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I want to build trading systems based on two things:

1)Fractal Theory

2)Harmonics Pattern

I have read the book : The Misbehavior of Markets: A Fractal View of Financial Turbulence By Mandelbrot but he didn’t show how to find fractal in time series. Moreover I don’t have time to go through all books with this topic, because I have work afterhours. So my question to you is:

-Do you know best measures for fractal theory or harmonics patterns in Time Series of Stock?

-Do you know some helpful publications/books connected with this topic – how to look for patterns/measures?

-Do you have any suggestions about construction of such trading systems?

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I find your question way too broad and open ended to answer. It sounds like you want others to deliver you the done deal to plug in. Maybe you can focus on a more specific issue and ask more targeted questions? –  Matt Wolf Jul 19 '13 at 11:29
    
This your opinion. I am just looking for some starting point and I don't want to read all the random books in the way, but good ones. –  Zimas Jul 19 '13 at 11:33
    
Asking for book recommendations is of course fine, asking others to pretty much guide you through the construction, well, pretty much delivering you the setup on a silver platter is maybe asking for a little too much. Maybe that is not your intention, it just comes across to me as such. Maybe you could rephrase the question? –  Matt Wolf Jul 19 '13 at 11:42
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Depending on what you look to use such system for one of my previous answers may be of help: quant.stackexchange.com/questions/8242/multi-fractals-models –  Matt Wolf Jul 19 '13 at 12:13
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I only try to answer questions or reference papers I myself have worked on or believe I understand. But I suffer from an overoptimistic nature ;-) –  Matt Wolf Jul 19 '13 at 14:07
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1 Answer

up vote 2 down vote accepted

Perhaps to detect fractal behaviour you could fit something like a Daubechies wavelet. That is, $W(a,b) := \frac{1}{\sqrt{|a|}} \int_{-\infty}^{\infty} f(t) \phi((t-b)/a)dt$. Then you want to check the set $\{W(a,b) : a \in \mathbb{R}_+\}$ where $a$ is the scale, for some fixed $b$. If all the coefficients are similar then this might be some indication of fractal like behaviour at least in that time localisation.

Good to review stochastic calculus or econometric estimators that take in multiple frequencies for possible solutions.

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