A study in chaos

G

gtor514

First time poster here.

A search for "chaos" on the internet brought me here to some of the threads on ET. I was encouraged by some of the discussion both for and against the idea that chaos or random movements rule the market. I've been intrigued with this idea so I decided to begin doing some hard practical research and study.

What I decided to do was plot a random logistic map on my charting package against a chart for the GBPUSD.

The logistic map equation I use is ...

x[n+1] = r * x[n] * (1-x[n])

I plot this along a chart using only a beginning price to put me in the ballpark of my chart. I have two inputs that I must choose, they are "r" and my initial "x[n]"

Initially my goal is not to find some sort of indicator for the market but determine if chaos is a reasonable approach to study the markets. What I found was very encouraging. I found perfect fibonacci retracements and extensions. Trendlines, support and resistance, gann fans that worked, patterns like head and shoulders, elliot waves and everthing else that traders use to study the market.

I am encouraged by this first part of my study and feel it warrants further study. I ask for any opinions.
 

Attachments

The equation I am using is one of many that are used to describe chaotic motion. Remember, I am trying to answer the question: Do markets follow random or chaotic motion? Here is an excellent source for description of the logistic map equation.

http://mathworld.wolfram.com/LogisticMap.html

At first most of this may appear to be rather complex but it's actually pretty simple. What I am using is essentially a nonilinear dynamic system (equation) to describe the movements in the market. We know that chaos begins where r=3.5669.

Chaotic motion provides that knowing the previous movement (x[n]), we can predict the next movement (x[n+1]) knowing the r of our system. The equation that I have shown is that of a parabola. Plot it in x[n+1] vs x[n] in excel and you can see this as in the attachment. Just select an arbitrary r and x[n].

Now what we do is plot this system over time as applied to price and we have the image that I provided in the first plot. Further investigation of mine showed that I could have excellent results of predicting the market if I adjusted "r" in my equation to match prior motion. A common value that occured was r=3.236= SQRT(5) + 1 in a ranging market or price that followed in a channel. The problem is that "r" shifts between the chaotic and non chaotic motion.
 
End-of-day data is nearly useless for this kind of analysis. Closing prices are completely arbitrary and don't have much more significance than say.. the prices at 2PM.. or 1PM each day. Tick data should really be used in these cases. The larger the timeframe the more unpredictable it is.
 
Quote from sunnyskies:

genetic algorithms have more promise
More...
yawn, yawn.

PS: could always do an ET search. might be easier to go with trend & chop finding. write me if you ever make money with it.
:cool:
 
same goes for me. i use my own opinion - fair value, below fair value and above fair value to support my trading, not some math bs.
 
Quote from sunnyskies:

genetic algorithms have more promise
More...

Been there, done that and with more advanced stuff that you have ever heard about.

The 'ol human psychology does not change over time that much and one doesn't need any fancy code to display it. Just knowing how to interpret what you see on the screen.

We'll see pretty nice swings the coming days (have already seen some nice ones) when these automated bots get their nuts in a tangle because of a little storm.

Sherlock

:cool:

PS What chaos? There ain't no chaos! Just learn to read what the different market participants are doing.
 
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