Model’s description

Firstly, I whish to remark that the different Technical tools named in this work, were used to make diagnostics about the probable price behavior, find the triggers (sell price and buy price), and to calculate the stop loss, and the price target, every day since more than a year.

Well now, to develop this work as objective as possible, and get rid of all subjective coming from trader criteria, in order to apply the concepts developed above, we use a simple Microsoft Excel model, where we try to find, in historical data the accomplish of this system objectives.

The population defined for each currency pair under study, could be seen in the following tables:

- EURUSD:


- CHFUSD:


- GBPUSD:


- YENUSD:


Step 1

Using Metatrader trading platform, V 4.00, we are able to see the currencies prices in real time. This system allows us to see the different quotation charts of all majors currencies in Forex and besides, the quotation of NYSE most important stocks, and gold.

This application not only let us see real time quotation, but also keeps historical record of each pair in it’s different time frames.

We proceed to isolate a significant number of records (sessions) in a continuous time series: date (and hour, in the case of 4 hours sessions) maximum price of the session (HIGH), minimum price (LOW), opening price (OPEN) and close price (CLOSE or LAST PRICE).

Ex.: EUR/USD, Dialy


Then we proceed to apply the Zigzag oscillator in the chart, in order to identify the bullish or bearish rallies, their end and duration for each studied session. In the case of bullish rallies, we take the minimum price of the session (low) as start, and the maximum (high) as the end. This last one, becomes the next bearish rally beginning.

To explain the graph analysis, we choose a random set of time for EURUSD quotation, and applied the ZigZag oscillator.

In the following chart of a week session (Chart 4) you can see a bullish rally that starts on 09/03/2003 with a minimum price at 1.0762, that ends on 12/30/2004 at 1.3665 USD dollars against Euro.


To this bullish rally of 2903 basic points, we apply the ZIGZAG oscillator (red line) showing 3 trend lines:
The first one bullish till 1.2930 day 02/19/2004, second bearish until 1.1759 day 04/26/04 to finally return the bullish trend with it’s third leg.

After isolating the major trend, in this particular case for week sessions, we start analyzing the currency behavior inside it. That’s why we apply the ZigZag oscillator to a 1 day chart (next inferior time frame) in order to find out through charts the minor trends or sub trends, and it’s corrections.

Then we proceed to isolate the first week dominant trend (Chart 5) starting at 1.0762 ending day 02/18/2004 at 1.2930 in the maximum of the session. When we apply the ZigZag oscillator, we found out 5 sub trend lines: 3 bullish (A1, A3 and A5), and 2 bearish (B2 and B4).



According to what we say before, we can see that A1, A3, and A5 are minor bullish trends that correspond with the major one, while B2 and B4 are just price corrections.

Continuing with the model development, we put together the tables for each currency under study, where we list every price rally, showing it trend: Bullish or Bearish and the start and end price. In the particular case of EURUSD, daily session we came out with the following results.



As you can see on table 8 the Number 2 rally, starts on day 05/18/1995 at 1.3380 dollars per Euro, and ends the day 05/26/1995, with a maximum price of 1.4235. This rally last 7 days, or 168 hours and represents 855 basic points.


Step 2

Afterwards, we move the following fields-data to a new table: minor rally number, start price, end price, duration (in hours), and the distance in basic points or pips.



Then, we move the major trend direction to the new table, came up from the application of the Zigzag Oscillator to the major period under study.


After the legs of the ZigZag were found (bullish and bearish rallies), we apply the Fibo’s ratios at any leg (“zig” or “zag”) that coincide with the major trend (In this case, Week), and so, we check if effectively the price retracements will go to the Fibo’s zones, or zones define by this special numbers.

Beginning with the graph example, where it explains the Zig Zag application, we continue the main analysis with the objective of verify graphically the behavior of the Fibo’s ratios in the retracements.

Inside the major trend we isolate in Graph 5, we proceed to apply the ratios of Fibonacci to the bullish rallies A1, A2, and A3.

In case of Rally A1, we take the complete distance from its minimum price at USD 1.0762, to the end at 1.1862 dollars per Eur. Then, we apply the Ratios of Fibonacci trying to see where the prices go after have reached the peak, and started the retracement.



In case of the bullish rally A1 with 110 basic points, and applying the Fibonacci Retracement ratios, we calculate the price for any ratio, trying to find the possible zones where the quotations could stop, so:


Looking at graph 6, and after the price retracement have begun, in opposite direction of the major trend, the price goes to the 23.6% zone. Firstly, the price couldn’t break this zone, and start to reduce the speed, and begun a change direction turning bull. This change is not considerer by the Zig Zag Oscillator, because the slope is lower than 12%.

