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October 5th, 2010, 12:20 AM  #1  
Member Joined: Sep 2010 Posts: 63 Thanks: 0  Some thoughts on Fibronacci Numbers and Stocks
Just brain storming at the moment: Some thoughts People in technical analysis often look at successive points were trend lines change. If you take the difference of these two points for two successive trend lines then supposedly the ratio should be close to the ratio of a Fibonacci number. Here are some of the ratios: 21/34 = 0.61764 ~ 0.618 34/21 = 1.61904 ~ 1.619 21/55 = 0.38181 ~ 0.382 55/21 = 2.61904 ~ 2.619 21/89 = 0.23595 ~ 0.236 89/21 = 4.23809 ~ 4.238 http://theforexbooks.com/index.php/D...rkDeaton.html For this to be fractal like it should be somewhat scale independent. However, in long time scales the fundamental of the company should dominate over short term emotion so the question is how to separate these two signals? My hypothesis would be that in the long term the average growth rate should match the fundamentals. This should give some relationship between how amplitude scales with time Stocks generally follow exponential growth curves. The fabroci sequence is also exponential as is any linear time independent finite difference equation. Quote:
Where I would like to go with this  Explore how various fabroci ratio's scale with time  Explore how the ratio's are influenced by the fundamentals of the stock.  Find the distribution of fabroci ratio's for a given time scale Anyway, if their is anything two these fabroci numbers then it would be nice to include them in noise models such as those used to estimate the valuation of options. I think I'm quite short of tying this into any strong theoretical framework at the moment. For instance I would be curious of how the noise is based on human factors vs market factors. I would also like to know why fabonacii ratio's are important or are they only important because people think they are important.  
October 5th, 2010, 01:06 AM  #2 
Member Joined: Sep 2010 Posts: 63 Thanks: 0  Re: Some thoughts on Fibronacci Numbers and Stocks
Some more thoughts from the above we can get the form of the difference equation which may describe the noise: The ratio of the difference of successive trends is: (x1x2)/(x2x3)=(+/)Rn x1x2=(+/)Rn(x2x3) Rn(x1(1Rn)x2)=(+/)x3 where Rn is a Fibronacci ratio: Now how might one combine equations of this form for various Fibronacci ratios to get some kind of noise model. And still get the same ratio properties for trend lines. 
October 5th, 2010, 01:45 AM  #3  
Member Joined: Sep 2010 Posts: 63 Thanks: 0  Re: Some thoughts on Fibronacci Numbers and Stocks Quote:
These are Fibronacci ratios. Now this doesn`t relate to trend lines but perhaps gives some of the answers. I wonder what sort of noise properties this type of random process would have.  
October 5th, 2010, 05:06 AM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Some thoughts on Fibronacci Numbers and Stocks Quote:
 
October 5th, 2010, 01:25 PM  #5  
Member Joined: Sep 2010 Posts: 63 Thanks: 0  Re: Some thoughts on Fibronacci Numbers and Stocks Quote:
Quote:
On another note, I haven't thought of any reasons why the trends should be related by fibronacci numbers but I thought a bit about retracements. I gave a noise model where the next value takes on one of two values y(n)=y(n1)*a y(n)=y(n1)/a each with separate probabilities. Now say their was some target value y*(n1) based on what people perceived the fundamentals were. If their was some kind of oscillatory restoring force (like a feedback loop) with momentum (similar to a spring system) that that would give retracements and because this would act as a linear filter then the same ratio's between successive values would hold.  
October 5th, 2010, 05:33 PM  #6  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Some thoughts on Fibronacci Numbers and Stocks Quote:
 
March 18th, 2011, 11:33 AM  #7 
Member Joined: Sep 2010 Posts: 63 Thanks: 0  Re: Some thoughts on Fibronacci Numbers and Stocks
Here's what I was looking for: http://en.wikipedia.org/wiki/Elliott_wave_principle I'll start a new thread on this shortly. 

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