# Double Top: A Reversal Pattern. Checking the History

04 march 2022 126 4

In the proposed article, we will talk about paired patterns of graphical analysis “Double Top” and “Double Bottom”.

Jack Schwager characterises in his book «Technical Analysis. Full Course» these patterns the following way:

“Double tops and double bottoms are exactly what their names imply. Of course, the two tops (or bottoms) that make up the pattern need not be exactly the same, only in the same general price vicinity. Double tops and bottoms that materialize after large price moves should be viewed as strong indicators of a major trend reversal”.

Hypothesis

The formation of «Double top» and «Double bottom» indicates a trend reversal.

﻿﻿﻿﻿﻿﻿﻿﻿﻿﻿﻿﻿﻿﻿Double top reminds the «М» letter on charts as it includes two consequent peaks of almost the same price level with a correction between them.

﻿Double bottom reminds the «W» letter:

Method of event measurement

We will use the ZigZag indicator in our study to measure tops and bottoms on charts with materialization of the considered patterns.

ZigZag is a trend indicator that is why it shows the lines on the chart connecting local minimums and maximums which delineate the trend’s direction. This indicator includes three parameters. It determines the performance of ZigZag and which minimums and maximums it will take into account. Changes in parameters influence the sensibility rate of the indicator to the price movement. If we increase the values for a calculation, the number of local minimums and maximums will decrease respectively the least number of lines will be displayed, and theoretically less patterns will be materialized but larger in size (price movements are also being enlarged).

For the research, we will take ZigZag with parameters of 5.3.3 (small patterns will be materialized), and with parameters of 12.5.3 (major patterns will be materialized). The second group of parameters is set in the ZigZag indicator by default.

“Double top”: a sell signal

ZigZag [0] < ZigZag [1]

ZigZag [0] < ZigZag [2]

ZigZag [2] < ZigZag [1]

ZigZag [3] > ZigZag [2]

Close [i] < ZigZag [2]

W <= WMAX

ZigZag [0] > ZigZag [1]

ZigZag [0] > ZigZag [2]

ZigZag [2] > ZigZag [1]

ZigZag [3] < ZigZag [2]

Close [i] > ZigZag [2]

W <= WMAX

Besides, we will carry out the test against patterns in two combinations regulating a notional parameter:

W, Distality of Tops/Bottoms.

Distality W in % must not raise the threshold value of WMax:

= ( Max( ZZ[1], ZZ[3] ) - Min( ZZ[1], ZZ[3] ) ) /

( Max ( Max ( ZZ[1], ZZ[3] ), ZZ[2] ) – Min ( Min ( ZZ[1], ZZ[3] ), ZZ[2] ) ) * 100

Let us show the “Double top” pattern with the W parameter indicated above:

What does the W notional parameter show?

The less W is, the closer the prices of tops and bottoms, and the more explicit the “Double top” formation.

For the “Double bottom”, the situation is mirrored.

Now, we specify conditions of the opening and closing of a trading position.

After the pattern’s materialization, a position opens at the open of the next bar:

• Double top: a sell;

Closing a position:

The lifetime of the position is set at 5, 10 ,or 15 in all bars.

Let us carry out the test on a large amount of historical data of various financial instruments and on the basis of two timeframes against signals which are generated by the “Double top” and “Double bottom” patterns.

Data used

Let us specify the list of financial instruments and their timeframes against which we will carry out the test of trading signals:

• 25 currency pairs (Forex);
• 6 commodity futures (Commodities);
• 2 US stock indices (US indices);
• 30 US stocks (US stocks);
• 58 RF stocks (RF stocks);
• 1 RF stock index (RF index).

Timeframes used:

• H1 (1 hour): the history for the period of 5 years,
• D1 (1 day): the history for the period of 10 years.

The total is 1 981 114 values.

Having specified all the conditions and set necessary parameters, we can start testing!

#### Analysis of the results

First, we will estimate the results based on the sample size.

