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Fractal dimension indicators and their use

Fractal dimension indicators and their use

Last updated 2399 days ago by JohnLast Comments (1)
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От 04 октомври 2011

Here I just compile some things I have written on TSD and Forex Factory. 

Fractal dimension use

 

The FGDI is the fractal dimension graph indicator (slight upgrade of the FDI fractal dimension indicator).


If the FGDI is lower than 1,5 level that means that the time series are persistent

If the FGDI is higher than 1,5 level than means that the times series are antipersistent

If the FGDI is equal to 1,5 there is a 50/50 probability.

The FGDI estimates the fractal dimension of the times series. 
The fractal dimension = 2 - Exponent of Hurst (H)

So if the exponent of Hurst is equal to 0.5 we have a FGDI equal to 1,5.
Exponent of Hurst of 0.5 means that the movement is random without long term memory processes.
Exponent of Hurst > 0.5 - persistent
Exponent of Hurst < 0.5 - antipersistent

This is explained elsewhere and I just remember that basic stuff. The FGDI (FDI) according to me is better than the fractal dimension indicator published by Ehler, and moreover its mt4 implementation is not free but in the elite section of TSD.

The IVAR is similar to the FDI but its scale is different. The center line is 0.5.

The interpretation is the same when it goes below 0,5 the movement is persistent and vice versa, it is antipersistent.

According to the statistical mechanics if the time series are random walk the H should be equal to 0.5.

Hurst has discovered that a lot of natural phenomena follow a "biased random walk" or trend with noise. The strength of the trend can be measured by how the Hurst exponent is above 0.5 (that means FDI and FGDI below 1,5 and Ivar below 0.5)

In fact all those formula are estimating the Hurst exponent. I think that the easiest is to understand the Rescaled range analysis as a method, to understand what is going on. I precise that I have no high education in mathematics and I was able to understand the logic. 

The fundamental principle is if the time series are random their range will increase with the square root of time (this is original idea of Einstein in his paper for the Brownian motion). Einstein found that the distance a random particle travels increases with the square root of time used to measure it.

And Hurst decided to make a ration dividing the Range by the the standard deviation of the observations (R/S) R- range S - standard deviation.

So 

R/S = (a*N)^H

R/S = rescaled range N = number of observations a = a constant H = Hurst exponent

So we expect to have H=0.5 if the price time series are random. But they are not folks, that does not mean that they are easily predictable either .

All this may seem very theoretical. The exponential moving average is either theoretical but easy to use. This is the same.

Comments

  • JohnLast 2381 days ago

    Please look at the change of the market structure between the pruple zones and the blue zones. The market change its regime during those periods. And that has very practical consequences, for  example imagine you have trained (optimized your model) during blue zone and all of a sudden the market is going into a purple zone. What is going to happen. I guess your system may fail to work, and of course a constant optimization bar per bar would not help. You are going to optimize for completely different market states all of the time. And that lead to the hypothesis that your results would be not very consistent. And whatever you optimize it would be based on luck because you do not know beforehand how much those market states are going to last and how they would change. 

    So the question arise what we can do?

    1. We can take into account those shifts in market structure when we optimize our systems. We need a stable market structure in order to succeed. 

    2. We can design a a system that would work on both market conditions. Could we? Yes we can, for example buy and hold would work on both market conditions provide the market is trending upwards. However we go from one uncertainty into another (market trend direction and the profitability of the Buy & Hold strategy).

    Whatevever we do there are uncertainties. Howver the market state teches us not to take a directionnal signal when the market state is not persistent.