What is fractal analysis

2024 Author: Howard Calhoun | [email protected]. Last modified: 2023-12-17 10:16

Fractal analysis is a kind of artistic perception of an object within the boundaries of identical geometric shapes.

For example, the hostess bakes a pie in the oven on a rectangular baking sheet. The finished product cuts into identical rectangles, reminiscent of the shape of the whole product. Portion pieces have the same color, taste and composition as the whole pie. A fragment of a pie and a whole pie are identical in everything. A cut pie can be called a fractal. Because the whole is made up of similar pieces.

Entity of the object

The principle of similarity is applicable in exchange trading. Prices of market instruments are considered on long and short time frames and find a striking similarity in the behavior of the chart on minutes and days, for example.

The theory of fractal analysis sounded in the last quarter of the twentieth century. The new word was introduced into market science by the mathematician Benoit Mandelbrot. The researcher replaced the word “recursion”, which had set the teeth on edge, with the Latin “fractal”. An American and French scientist gave the financial world a way to study by sequentially splitting observation intervals and searching for symmetry on long and short movement chartsprices.

Understand the geometry and win

Fractal as an indicator shows the minimum and maximum price on an odd number of periods of the selected time interval. The rational number of periods that has taken root in practice is five.

For a combination of 5 candles, a fractal is drawn if a symmetrical figure is fixed:

• for the green “up” fractal, the last two candles to the left and right of the central one display prices below the high;
• for a red down fractal, the left and right pair of candles should show above the low.

The number of candles in the combination can be increased. Obviously, for 9 candles, the groups of candles on the left and right consist of four periods.

When superimposed on a price chart, a fractal is indicated by a short arrow. The "up" fractal shows the price rise to a maximum in the selected time period, and the "down" fractal shows the minimum in the same time interval.

Trading practice systematized fractals on:

• standard, when the middle candle indicates reaching one extremum;
• non-standard, when the middle candle reflects both extremes.

The appearance of a non-standard candle signals a clash of interests between sellers and buyers. The market at this moment must choose one of the directions of movement.

Application of fractal analysis

Breaking the whole into many similar figures is used in many industriesknowledge, such as:

• math;
• architecture;
• economics and finance;
• design.

Our article is addressed to the reader with stock exchange interests.

All price series have the property of statistical similarity. Minute, hourly and daily charts with fractals look the same so that if you exclude the marking of the coordinate axes, then it is not known which period is considered.

Methods of fractal analysis

Fractal mathematics based on the R/S-analysis algorithm is used to describe the price evolutions of an exchange asset and the subsequent forecast of the price movement on any time periods. The dimensionless value of the ratio of the range R of the observed parameter to the standard delta of observations S – basis of the normalized analysis method.

You can estimate the strength of the trend on the asset chart and the level of random price walks using the normalized range analysis method for exceeding the value of 0, 5.

The meaning of calculations and constructions is to determine the color of the informational noise of the market. The algorithm of the method involves the calculation of the Hurst exponent H - a fractal characteristic of the analyzed time period - as well as the noise quality:

• 0, 5±0, 1 – “white noise”; chaos of the time period; low confidence forecast;
• ≧ 0, 6 - "black noise"; orderliness of chaos; trend strength; high confidence forecast;
• 0, 3±0, 1 – “pink noise”; zone of antipersistence – change of direction of increment growth to the opposite one:growth in the early periods signals a decrease in the future, and vice versa, a downward trend in the past increases the likelihood of growth in the future.

For "manual" trading, these are too burdensome constructions. Complex mathematics is needed to develop trading robots.

In the realm of currency pairs

Fractal analysis of the pair is appropriate and in demand in the currency market due to large trading volumes.

Of course, preferences in the choice of currency traders vary. But for study it is useful to study the charts of popular pairs:

• euro/dollar;
• pound/dollar;
• dollar/yen;
• euro/yen;
• Australian dollar/USD.

To get your hands on it, open a demo account with any broker. Connect the trading program and display the charts of currency pairs for the current month (June) on the screen as separate sheets. Label each chart with Fibonacci lines. Look for characteristic patterns of five candlesticks - up and down fractals.

Euro/yen review

Here, the currencies of two systems have united - European and Asia-Pacific. Each currency has its own influence factors. The Japanese currency is traded according to the speeches of the Ministry of Finance of Japan, according to the reports of the Tankan Bank and on the demand for Japanese-made equipment, taking into account customs duties and import quotas for North American consumers.

Although the list of factors affecting the euro exchange rate will take half a page, the currency of the Old World is a rather power-based monetary unit."Japanese", on the contrary, makes sharp movements.

Significant changes in the yen in short trading periods constitute an increased risk, because the quote has an accuracy of two decimal places. For comparison: the bond with the ruble has an accuracy of three decimal places, and in conjunction with the Swiss franc it reaches five decimal places.

But the volatility of the yen during the day makes trading the euro-yen pair profitable. The most productive operation time for this tandem is from 9 am to 10 am Moscow time. Both Asian and European platforms are open at this hour. When placing an order to buy or sell, you should not forget about the stop loss. In the pair's trading practice, a case of a price change of 600 points was recorded during one trading session. Take care of the deposit - put limits on a sharp change in the rate.

So, euro/yen. As an illustration - a screen for June 26. Hourly timeframe. Key levels: 125.87, 125.54, 125.07, 124.71, 124.06, 123.81 and 123.40. The pair has been forming a local uptrend since June 15.

In case of a breakdown of the level of 125.07, the price will go for consolidation in the range of 124.54 – 125.87. It is not visible above.

When the price drops to 124.06, a deep correction is possible with trading in the range of 123.81 – 123.40. Deeper is not yet visible.

Advantages and disadvantages

The advantage of fractal market analysis lies in its applicability to any instrument:

• stocks and bonds;
• goods;
• currencies;
• futures.

At any time interval, you can search and split. But the accuracy of the forecast decreases with a decrease in the period: the prediction on daily charts is much more accurate than on five-minute charts.

The disadvantage is that the indicator is lagging. A fractal is formed only after the appearance of a candle following the minimum or maximum. That is, the wrong reaction to volatility is possible. The fractal method is best suited for long periods when inevitable pullbacks are not critical for the player. You can use the adjustment to change your own volumes. At short intervals, you will have to use figures in combination with other methods of building a forecast.

Apocrypha of the Ancestors and Companions

Beginner traders should read the main books on technical analysis.

First on the list will be "(Un)obedient Markets: A Fractal Revolution in Finance" by mathematicians Mandelbrot B. and Hudson R. This is the ABC of fractal analysis of financial markets. It is necessary to forget about the simplified forms of everyday trading slang for a while. Beautiful, in places even with vignettes, sentences, the writer explains in detail what and why, where and why is shifted from theory to practice of the game.

Having familiarized yourself with the basics of detecting fractals on the price chart of any exchange instrument, you should take care of the psychological component of trading. A second book will help, titled How to Buy Low and Sell High: A Guide for the Smart Investor. Writer Nyman E.tell you how to resist the pressure of the market crowd; how to increase the probability of a positive result by a sober control of one’s own opinion; how to get out of poverty and keep all the safety of the family.

The third trader's guide is called Trading Chaos. Increasing profits by technical analysis methods” by widely cited traders Williams B. and Gregory-Williams J. The book proves that chaos is the greatest order in a complex system, including market reality.

Saying goodbye to patient readers, let's add: mathematics is the head of the whole world order. Following Fibonacci levels, Elliott waves and Mandelbrot fractals, young enlightened minds will create more than one theory for the emerging market space.