Small patterns (ZigZag (5.3.3)):

W <= 5%

For the 1-hour timeframe (H1):

 Market segment Number of candlesticks Number of events Forex 655777 1634 Commodities 115959 224 US indices 52783 107 RF index 11421 26 US stocks 234556 591 RF stocks 612555 1582 Total 1683051 4164

For the 1-day timeframe (D1):

 Market segment Number of candlesticks Number of events Forex 67432 199 Commodities 15463 41 US indices 5455 15 RF index 2519 6 US stocks 72925 209 RF stocks 134269 355 Total 298063 825

W <= 10%

For the 1-hour timeframe (H1):

 Market segment Number of candlesticks Number of events Forex 655777 3467 Commodities 115959 455 US indices 52783 219 RF index 11421 53 US stocks 234556 1243 RF stocks 612555 3045 Total 1683051 8482

For the 1-day timeframe (D1):

 Market segment Number of candlesticks Number of events Forex 67432 403 Commodities 15463 98 US indices 5455 33 RF index 2519 10 US stocks 72925 442 RF stocks 134269 792 Total 298063 1778

Major patterns (ZigZag (12.5.3)):

W <= 5%

For the 1-hour timeframe (H1):

 Market segment Number of candlesticks Number of events Forex 655777 826 Commodities 115959 115 US indices 52783 68 RF index 11421 11 US stocks 234556 324 RF stocks 612555 704 Total 1683051 2048

For the 1-day timeframe (D1):

 Market segment Number of candlesticks Number of events Forex 67432 94 Commodities 15463 22 US indices 5455 9 RF index 2519 5 US stocks 72925 88 RF stocks 134269 133 Total 298063 351

W <=10%

For the 1-hour timeframe (H1):

 Market segment Number of candlesticks Number of events Forex 655777 1691 Commodities 115959 260 US indices 52783 148 RF index 11421 19 US stocks 234556 675 RF stocks 612555 1419 Total 1683051 4212

For the 1-day timeframe (D1):

 Market segment Number of candlesticks Number of events Forex 67432 183 Commodities 15463 41 US indices 5455 19 RF index 2519 5 US stocks 72925 190 RF stocks 134269 315 Total 298063 753

The total number of candlesticks and events:

 Event Number of candlesticks Number of events Small patterns W <= 5% 1981114 4989 W <= 10% 1981114 10260 Major patterns W <= 5% 1981114 2399 W <= 10% 1981114 4965

Then, we will measure the share of Tops and Bottoms in % in the total number of initial candlesticks on the basis of timeframes:

Small patterns (ZigZag (5.3.3)):

For the 1-hour timeframe (H1):

 Parameters of Tops/Bottoms Forex Commodities US indices RF index US stocks RF stocks W <= 5 % 0.25 0.19 0.20 0.23 0.26 0.26 W <= 10 % 0.53 0.39 0.41 0.46 0.53 0.50

For the 1-day timeframe (D1):

 Parameters of Tops/Bottoms Forex Commodities US indices RF index US stocks RF stocks W <= 5 % 0.30 0.27 0.27 0.24 0.29 0.26 W <= 10 % 0.60 0.63 0.60 0.40 0.61 0.59

Major patterns (ZigZag (12.5.3)):

For the 1-hour timeframe (H1):

 Parameters of Tops/Bottoms Forex Commodities US indices RF index US stocks RF stocks W <= 5 % 0.13 0.10 0.13 0.10 0.14 0.11 W <= 10 % 0.26 0.22 0.28 0.17 0.29 0.23

For the 1-day timeframe (D1):

 Parameters of Tops/Bottoms Forex Commodities US indices RF index US stocks RF stocks W <= 5 % 0.14 0.14 0.16 0.20 0.12 0.10 W <= 10 % 0.27 0.27 0.35 0.20 0.26 0.23

Let us note that the more explicit the patterns are and the larger the figures, the less their share in the total number of candlesticks and the less likely they can appear on charts.

Now, we will view the results of the performance of trading signals obtained as a result of materialized Tops and Bottoms.

