 1 week
GBPUSD wa vp > 2 115.26 2391.03 0 56 42.42 1.7 0 − 27.19 717.01 − 525.54 − 3589.3 132 1 week
USDCAD wa vp > 2 89.01 1237.6 0 64 48.48 5.8 0 − 24.79 494.64 − 612.34 − 3272.6 132 1 week
USDJPY wa vp > 2 110.19 1603.95 0 62 46.97 15.38 7.38 − 23.4 1104.06 − 1162.57 − 3088.18 132 1 week
XAUUSD wa vp > 2 263.46 3173.82 0 58 43.94 1.91 11.09 − 10.76 1078.76 − 867.49 − 1420.57 132 1 week
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 67.33 1372.13 0 49 37.12 25.11 9.44 − 61.41 796.95 − 576.59 − 8106.67 132 2 weeks
EURUSD wa vp > 2 110.62 1656.81 0 61 46.21 4.56 8.37 − 20.07 597.12 − 623.28 − 2649.48 132 2 weeks
GBPUSD wa vp > 2 110.71 2391.03 0 56 42.42 1.7 0 − 22.75 717.01 − 525.54 − 3003.34 132 2 weeks
USDCAD wa vp > 2 69.99 898.13 0 58 43.94 12.61 0 − 43.19 358.85 − 612.34 − 5701.62 132 2 weeks
USDJPY wa vp > 2 105.79 1603.95 0 60 45.45 20.94 7.38 − 21.21 735.11 − 1162.57 − 2800.13 132 2 weeks
XAUUSD wa vp > 2 278.71 3173.82 0 62 46.97 4.74 9.39 0.49 1078.76 − 867.49 64.24 132 2 weeks
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 85.68 1372.13 0 53 40.15 15.32 9.24 − 50.12 796.95 − 617.87 − 6616.23 132 3 weeks
EURUSD wa vp > 2 105.97 1656.81 0 56 42.42 4.56 8.54 − 11.86 701.14 − 716.47 − 1565.81 132 3 weeks
GBPUSD wa vp > 2 140.58 2513.98 0 55 41.67 1.89 0 − 19.1 1457.53 − 525.54 − 2521.42 132 3 weeks
USDCAD wa vp > 2 107.34 1237.6 0 63 47.73 12.61 0 − 12.92 494.64 − 612.34 − 1705.3 132 3 weeks
USDJPY wa vp > 2 106.59 1603.95 0 63 47.73 20.94 7.38 − 20.5 735.11 − 1162.57 − 2706.32 132 3 weeks
XAUUSD wa vp > 2 268.91 3173.82 0 57 43.18 4.74 11.09 − 11.59 1078.76 − 867.49 − 1529.57 132 3 weeks
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 98.64 1372.13 0 51 38.64 25.11 9.24 − 36.22 796.95 − 617.87 − 4780.61 132 4 weeks
EURUSD wa vp > 2 88.51 1656.81 0 51 38.64 4.56 8.54 − 31.86 701.14 − 716.47 − 4205.74 132 4 weeks
GBPUSD wa vp > 2 112.66 2391.03 0 57 43.18 1.7 0 − 20.19 761.81 − 525.54 − 2665.16 132 4 weeks
USDCAD wa vp > 2 115.77 1237.6 0 66 50 12.61 0 2.27 494.64 − 525.78 299.69 132 4 weeks
USDJPY wa vp > 2 75.61 1603.95 0 59 44.7 20.94 7.38 − 8.98 735.11 − 1162.57 − 1185.21 132 4 weeks
XAUUSD wa vp > 2 251.54 3173.82 0 60 45.45 4.74 9.39 − 6.18 1078.76 − 867.49 − 815.25 132 4 weeks
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 98.09 1372.13 0 53 40.15 9.32 9.24 − 45.19 796.95 − 617.87 − 5964.52 132 5 weeks
EURUSD wa vp > 2 100.31 1647.81 0 61 46.21 4.56 8.54 − 19.81 701.14 − 716.47 − 2614.41 132 5 weeks
GBPUSD wa vp > 2 110.94 2391.03 0 55 41.67 1.35 0 − 24.24 761.81 − 525.54 − 3199.5 132 5 weeks
USDCAD wa vp > 2 115.99 1237.6 0 65 49.24 12.61 0 − 11.43 494.64 − 525.78 − 1509.35 132 5 weeks
USDJPY wa vp > 2 118.15 1603.95 0 56 42.42 20.94 7.38 − 10.75 735.11 − 1276.02 − 1418.47 132 5 weeks
XAUUSD wa vp > 2 237.39 3173.82 0 62 46.97 4.74 11.09 3.45 1140.33 − 867.49 455.64 132 5 weeks
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2015.02.22–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 72.82 1372.13 0 50 37.88 1.58 9.24 − 67.62 767.83 − 617.87 − 8926.21 132 6 weeks
EURUSD wa vp > 2 109.71 1656.81 0 58 43.94 4.56 8.54 − 26.49 701.14 − 716.47 − 3496.24 132 6 weeks
GBPUSD wa vp > 2 114.32 2391.03 0 56 42.42 5.18 0 − 20.71 761.81 − 525.54 − 2733.88 132 6 weeks
USDCAD wa vp > 2 115.54 1237.6 0 67 50.76 12.61 0 − 6.51 494.64 − 543.58 − 858.88 132 6 weeks
USDJPY wa vp > 2 88.26 1603.95 0 54 40.91 17.77 10.6 − 41.03 641.18 − 1276.02 − 5415.52 132 6 weeks
XAUUSD wa vp > 2 276.51 3173.82 0 61 46.21 4.74 11.09 13.58 1078.76 − 867.49 1792.94 132 6 weeks

