The Mandelbrot set is the most famous illustration of a fractal in two dimensions. The same mathematics can be used in one dimension to describe financial market price activity. Source: Wikipedia
The other day I caught part of an interview with a spokesperson for Elliott Wave International on Bloomberg TV. Elliott Wave International is an organization devoted to promoting the use of a market-analysis technique developed in the 1930s by Ralph Nelson Elliott, called the wave principle. The most important thing to come out of the interview, to my mind, was an off-hand comment by the spokesperson that stock-price movement "is a fractal."
A fractal is a mathematical waveform with a texture that is of the same form at all spatial-frequency scales. For example, we've all seen those neat illustrations hung in hotel lobbies and meeting rooms that include what appear to be strikingly realistic silhouettes of mountain ranges. Artists make those illustrations by simply tearing a piece of construction paper, and airbrushing past the torn edge. Since construction-paper tears and mountain-range silhouettes are both fractals, the torn paper edge bears an uncanny resemblance to a generic mountain range.
The most famous fractal illustration, and the one mathematicians use most often to illustrate the properties of fractals, is the Mandelbrot set. I think people like to use it as an illustration because it's amazingly beautiful. It also has the advantage of clearly illustrating fractal properties. Unfortunately, it has no practical value, so using it to illustrate fractals leaves the impression that fractals have no practical value.
Nothing could be further from the truth.
Like all fractals, the Mandelbrot set repeats itself on all length scales. It thus displays the property of self similarity. Similarly, if you take a typical stock-price chart covering a time span of, say, one month, and compare it to an intraday chart, the two will look remarkably similar, and will also bear a striking resemblance to the mountain-range silhouette, and the torn paper. They're all fractals.
Self-similar charts, such as stock price charts, all have two spatial frequency properties: they're combinations of "tones" at a wide range of spatial frequencies, and the amplitude of any one tone is inversely proportional to its spatial frequency. Tones at lower spatial frequencies - so they take up more of the chart horizontally - also have proportionally higher amplitudes - so they take up more of the chart vertically.
Comparison of stock-price charts covering a wide range of time spans shows that they also show self similarity, and are therefore fractals. Financial markets exhibit this behavior because they are chaotic systems. That is, there are a large number of independent actors making buy/sell decisions based on different interpretations of the same enormous, but incomplete, data set. Each actor moves the price of an individual financial instrument slightly, but none has enough pricing power to exercise significant control alone. Everyone has an effect, but nobody has a controlling effect.
That is what drives fundamental stock analysts bonkers. Each property of the underlying company, each news item about the company, each pronouncement by a politician, has an affect - often a noticeable effect - but none of them has a determining effect. There's just too much else going on that also has an effect.
It is important to recognize that there are varying degrees of self-similarity. The Mandelbrot set displays the strongest type of self-similarity (exact self-similarity), meaning that it appears exactly the same at all spatial scales. Stock prices, on the other hand, display the weakest type of self-similarity (statistical self-similarity), meaning that the figure has numerical or statistical measures that are preserved over different spatial scales. The fact that stock charts have only statistical self-similarity is what makes stock-price movements inherently unpredictable.
Because Elliott wave analysis starts from the observation that charts of financial-market prices are fractals, the wave principle, out of all technical analysis tools, has the best hope of making sense of financial-market price movements. Elliott's original work was hampered by the fact that understanding of fractals was limited in the 1930s, and understanding of chaotic systems was effectively nil until the 1960s. Some misunderstandings, such as the representation of waves as triangular, rather than sinusoidal, still persist, but anyone interested in learning technical analysis could do a lot worse than beginning with Elliott wave analysis.
That makes sense.
What a blog. I can't believe some of these comments.
This particular editorial was very exciting to browse, I enjoyed it a whole lot of. I'm going now to e-mail it to my collegues to permit all of them examine this too. Thank you completely.
Great article! Your style is so refreshing in comparison to most other writers. Thanks for posting when you get the chance to, I will be sure to return!
Thank you for your help!
Do you consider the housing crisis is over and we have entered a new realty industry? I consider the economy requirements to fully recover prior to we have enough individuals confident enought to buy new homes. In this marketplace its challenging to make a long term investment and burden oneself with more debt with as a lot uncertainty is within the air.
This post was very unique to see, I was pleased with it completely. I'm going now to mail it to my collegues to permit them look over this too. Thank you a whole lot of.
Wow i just like this ringtone very much. Thank you a lot for this, just love it.
Thanks for such interesting post as I have been able to find here. I agree with most of what is written and I'll be returning to this website again. Thanks again for sharing this material.
I totally love your blog! Thank you for the post, very informative. wty1d8
Hey very nice blog!! Man .. Beautiful .. Amazing .. I will bookmark your blog and take the feeds also...
very well information you write it very clean. I'm very lucky to get this info from you.
It sounds like you're creating problems yourself by trying to solve this issue instead of looking at why their is a problem in the first place. chase sapphire
Thanks very much for this, the time spent was well worth it, keep up the good work and ill be sure to revisit this website again real soon. Well done.
Is Gettting MCSE Certified that important?
What is the hot computer certification right now?
Thanks for such a good blog. This is what I looked for.
All I can say is keep it up. This blog is so necessary in a time when everyone just wants to talk about how deadful things are. I mean, thanks for bringing intelligence back to the web, its been sorely missed. Fantastic stuff.
I want to thank you for the effort you have made in publishing this article. I am trusting the same best work from you in the next articles
I found this blog while searching in Google. There is a lot of good information here on interesting subjects. I will probably contact you through the contact page regarding a project of mine. Keep up the good work.
Thanks for this great Article. Really great topic to write about on my Website. I probably make a bookmark from another site.
Thanks for taking the time to discuss this, I feel strongly about information and love learning more on this. If possible,it was very helpful for me.
I just come across your weblog and think this is a excellent article which i appreciate reading and provide me personally some great info for the concern. I have check for couple of other content articles in your blog and found really educational and I understand numerous point too from your meaningful posts. I will go to your website a lot more regularly as I believe it's advantage me a lot.
Thanks for creating this great informational resource.
I would like to thank you for the endeavors you have made in publishing this article. I am trusting the same best work from you in the next articles
This is a good site. The content is very informative.
Very good blog. I will return.
Great blog, I will definatly come back to visit.
Heyy, Found your blog on Yahoo and I am so glad I did! Keep it up! =)
Good post
I like the layout of your website and I’m going to do the same thing for site. Do you have any tips? Please email ME.
Super text, I will add this blog to my favorites.
Pretty impressive post. I just came across your blog and wanted to say that I have really enjoyed reading your opinions. Any way I'll be subscribing to your feed and I hope you post again soon.
Thanks for the interesting content!!!
Good job!
huh? “what did you just said?”LOL is this another fobism….. i know i know its old.
Very nice article and the main point is the smooth way of explanation. Its easy to understand for any person. thank u sir for sharing this.
I'm excited to be finally posting online after all these years. There really is no mystery about it, is there? I just dropped by your blog and had to write. I'm a recent college grad, journalism major if you must know, and I absolutely love photography. I've got my site up but it's nothing to boast about yet. None of my stuff's been posted. Soon as I figure out how to do that, I'll spend the day posting my best pictures. anyway just thought I'd drop a line. I hope to return with more substantial stuff, stuff you can actually use. SPG
The artical is so excellent!
The artical is so fantastic!
Have a excellent day!
Have a good day!
The artical is so good!
Good post, thanks
Great post!
I find myself coming to your blog more and more often to the point where my visits are almost daily now!
You certainly deserve a round of applause for your post and more specifically, your blog in general. Very high quality material.