We will assess the results with the two following criteria:

• Momentum (m) reflects the average change in quotes of financial instruments at the moment of closing a position, in %. A positive value of the momentum indicates profitability of the signal performance, a negative value indicates loss-making.
• SPP, the share of profitable positions, %.

We take the following notations:

«H1 / 5», closing a position at the 5th candlestick over the 1-hour timeframe;

«H1 / 10», closing a position at the 10th candlestick over the 1-hour timeframe;

«H1 / 15», closing a position at the 15th candlestick over the 1-hour timeframe;

«D1 / 5», closing a position at the 15th candlestick over the 1-day timeframe;

«D1 / 10», closing a position at the 10th candlestick over the 1-day timeframe;

«D1 / 15», closing a position at the 15th candlestick over the 1-day timeframe;

W, distality of Tops/ Bottoms, %;

Volatility coefficient:

• For the daily timeframe: a ratio between the average volatility of 5 candlesticks after the opening of a position and the average volatility of 20 candlesticks preceding the opening a position.
• For the 1-hour timeframe: a ratio between the average volatility of 5 candlesticks after the opening of a position and the average volatility of the same hours during the following 4 days.

If the value of volatility coefficient is more than 1, it indicates a greater volatility after the signal in comparison with volatility before the signal, if the value is less than 1, it is the opposite.

Small patterns (ZigZag (5.3.3)):

The Number of Tops/Bottoms, the Momentum in %, and the Share of profitable positions, and Volatility coefficient on a term-to-term basis of the hold of positions, timeframes, and market segments with distality of Tops/Bottoms at most 5%

 W<=5% Indicator Forex Commodities US indices RF index US stocks RF stocks All Н1/5 Number of signals 1634 224 107 26 591 1582 4164 Momentum 0.011 -0.042 0.007 0.159 0.073 -0.028 0.006 SPP 50.7 53.0 50.5 53.9 50.3 42.9 47.0 Volatility coefficient 1.00 0.98 1.04 0.94 1.05 1.17 1.09 Н1/10 Number of signals 1634 223 107 26 591 1580 4161 Momentum 0.000 0.033 0.008 0.313 0.007 0.012 0.012 SPP 50.3 57.2 52.3 65.4 48.3 44.6 47.6 Volatility coefficient 1.00 0.98 1.04 0.94 1.05 1.17 1.09 Н1/15 Number of signals 1632 223 107 26 591 1578 4157 Momentum -0.001 0.089 0.031 0.365 -0.059 -0.047 -0.029 SPP 50.0 60.8 51.4 61.5 47.1 45.5 47.8 Volatility coefficient 1.00 0.98 1.04 0.94 1.05 1.17 1.09

 W<=5% Indicator Forex Commodities US indices RF index US stocks RF stocks All D1/5 Number of signals 199 41 15 6 209 355 825 Momentum -0.003 -0.039 0.472 -0.810 -0.095 0.632 0.276 SPP 47.1 38.4 55.0 33.3 49.3 46.0 46.7 Volatility coefficient 1.03 1.06 1.30 0.74 1.08 1.24 1.14 D1/10 Number of signals 199 41 15 6 208 355 824 Momentum 0.024 0.604 0.265 0.528 -0.184 0.877 0.415 SPP 50.4 56.0 60.0 33.3 47.9 51.7 50.7 Volatility coefficient 1.03 1.06 1.30 0.74 1.08 1.24 1.14 D1/15 Number of signals 197 41 15 6 208 354 821 Momentum 0.145 0.602 0.221 0.116 -1.025 0.710 0.149 SPP 52.1 51.5 50.0 50.0 44.9 49.9 49.2 Volatility coefficient 1.03 1.06 1.30 0.74 1.08 1.24 1.14

The Number of Tops/Bottoms, the Momentum in %, and the Share of profitable positions, and Volatility coefficient on a term-to-term basis of the hold of positions, timeframes, and market segments with distality of Tops/Bottoms at most 10%

