Do you see patterns in Random Walks?

[dtrader98]

Quote from MAESTRO:

... However, I think there is enough meat to discuss at the general (conceptual) level without revealing the actual implementation (which is by far is not trivial).

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

 

[axiszen]

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

Quote from MAESTRO:

Argument #4

Let’s construct a simple one dimensional discrete random walk using the following rules. We would flip an unbiased coin and every time it lands on “heads” we would draw a step (size 1) up and every time it lands on “tails” we would draw a step down. It is well known that on average this random walk would deviate from it’s initial starting point by sqrt ( 2 * N / pi) where N is the number of flips (mean deviation of the walk). This walk will have standard deviation equal to sqrt (N).

The chart below is a weekly chart for SPX. The lines above and below present one standard and one mean deviation of 100 point steps (steps are plotted on the chart in green). It is self evident that this particular chart is extremely close to a pure random walk outcome. It could be shown that if we used not a constant step but a percentage based step the similarity would be even closer. Also, if we take under consideration the reduction of the US dollar buying power over this period of time we would have an exact match between SPX weekly chart and pure random walk. These observations were confirmed by us without a hint of a doubt on hundreds different securities and on thousands different time frames.

 

[shopster]

Quote from atlTrader666:

I'm interested in the more esoteric technical analysis and why people believe it (against all evidence)... Aside support and resistance and some momentum patterns, the rest of TA seems like nonsense. Academics have tested TA strategies for half a century and they all call it bullsh1t. There is vague proof of short-term momentum. Only Benoit Mandelbrot discovered something valid: volatility tends to cluster. You can't make money of that though since traders have intuitively known and incorporate higher premiums in their options trading when volatility increases.

My question: If you were to create a random walk in Excel do you think you would differentiate the chart from say a stock market chart?

Seriously guys Google image a random walk chart or create one in Excel and you will be amazed at the amount of double tops/bottoms, bull/bear flags, breakouts from consolidation areas, etc. that you will discover. Even Fibonacci lines will look like viable entry & exit points.

.......................................................................

" 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

 

[Samsara]

Quote from dtrader98:

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

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.

 

[SunTrader]

Quote from MAESTRO:

......, however the reason why they are there is what I am trying to research.

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.

 

[axiszen]

Quote from MAESTRO:

Argument #4

Let’s construct a simple one dimensional discrete random walk using the following rules. We would flip an unbiased coin and every time it lands on “heads” we would draw a step (size 1) up and every time it lands on “tails” we would draw a step down. It is well known that on average this random walk would deviate from it’s initial starting point by sqrt ( 2 * N / pi) where N is the number of flips (mean deviation of the walk). This walk will have standard deviation equal to sqrt (N).

The chart below is a weekly chart for SPX. The lines above and below present one standard and one mean deviation of 100 point steps (steps are plotted on the chart in green). It is self evident that this particular chart is extremely close to a pure random walk outcome. It could be shown that if we used not a constant step but a percentage based step the similarity would be even closer. Also, if we take under consideration the reduction of the US dollar buying power over this period of time we would have an exact match between SPX weekly chart and pure random walk. These observations were confirmed by us without a hint of a doubt on hundreds different securities and on thousands different time frames.

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

 

[SnakeEYE]

Ax,what is your market analogy for the ''beat''?

 

[axiszen]

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.

Quote from SnakeEYE:

Ax,what is your market analogy for the ''beat''?

 

[SnakeEYE]

Quote from axiszen:

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.

Your conclusions then - timing is impossible?"Cycles" is also a vague notion.

 

[Hansel H]

Quote from MAESTRO:

PATTERNS DO EXIST, however the reason why they are there is what I am trying to research.

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.