After the price stops, it moves to the 38.2% zone, where its value is USD 1.1442. According to the results of Zig Zag Oscillator, the quotation stopped in an intermediate zone between 38.2% and 50%.

Secondly, we study the Rally A2. This rally begin after the B2 retracement has finished, at USD 1,1375 per Eur, and finishes on 01-12-2004, with a price value of 1,2900 dollars per Eur (Graph 7).


Besides, we apply again Fibonacci’s retracement ratios, to know the possible quotation behavior,


In this case, we can see a price retracement with a minimum value at 1.2334 dollars per Eur, near to the Fibo’s ratio, 38.2%. After that, the quotation rebound, and continues with the dominant trend.

Finally, and following with the bullish trend on Rally A5, the price goes to 1.2930 and change later the dominant trend, as we can see in graph 5. To confirm a change of the dominant trend, the retracement must be more than a 100% of the last rally, in the present example the price need to break 1,2317.

Continuing with the Statistic Analysis, we calculate the price values of any currency pair under study. In this example of EURUSD, you can see them in the next table:


As you can see in Table 13, the Bullish rally number 4 begins at 1.3836 dollars per Eur and ends at 1.4249. We apply the Fibo’s ratios, and we obtain the corresponding prices. For example, for ratio 23.6% the price is 1.4152 dollars per Eur. In others words, once the quotation rebounds at maximum USD 1.4249 per Eur, should go back to the first target of USD 1.4152.


Step 3

Once the prices targets for any rally were obtained, we proceed to probe the objective success of the system. Previously, we define 3 scenarios, or zones around the price, and test the truthfulness of the retracements go to these values or zones.

Each zone was defined with a percentage of the rally distance (zig or zag). For more information, we refer that we select the complete rally of the leg of the Zig Zag under study, for example: 100 pips, and if the price goes to the zone defined in more or less 7,5% (in this case in more or less 7,5 basic points) of the Fibonacci’s price, so the propose target is accomplished.

The scenarios are:

- 15% Zone: +/- 7.5% of the total rally, above the Fibo’s price.
- 20% Zone: +/- 10% of the total rally, above the Fibo’s price.
- 25% Zone: +/- 12.5% of the total rally, above the Fibo’s price.

Then, using the logical formula, we try to prove if the retracement of the price will go into the define zone.

In case that the final price of the next rally (mean the retracement), go into the Fibo’s define zone, the logical sequence is True, and so, successful. In the other hand, is False, and do not achieve the target.


Step 4

Finally, we proceed to calculate the number of retracements which go to the objective zone inside the dominant trend. In the present example, where we analyze the behavior of the currency pair EURUSD, Diary, we obtain the following results for the 15% zone:


As we see at table 14, we obtain a success of more than 70% of the propose objective. We refer that the retracements go to the Fibo’s price zone, when the minor trend correspond to the major. Meanwhile in case that the minor trends have different direction to the Major ones, the Fibo’s ratios have not got a significant success.

Thank you very much to all readers for continuing the interest till the end. We want to invite you to see the final part where we offer the investigation results, and the final conclusion.


Final Results

Then, and based on the model developed to prove the original hypothesis, we came to the following results:

- Pair EUR/USD:


- Pair USD/CHF:

- Pair GBP/USD:

- Pair YEN/USD:

If after finishing this job, someone ask me if it is possible to predict the future, mi answer will still be “NO”. I don’t believe that could be, in fact, I don’t believe either we can predict what will happen in the next minutes…

Although this seems the opposite of the objective of this work, I personally want to remark the difference between one thing and the other.

As a technical analyst and according to what was explained above, I maintain technical analysis postulates, and use them with statistics and mathematical tools, to forecast probable target price zones.

And here is the difference: in one hand, you have the certainty, in the other the probability. I personally believe there is no complete certain of what will happen, but using some specific tools, you can determinate probabilities in a defined scenario.

We use mathematic and statistics tools to analyze hundreds of data in order to prove the objective of this work.

That’s why we can affirm than more than 70% of the times, using Fibonacci retracements and ZigZag oscillator, we can determinate the target zones where prices will go, when they show retracements against major trend.

As a conclusion of this work, we propose to you to use Fibonacci tools in intermediate time frames, in order to obtain better results in markets with a defined trend, excluding moments of excessive volatility, but with enough price fluctuation, becoming and excellent tool for short term technical traders.

Finally, I want to invite you all to extend the application of this system to smaller time frames, and to the rest of the currencies in FOREX Market, and also, to other markets, such as futures, options, or any stock market.