 W<=10% Indicator Forex Commodities US indices RF index US stocks RF stocks All Н1/5 Number of signals 3467 455 219 53 1243 3045 8482 Momentum 0.007 0.072 -0.045 0.197 0.050 -0.032 0.003 SPP 49.9 53.1 45.2 60.4 50.3 44.9 47.8 Volatility coefficient 1.01 0.99 1.05 1.00 1.07 1.17 1.10 Н1/10 Number of signals 3467 454 219 53 1243 3042 8478 Momentum -0.006 0.126 -0.049 0.462 -0.020 0.022 0.013 SPP 49.7 55.5 47.5 66.0 48.6 45.1 47.6 Volatility coefficient 1.01 0.99 1.05 1.00 1.07 1.17 1.10 Н1/15 Number of signals 3464 454 219 53 1242 3040 8472 Momentum -0.007 0.237 -0.003 0.442 -0.128 -0,047 -0.040 SPP 50.4 57.5 47.0 64.2 47.1 45.6 47.7 Volatility coefficient 1.01 0.99 1.05 1.00 1.07 1.17 1.10

 W<=10% Indicator Forex Commodities US indices RF index US stocks RF stocks All D1/5 Number of signals 403 98 33 10 442 792 1778 Momentum 0.050 -0.133 0.656 -0.137 -0.061 0.354 0.167 SPP 48.3 45.0 54.9 40.0 48.6 48.1 48.2 Volatility coefficient 1.06 1.01 1.20 0.93 1.07 1.24 1.14 D1/10 Number of signals 402 98 33 10 441 791 1775 Momentum 0.089 0.406 0.795 1.916 -0.304 0.191 0.083 SPP 53.8 53.8 55.8 60.0 45.7 47.6 48.9 Volatility coefficient 1.06 1.01 1.20 0.93 1.07 1.24 1.14 D1/15 Number of signals 400 98 33 10 441 788 1770 Momentum 0.185 0.528 1.009 1.201 -0.580 0.072 -0.018 SPP 52.6 50.6 61.1 60.0 46.8 47.5 48.8 Volatility coefficient 1.06 1.01 1.20 0.93 1.07 1.23 1.14

Major patterns (ZigZag (12.5.3)):

The Number of Tops/Bottoms, the Momentum in %, and the Share of profitable positions, and Volatility coefficient on a term-to-term basis of the hold of positions, timeframes, and market segments with distality of Tops/Bottoms at most 5%

 W<=5% Indicator Forex Commodities US indices RF index US stocks RF stocks All Н1/5 Number of signals 826 115 68 11 324 704 2048 Momentum 0.012 0.012 -0.007 -0.149 0.001 -0.048 -0.021 SPP 48.7 62.2 53.0 36.4 48.3 45.0 47.5 Volatility coefficient 1.07 0.98 0.99 1.15 1.15 1.43 1.26 Н1/10 Number of signals 826 115 68 11 324 703 2047 Momentum 0.013 -0.090 0.044 -0.152 -0.017 0.100 0.041 SPP 47.9 64.2 51.3 36.4 48.9 46.7 48.3 Volatility coefficient 1.07 0.98 0.99 1.15 1.15 1.43 1.26 Н1/15 Number of signals 825 115 68 11 324 703 2046 Momentum 0.002 -0.205 0.088 -0.121 0.025 0.140 0.064 SPP 50.0 59.6 56.3 54.6 50.0 47.9 49.6 Volatility coefficient 1.07 0.98 0.99 1.15 1.15 1.43 1.26

