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Message started by Yury R on 07/22/08 at 15:57:55

Title: Chaos theory
Post by Yury R on 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.

Title: Re: Chaos theory
Post by Co0olCat on 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... ;)

Title: Re: Chaos theory
Post by statstrader on 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_8?ie=UTF8&s=books&qid=1232673733&sr=1-8

Title: Re: Chaos theory
Post by Yury R on 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.

Title: Re: Chaos theory
Post by Algo Designer on 01/23/09 at 12:39:20

I am intrigued by this book as well.

Title: Re: Chaos theory
Post by Yury R on 01/23/09 at 13:13:16

can send you a link to download ;D

Title: Re: Chaos theory
Post by statstrader on 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.

Title: Re: Chaos theory
Post by bluelou on 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

Title: Re: Chaos theory
Post by Yury R on 01/29/09 at 11:14:46

what is "b/c"?

Title: Re: Chaos theory
Post by bluelou on 01/29/09 at 14:19:09

because

Title: Re: Chaos theory
Post by Yury R on 01/29/09 at 15:24:27

TL! (I mean, thanks a lot!)

Title: Re: Chaos theory
Post by Random on 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 ;)

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.

Title: Re: Chaos theory
Post by Yury R on 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.

Title: Re: Chaos theory
Post by bluelou on 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.

Title: Re: Chaos theory
Post by Random on 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.

Title: Re: Chaos theory
Post by bluelou on 02/13/09 at 01:08:37

Random,
I think I get it now. You want to model the data generating process to create OOS data, right? I think that Yury is right that this may not help you create a better trading model - if that's your goal. After all, even your synthetic OOS data would be a random realization.

I guess the upside is that you wouldn't be limited to historical data sets and that could help you create a more robust model.

Title: Re: Chaos theory
Post by statstrader on 02/13/09 at 21:39:16

There was a very similar experiment carried out by Meyer and Packard(1992), whereby they emulated a data generating process based on a well known chaotic generator known as a Mackey-Glass equation used to model blood flow. They ran genetic algorithms over many samples of data and optimized some boolean condition statements to predict an outcome based on embedded variables of the data set.
Their conclusion was that the prediction scheme was very robust on both training/optimizing and OOS data. Packard went on to co-found prediction company as discussed in the laymen's book, the predictors
(How a Band of Maverick Physicists Used Chaos Theory to Trade Their Way to a Fortune on Wall Street).

The above experiment is described succinctly in the book, an introduction to genetic algorithms, by M. mitchell. Also, google books
currently has a free preview of this section for those interested
(p. 56, predicting dynamical systems).

The unfortunate problem with this approach is that the data generating process of the markets is not the same as the Mackay-Glass, logistic, or any other well known chaotic model. It is more akin to an EEG process, which fills up a phase state-space with very little predictive signature. There are quite useful tricks to be found if you play around long enough with the concepts, however. 8-)

P.S. bluelou, hope everything is going well on your trading.
I just wish we could find more good thinkers to add to all the discussions. I check quite frequently, and rarely see anyone outside of Yury post (although I do certainly appreciate hearing from him). :(

Title: Re: Chaos theory
Post by Yury R on 02/13/09 at 23:00:41

Cheers :D

Title: Re: Chaos theory
Post by Random on 02/16/09 at 12:34:13

Sorry - I didn't mean use the data from the chaotic generator to create a trading strategy. The trading strategy should only be created from realised empirical data - otherwise, using a model-based DGP may introduce (potentially dangerous) side-effects into the resulting trading model. What I meant was to just use the model-generated data purely to test the final strategy for robustness. In a way, it might even be possible to test the strategy against an ensemble of data from using a range of paremeters for the chaotic-DGP (thus perhaps testing performance in a regime-switch?).

Of course, I'm not at all versed in the mechanics of chaos theory; just thought I'd just throw some ideas around.