AdSMA

The following tables expand on returns emerging through the implementation of the AdSMA trading system, for the six verification periods.

Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 66.42 1372.13 0 54 40.91 25.11 4.87 − 37.79 767.83 − 568.92 − 4988.36 132 1 week
EURUSD wa vp > 2 95.12 1656.81 0 61 46.21 2.42 8.54 − 30.72 596.09 − 550.55 − 4054.69 132 1 week
GBPUSD wa vp > 2 113.05 2391.03 0 55 41.67 6.01 7.87 − 38.13 717.01 − 522.71 − 5033.62 132 1 week
USDCAD wa vp > 2 95.59 1124.05 0 54 40.91 5.8 6.87 − 26.25 461.55 − 690.66 − 3464.66 132 1 week
USDJPY wa vp > 2 118.71 1603.95 0 52 39.39 17.77 7.38 − 23.81 735.11 − 1276.02 − 3142.76 132 1 week
XAUUSD wa vp > 2 235.4 3061.57 0 61 46.21 1.29 2.79 − 29.91 987.86 − 791.04 − 3948.44 132 1 week
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 74.17 1372.13 0 55 41.67 25.11 9.24 − 32.53 767.83 − 577.98 − 4293.32 132 2 weeks
EURUSD wa vp > 2 75.29 1656.81 0 61 46.21 4.44 9.57 − 30.68 596.09 − 514.48 − 4049.66 132 2 weeks
GBPUSD wa vp > 2 147.73 2391.03 0 63 47.73 6.01 8.22 − 9.34 857.99 − 509.9 − 1232.97 132 2 weeks
USDCAD wa vp > 2 116.97 1237.6 0 61 46.21 4.19 7.36 − 15.48 494.64 − 690.66 − 2043.6 132 2 weeks
USDJPY wa vp > 2 134.51 1603.95 0 57 43.18 17.84 7.38 − 15.18 735.11 − 647.62 − 2003.45 132 2 weeks
XAUUSD wa vp > 2 239.79 3169.06 0 55 41.67 1.29 2.79 − 37.39 1077.14 − 812.79 − 4934.89 132 2 weeks
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 75.82 1372.13 0 55 41.67 25.11 9.24 − 41.35 949.56 − 582.82 − 5458.09 132 3 weeks
EURUSD wa vp > 2 76.28 1348.64 0 56 42.42 2.74 9.55 − 18.99 561.13 − 550.55 − 2506.13 132 3 weeks
GBPUSD wa vp > 2 125.24 2513.98 0 58 43.94 6.01 7.87 − 16.62 1457.53 − 504.92 − 2194.28 132 3 weeks
USDCAD wa vp > 2 117.38 1237.6 0 55 41.67 12.61 7.36 − 29.91 494.64 − 690.66 − 3948.16 132 3 weeks
USDJPY wa vp > 2 141.01 1603.95 0 57 43.18 17.84 7.38 − 13.62 735.11 − 623.73 − 1797.72 132 3 weeks
XAUUSD wa vp > 2 239.76 3169.06 0 59 44.7 1.59 2.79 − 36.04 1077.14 − 863.66 − 4756.7 132 3 weeks
Symbol d-BackTest PS method Avg (PF) Max PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 66.44 1372.13 0 55 41.67 9.02 4.87 − 40.2 767.83 − 651.05 − 5306.6 132 4 weeks
EURUSD wa vp > 2 74.42 1656.81 0 54 40.91 2.74 9.57 − 29.14 701.14 − 550.55 − 3846.69 132 4 weeks
GBPUSD wa vp > 2 115.48 2513.98 0 55 41.67 2.31 7.87 − 37.78 1457.53 − 622.19 − 4987.4 132 4 weeks
USDCAD wa vp > 2 130.97 1237.6 0 58 43.94 4.19 7.36 − 35.58 494.64 − 690.66 − 4696.45 132 4 weeks
