## Thursday, May 7, 2009

### Fractional Bands

Let's consider again the equation (1) from yesterday:

$\sigma _{FBM}=(\frac{1}{N}\sum_{i=1}^{N}(x_{i}-\bar{x})^{2})^{H}=\sigma _{WBM}^{2H}$

We were facing the technical problem of having very small real variations of prices, leading to very small standard deviations. This can however be easily solved by converting all our values in PIPS. For EUR/USD, it simply consists in multiplying all the prices by 10000. If we then apply the above equation to PIPS, and convert it back to the scale of real prices (by dividing by 10000), we can then get a proper representation of bands, which, given that they are strictly obeying the model of FBM we are working with, I shall name Fractional Bands.

Here is a representation of these fractional bands for the 5 mn timeframe of EUR/USD, the red bands are the Fractal Bands defined as earlier, with the default parameters, the yellow bands are the Fractional Bands, with the same default parameters (without α, which we don't need anymore since we are not using equation (2)):

We can also compare the Fractional Bands (in yellow) with the Bollinger Bands (in blue-green) , to confirm what we expect from the above equation:

We indeed see that whenever the Fractal Dimension crosses the 1.5 line (i.e. whenever H crosses the 0.5 mark), the respective bands cross as well. The Fractional Bands are therefore narrower for a side-market and wider for a trendy market (even wider than the Fractal Bands for a very trendy market).

The paramaters for the Fractional Bands are the same as for the Fractal Bands except that there is no α, and in addition, we have the following parameter:
PIP_Convertor (integer): the factor necessary to convert real price to PIPS, default is 10000 (for EUR/USD)

As for the strategy, I am not sure whether there is one for this indicator alone, it seems to cross the prices quite often, especially during a side-market, it may however be combined efficiently with the FGDI and/or the Fractal Bands.

Anonymous said...

Fractional Bands are great instrument of technical analysis. In fact I really like to plot fractal and fractional bands together (there are inner and outer bands that I appreciate a lot).

My preferred settings are 20, as the usual Bolinger Bands (I do recommend to read his book, Bolinger on Bolinger bands for an adequate understanding of this instrument just a few tips are insufficient ;)).

The casual Bolinger bands are not useless. They are used together with the new bands. In fact as far as I understand when we have a low volatility and blue dimension (for red is also true but more dangerous because you have to look for important variation of the Hurst Exponent). We can be quite sure that the price will reverse (of course additional instrument is necessary).

On the other hand the fractional bands when they are widening are a sign for a great change in the fractal dimension structure of the price. And on this point when the reaction is really powerful we cannot see when the bands reverse. And this is important and is used by Bolinger himself. Something like i-BB-width you can download here
http://www.kimiv.ru/index.php?option=com_remository&Itemid=13&func=select&id=2

Jean-Philippe said...

I agree with you. I also like to use the classic Bollinger Bands in addition to the fractal and fractional ones.

I also agree that the indication of increasing volatility is a more reliable one than the indication of direction, which, no matter what, remains uncertain.