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qroach Full Member Offline Posts: 102 London Gender:	Chaos theory 07/22/08 at 15:57:55 Has anybody used it, heard of somebody using it? Hurst exponents, fractal dimensions or whatever ... Have read some material on it but still don't get what to do with it.
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Co0olCat

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Re: Chaos theory
Reply #1 - 07/22/08 at 16:19:13

These things are used in one of methods to model data. The basic idea is that a multifractal process under some conditions can generate series similar to financial time series.

A number of papers had shown that this series have close characteristics to empirical data. Under the assumption that this is the case one can reverse the problem. By assuming that the empirical data was generated by a multifractal process one can estimate its parameters including Hurst exponents. The results show that this is more accurate than GARCH (maybe even FIGARCH, not sure though).

For more info I would recommend to check publications and lecture notes of my Alma Mater:

http://www.bwl.uni-kiel.de/gwif/downloads.php?lang=en

Once the parameters are estimated one can use analytical tools to make options pricing... Wink

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statstrader

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Re: Chaos theory
Reply #2 - 01/23/09 at 01:26:21

From my personal research in this area, I would be very careful to imply that markets are chaotic in the predictable sense.

A simple way to observe chaotic signatures is in state phase space. The idea is that even though some time series may look completely random (and even pass tests for randomness!), there are some of these series that can be generated by a perfectly deterministic process. The often referenced diagram of the logistic equation has a very specific attractor signature that implies determinism, you can clearly see the logistic equation has a deterministic (parabolic) signature in state phase space. This is not typically the case in market time series (which looks more like a cloud, similar to a Gaussian random series).

A great practical intro to this subject I would recommend, if you are interested is:

"Chaos theory tamed," by Garnett Williams.

http://www.amazon.com/Chaos-Theory-Tamed-Garnett-Williams/dp/0309063515/ref=sr_1...

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qroach Full Member Offline Posts: 102 London Gender:	Re: Chaos theory Reply #3 - 01/23/09 at 11:19:26 Thanks, statstrader, a lot. You've probably saved me plenty of time as I am a little bit tired of all sorts of hand-waving introductions to chaos theories.
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Algo Designer Forum Administrator Offline Nihil desperandum Posts: 182 Sydney Gender:	Re: Chaos theory Reply #4 - 01/23/09 at 12:39:20 I am intrigued by this book as well.
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qroach Full Member Offline Posts: 102 London Gender:	Re: Chaos theory Reply #5 - 01/23/09 at 13:13:16 can send you a link to download
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statstrader Newbie Offline I like this forum! Posts: 27	Re: Chaos theory Reply #6 - 01/24/09 at 01:20:57 Don't know of any links, but c'mon guys... at 15.00 used on amazon, you can't go wrong. Compare that to any of the Wiley's, which are typically close to $100/book, you are certainly getting a bargain here.
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bluelou

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Re: Chaos theory
Reply #7 - 01/28/09 at 23:50:33

I use a couple of methods in live trading that are related to those mentioned in the TOC of the book (Haven't read the book yet, though).

I mostly trade intraday and I can't say if I've seen any evidence of determinism b/c that's not how I use these measures. Instead, I use them b/c they can be more efficient and better quality estimators of autocorrelation, volatility, and higher moments than the usual descriptive statistics.

-BlueLou

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qroach Full Member Offline Posts: 102 London Gender:	Re: Chaos theory Reply #8 - 01/29/09 at 11:14:46 what is "b/c"?
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bluelou Newbie Offline I like this forum! Posts: 6 NY, NY Gender:	Re: Chaos theory Reply #9 - 01/29/09 at 14:19:09 because
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qroach Full Member Offline Posts: 102 London Gender:	Re: Chaos theory Reply #10 - 01/29/09 at 15:24:27 TL! (I mean, thanks a lot!)
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StatEdges

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Re: Chaos theory
Reply #11 - 02/12/09 at 11:07:04

I remember reading an interview with Jim Simons where he claimed that using chaos is a dead end. Of course, it could be a misdirection Wink

Whilst it may be subjective whether or not to use it in terms of time series prediction; to me it seems that it would be very useful for out-of-sample testing, especially if you can come up with a good model which closely resembles empirical data.

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qroach

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Re: Chaos theory
Reply #12 - 02/12/09 at 15:43:29

A model can very closely resemble empirical data, but have no immediate directional predictive power.

Take variance gamma process - very easy to generate a walk, how much more closely can you possibly model the data etc... and yet it will not tell you whether to buy or short ever. It can be good for obtaining better prices for derivatives though but that is a different story.

What I am trying to say is that a directional model might only be good if it doesn't resemble empirical data very well, may be even doesn't resemble it at all, but is good for predicting short term return or long-term value as a dot or a straight line.

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bluelou

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Re: Chaos theory
Reply #13 - 02/12/09 at 16:04:33

You can use chaos-related measures in a trend-following model.

For example, if you're using a simple moving-average crossover strategy you can use the chaos-related measures as as an overlay to indicate signal strength and signal/noise. Thus, improving the accuracy of your entries and exits.

Unfortunately, there's no instruction manual for which measure to use for signal or noise. But, it can be done.

------
Statstrader, thank you for mentioning the chaos book. Just got it. It looks very accessible - which almost never happens with this type of literature.

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StatEdges

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Re: Chaos theory
Reply #14 - 02/13/09 at 00:52:22

I was thinking more in terms of out-of-sample testing for trading strategies. Seemingly, you can generate data which closely resembles the dynamics of your chosen market and test the robustness of your strategy for entries and exits. The problem is that you'll probably need to take slippage and liquidity risks in extreme market conditions into account separately.

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