Hello. In the thread "Can linear regression analysis really predict the future", see http://www.elitetrader.com/vb/showthread.php?s=&threadid=181558, there's an excellent discussion revolving around natural cubic splines and the mean deviation of a (classical) random walk after n steps [sqrt(2n/pi)]. MAESTRO, dtrader98 and others provided several bits and pieces of good information. At the end of the thread MAESTRO hints about quantum random walk, QRW, and I've been looking for more information about this. I have found several papers on QRW, most of them quite mathematical in nature, but few have discussed finance/stocks. Two of the papers I have found, written by Martin Schaden, are "Quantum Finance" and "A Quantum Approach to Stock Price Fluctuations" (both available through google). They are also pretty mathematical, but should be possible to penetrate. "Quantum Entanglements", a lecture series by the Standford physicist and professor Leonard Susskind is interesting, both to learn about quantum mechanics in itself and to pick up enough math and terminology to read papers such as the two mentioned. It's available on youtube. It would be nice if someone could shine some more light on quantum random walk in relation to short-term movement of stock prices. Regards, Henrik
With the deepest respect and the fondest admiration, I must point out that Maestro is one of the subtlest humorists on ET.
There is no relation. QM studies the interactions in microscale. Obviously, stock movements are the result of interactions in macroscale, especially when they are caused by fat traders with bear bellies.
Hi, I have not done much more research into this, but what is interesting is that the arcsine law distribution appears as the limit pdf for continuous-time quantum walks on Z. The arcsine law (as discussed by Maestro and others) also pops up in classic quantum walks on Z. A good paper with a counting type proof of the arcsine law is http://ocw.mit.edu/courses/mathemat...iffusion-fall-2006/lecture-notes/lec14_06.pdf for those interested. Henrik
Thanks for the link. Also note in the Study Materials (notes from lectures from previous years) the second section has 4 lectures applying to finance: http://ocw.mit.edu/courses/mathematics/18-366-random-walks-and-diffusion-fall-2006/study-materials/ But not necessarily dealing with QRW. It's awesome they post courses like this with exercises and solutions. I really enjoy studying these types of courses and subjects in my free time.
Yes, we're all so highly amused at his years-long campaign of <s>disinformation</s> "humor". There's another word for it: trolling. Seriously, stock prices have nothing to do with random walk, quantum or otherwise. The Efficient Market Hypothesis has been discredited. And why aren't we all glad about that? RW says trading is impossible. You can't trade random aka noise aka garbage. Why some traders are so hooked on random walk is mind-boggling. MAESTRO of course knows better, and he's snickering at all the followers praising him for his random-walk "insights". MAESTRO also knows the difference between cubic spline smoothing and cubic spline interpolation, but he insists his listeners use cubic spline interpolation because then they're modeling the price noise right along with the signal and that's just a real knee-slapper, that is. Newbies, beware.
I'm not so sure it's all trolling, certainly though, he likes to obfuscate. Certainly, thinking more about the nature of randomness in trading can't hurt.