USDJPY   123.39 1603.95 0 53 40.15 17.84 7.38 − 23.83 702.99 − 1162.57 − 3146.21 132 4 weeks
XAUUSD wa vp > 2 253.99 3169.06 0 53 40.15 0.72 2.79 − 46.31 1077.14 − 812.79 − 6112.68 132 4 weeks
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 70.24 1372.13 0 51 38.64 9.02 4.87 − 48.6 767.83 − 519.48 − 6415.7 132 5 weeks
EURUSD wa vp > 2 93.3 1656.81 0 55 41.67 2.74 8.54 − 19.28 701.14 − 550.55 − 2544.76 132 5 weeks
GBPUSD wa vp > 2 133.01 2513.98 0 58 43.94 2.31 7.87 − 17.97 1457.53 − 428.03 − 2371.56 132 5 weeks
USDCAD wa vp > 2 131.96 1237.6 0 63 47.73 4.19 7.36 − 20.51 494.64 − 690.66 − 2707.59 132 5 weeks
USDJPY wa vp > 2 108.75 1560.6 0 56 42.42 17.84 7.38 − 22.15 702.99 − 1162.57 − 2923.99 132 5 weeks
XAUUSD wa vp > 2 204.14 2745.06 0 50 37.88 0.76 2.79 − 64.08 987.86 − 687.42 − 8458.48 132 5 weeks
Symbol d-BackTest PS method Avg (PF) Max (PF) Min (PF) PF > 1 % PF > 1 Max (SharpeRatio) Min (DD) Avg (Profit) Max (Profit) Min (Profit) Sum (Profit) Weeks (2016.02.28–2017.08.27) Verification period (VP)
AUDUSD wa vp > 2 56.62 1169 0 52 39.39 1.91 9.24 − 68.08 654.08 − 651.05 − 8986.1 132 6 weeks
EURUSD wa vp > 2 86.38 1656.81 0 55 41.67 1.88 8.54 − 24.91 701.14 − 522.92 − 3287.76 132 6 weeks
GBPUSD wa vp > 2 140.03 2513.98 0 57 43.18 1.7 7.87 − 29.17 1457.53 − 458.47 − 3849.8 132 6 weeks
USDCAD wa vp > 2 109.66 1124.05 0 64 48.48 4.19 7.36 − 25.42 461.55 − 690.66 − 3355.62 132 6 weeks
USDJPY wa vp > 2 122.7 1603.95 0 61 46.21 17.84 7.38 − 15.28 702.99 − 1162.57 − 2017.34 132 6 weeks
XAUUSD wa vp > 2 247.01 3169.06 0 55 41.67 0.96 2.79 − 26.91 1077.14 − 678.56 − 3552.11 132 6 weeks

Appendix 6

Implementation of the Lag Method

figurex

Implementation of Different Verification Periods

figurey

Implementation of Different Neighbourhood Check

figurez

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Vezeris, D.T., Schinas, C.J., Kyrgos, T.S. et al. Optimization of Backtesting Techniques in Automated High Frequency Trading Systems Using the d-Backtest PS Method. Comput Econ 56, 975–1054 (2020). https://doi.org/10.1007/s10614-019-09956-1

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Keywords

  • d-Backtest PS method
  • Optimal historical data period selection
  • Backtesting optimization algorithms
  • Expert backtesting systems
  • MACD
  • SMA
  • PIVOT
  • Forex
  • Exchange rates (AUDUSD, EURUSD, GBPUSD, USDCAD, USDJPY)
  • Metals (XAUUSD)