Guess I was in sync. If anyone following along enjoys reading and is interested in a few good related layman books, I would suggest the following low cost paperbacks for coffee table perusal (no order, but sornette is the hardest to digest without a math/financial market bckgrnd). Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life Steven H. Strogatz Origin of Wealth: Evolution, Complexity, and the Radical Remaking of Economics Eric D. Beinhocker Why Stock Markets Crash: Critical Events in Complex Financial Systems Didier Sornette
Hi MAESTRO, I was wondering if you've given thought to the temporal correlation of the samples - or more precisely the temporal correlation of the deltas (residuals). A purely random (white noise) process is decorrelated from sample to sample, which seems to be the focus of the discussion. If the residuals have any temporal correlation, then the process is not white, and more importantly, not an independent random variable. Stochastic Processes 101. Would you be willing to plot the autocorrelation (discussed by The1 earlier), rather than the standard deviation? I agree with your assement of proportionality to sqrt(N), but this doesn't directly tell me what the PSD will look like. For us to have a truly random walk, the residuals will have a flat (white) PSD spectrum. Alternatively, the covariance matrix would also be useful by giving us a different perspective of the correlation. This is why it may be more useful to model price movements with an ARIMA process rather than a random walk where the samples are correlated (and potentially exploitable). ARIMA processes identify and characterize the system's temporal correlation. http://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average Thanks! - ax
....................................................................... " Even Fibonacci lines will look like viable entry & exit points............." http://www.elitetrader.com/vb/showthread.php?threadid=223293 here is the answer to the navel gazing going on in this thread.... stop flipping coins, it will give you joint pain. cheers, shop
Awesome, thanks a ton for the recommendations. Your explanation was particularly elegant. Both your and Maestro's accounts helped the big picture to coalesce for me.
Why? No that's ok, I don't need to know why. I misunderstood the premise from the start so I'll leave the academics to others.
Maestro: Upon further inspection, I believe your analysis is flawed. My apologies that you ran this against 10,000 cases, because you'll need to redo it. You neglected the critical time component in your analysis. No wonder you've got a "random walk". If I removed and ignored the critical component such as a beat from a song, it would sound completely random too! As an illustration, imagine SPX remained completely flatline during the entire year of 2006. Literally flat line. You'd have complete temporal correlation and it would not be random at all, correct? If it had been flat line, your results wouldn't have changed at all. I apologize for being blunt, but you're looking at the wrong metric. Are you a professional in the industry? Perhaps you'd be kind enough to disclose the organization as a public service. As described here by others, the market is not purely random - look at fat tail movements as a single example. A random walk isn't capable or representing those events because P^N would become ridiculously small. So small, fat tails would never happen. - ax
What I meant by the analogy is that if you remove the cycles and introduce a random component in time, then you will automatically induce a random response. Another analogy: Imagine the market operated as a sinusoid. We'd all make tons of money because we would know exactly WHEN to buy and sell short. Timing is everything as we all know. Now introduce random undersampling of that sinusoid. If you did this, not only would Harry Nyquist and Claude Shannon roll over in their graves, you would have the same "unpredictability" that Maestro shows. Random time intervals would again induce a random response. My apologies to Maestro for what is beginning to sound like a rant.
Patterns exist because the variables that determine price movements and the relations among those variables tend to change in patterned ways. The trader who can identify the variables and the manner in which their effects will change with price changes with > 50% frequency will profit. When a stock is moving the tendency for the majority of trades to occur on either the the bid or the ask accounts for the decline or rise respectively. Pronounced tendencies for transactions to occur on either the bid or ask can't be intelligently characterized as randomness although there is some randomness in transaction sequences that the nimble trader can exploit. The fact that some specifically programmed generators of RW's can sometimes produce an RW that somewhat resembles a stock chart is very nearly mere coincidence. There is no underlyling principle or set of principles to be discovered here that can do more than tenuously relate the logics of the two phenomena.