# Fractal Analisys

The **Fractal Analysis** is a powerful tool for fractal analysis of financial markets.

### Description

The utility conducts a time-efficient deep analysis of fractal structure of the market for various investment horizons, and also determines whether there is long or short memory and non-periodic cyclic dependencies.

Analysis is performed using the rescaled range series method (R/S analysis) for the user-defined amount of history data, starting from the current quotes, with the entire set of the timeframes supported by the MetaTrader 5 is available. Wide spectrum of the allowed depth for the studied history – 280, 400, 1000, 2000, 3000, 4000, 6000, 10000, 12000 bars – allows the investors with different investment horizons to make conclusions regarding:

- Market dynamics;
- Validity of the Hurst process and the fractal market hypothesis;
- Presence of cycles.

It is also possible to confirm the results by means of the Fractal Analyser, by verifying the results using a larger or smaller amount of data, while keeping the history depth.

### Representation of results

The Fractal Analysis displays a brief summary of the market, showing the key numbers and characteristics, simplifying interaction with the chart, which shows the following dependencies:

- Dependence of logarithm of the R/S-statistic
**Log(R/S)**on the logarithm of amount of data in the subset**Log(N)**. Inclination of the trend line is the Hurst exponent; - Dependence of logarithm of R/S-statistic
**Log(E(R/S))**expected value from**Log(N)**, and trend line with the inclination that is the expected value of the Hurst exponent; - Dependence of logarithm of V-statistic
**Log(V)**from**Log(N)**.

### Interpretation of results

First of all, please note that the utility outputs 3 significant graphs. Below is the method for working with the results. While the tool makes most conclusions on its own, it will be useful to know the operation logic.

- Description of information block on the right

**Parameters:**

- Variance – sample variance;
- Stand. Dev. – standard deviation;
- Significance – significance of the result. Specifies the number of standard deviations, by which the obtained Hurst exponent differs from the expected value;
- Signal color – "noise color". Parameter points the type of the signal spectrum.

**Resume (Process details):**

- Analyzed History – studied time period (in years and/or days);
- Process type – characteristic of the process.

**Interpretation:**

- Working with the main chart

- First, estimate the dynamics of the curve Log(R/S). Is it higher than expected curve? Are there significant deviations?
- Analyze the V-statistic. Try to find the maximum of the graph (see the screenshots), which slightly decreases and eventually goes up. If the Fractal Analysis finds out that studied process is significant, then this figure will indicate a probable non-periodic cycle. Draw a vertical line down from the found maximum and find a corresponding approximated value Log(N). Length of the non-periodic cycle will be equal to N=exp^(found value).

- Cycle length interpretation

Cycle length is the memory depth.

What is the memory depth? This idea is a key concept of fractal theory. Memory depth is a period when past data influences the present and future data. This information is crucial for technical analysts, who doubt the significance of a past technical figure.

### Description of Input Parameters

- Symbol - desired symbol;
- NumberOfBars - the number of analyzed bars starting from the current;
- Timeframe - analyzed timeframe;
- Chart lifetime - time to display the utility;
- X coordinate (datum point) - X coordinate of the anchor point;
- Y coordinate - Y coordinate of the anchor point;
- Chart Width - chart width;
- Chart Height - chart height;
- Log(R/S) curve color - color of the Log(R/S) curve;
- Log(R/S) curve style - style of the Log(R/S) curve;
- Log(R/S) trend color - color of the trend line;
- Log(E(R/S)) curve color - color of the Log(E) curve;
- Log(E(R/S)) curve style - style of the Log(E) curve;
- Log(E(R/S)) trend color - color of the trend line;
- Log(V) curve color - color of the Log(V) curve;
- Log(V) curve style - style of the Log(V) curve;