 W<=5% Indicator Forex Commodities US indices RF index US stocks RF stocks All D1/5 Number of signals 94 22 9 5 88 133 351 Momentum 0.281 0.313 -0.939 -0.020 -0.405 0.978 0.396 SPP 58.1 55.8 33.3 60.0 40.9 52.9 50.9 Volatility coefficient 1.12 1.10 1.11 0.84 1.07 1.27 1.17 D1/10 Number of signals 93 22 9 5 88 133 350 Momentum 0.518 0.163 -0.375 0.319 0.168 0.864 0.546 SPP 64.5 63.3 50.0 60.0 45.7 53.7 54.6 Volatility coefficient 1.12 1.10 1.11 0.84 1.07 1.27 1.17 D1/15 Number of signals 93 22 9 5 88 132 349 Momentum 0.532 -0.774 -0.482 0.145 -0.412 0.604 0.233 SPP 58.9 37.8 58.3 60.0 47.7 57.5 54.3 Volatility coefficient 1.12 1.10 1.11 0.84 1.07 1.26 1.17

The Number of Tops/Bottoms, the Momentum in %, and the Share of profitable positions, and Volatility coefficient on a term-to-term basis of the hold of positions, timeframes, and market segments with distality of Tops/Bottoms at most 10%

 W<=10% Indicator Forex Commodities US indices RF index US stocks RF stocks All Н1/5 Number of signals 1691 260 148 19 675 1419 4212 Momentum 0.022 0.097 -0.015 0.324 0.005 0.006 0.016 SPP 51.2 55.2 46.6 52.6 50.6 44.1 47.8 Volatility coefficient 1.08 1.01 0.99 1.40 1.16 1.41 1.25 Н1/10 Number of signals 1691 260 148 19 675 1418 4211 Momentum 0.017 0.108 -0.016 0.156 -0.013 0.075 0.043 SPP 51.1 58.4 47.9 42.1 46.7 44.9 47.3 Volatility coefficient 1.08 1.01 0.99 1.40 1.16 1.41 1.25 Н1/15 Number of signals 1689 260 148 19 675 1418 4209 Momentum 0.014 0.083 0.010 -0.368 -0.036 0.127 0.056 SPP 51.3 55.5 48.2 52.6 47.6 44.8 47.5 Volatility coefficient 1.08 1.01 0.99 1.40 1.16 1.41 1.25

 W<=10% Indicator Forex Commodities US indices RF index US stocks RF stocks All D1/5 Number of signals Commodities 41 19 5 190 315 753 Momentum US indices 0.537 -0.153 -0.020 -0.413 0.205 0.056 SPP RF index 55.8 46.7 60.0 45.2 50.0 50.4 Volatility coefficient US stocks 1.09 1.20 0.84 1.07 1.32 1.20 D1/10 Number of signals RF stocks 40 19 5 190 315 751 Momentum 0.357 0.368 0.452 0.319 -0.144 0.363 0.239 SPP 60.6 57.5 52.2 60.0 44.8 49.5 51.1 Volatility coefficient 1.10 1.08 1.20 0.84 1.07 1.32 1.20 D1/15 Number of signals 182 40 19 5 190 313 749 Momentum 0.417 -0.496 0.226 0.145 -0.119 0.428 0.240 SPP 57.1 44.6 58.3 60.0 51.3 52.7 53.0 Volatility coefficient 1.10 1.08 1.20 0.84 1.07 1.31 1.20

Let us summarize the obtained results using the following diagrams:

Small patterns (ZigZag (5.3.3)):

Major patterns (ZigZag (12.5.3)):

Conclusion

Momentums

The highest momentum is both for small (0.415%) and for major (0.546%) patterns shown by signals of Tops and Bottoms over the daily timeframe with the distance of Tops/Bottoms no more than 5% and with fixating a position at the 10th candlestick.

Momentums of well-pronounced patterns of “Double top” and “Double bottom” raise minimum significant values by 0.3% with the module for the daily timeframe.

The minimum value of the momentum of 0.15% with the module has not been reached over the hourly timeframe.

SPP

The share of profitable positions of signals of the 1-hour timeframe vary between 47.0% and 49.6%, signals of the daily timeframe vary between 46.7% and 54.6%.

Volatility

The volatility raises by 5% after the signal in comparison with volatility before the signal for all timeframes and parameters of patterns.

The use of patterns of “Double top” and “Double bottom” in the market forecasting over the daily timeframe has been identified.

Detailed results are shown in the Appendix:

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