Cool. Thanks James.

I think I'm going to declare victory (of a sort) on this one. I correctly identified that the process was {time dependent drift, random innovations}. I didn't get the precise form of the Henon map (not surprising as I've never heard of this before) but I did capture the spirit of the drift switching process.

EDIT: I had a look at the Henon map. I know almost nothing about chaotic systems, so I was interested to see that the time series is ergodic. Is this common in chaotic systems?

well, you bring up a good point that I will list below:

1.  Clearly, it is enough to predict distributions (rather than prices) to make money.  thorp would have a viable strategy for this process, conditioned on knowing the distribution....this is obvious.

2.  I used a two dimensional chaotic system to generate the mean drifts, which suggests that that a machine that expands the dimensions of the "feature space" may make sense in trying to predict certain elements of a distribution.

3.  In some sense, I agree with the evil Taleb that, it is NP hard and perhaps undecidable whether you are right or lucky....that is, I have a distribution that depends on a) a constant parm and b) a time dependent deterministic parm and thus c), if you were trying to calibrate this to any other model, then you would decide about your "correctness" by testing a trading model.....and that, to me, is dangerous, and yet, it seems like the only way.....to me, this is why I am dubious about some of the "trend following" HFs I've met...I would like to give them the NoniusChallenge...In fact, I may do so....

P.S.  If this sounds Reza-ish, kill me slowly with a blunt knife.

EDIT: I had a look at the Henon map. I now almost nothing about chaotic systems, so I was interested to see that the time series is ergodic. Is this common in chaotic systems?

I do not know if it is true in general, but, a lot of chaotic systems are ergodic....it may be true....basically, a typical situation is you have a system of ODEs that give rise to wildly different limit sets conditioned on the initial conditions.  google strange attractors.

Farmer was my TA....the real Farmer.

Johnny, not sure I agree that the sign switches at that rate......I get about 66% of the time it is positive.

I think, though, that in the limit it is the same sign...

yes, but there is a difference:

1. I am not a geek.

2. I gave the answer quickly.

3. I am not a geek...oh, I said that...

I get the same initial values as well....

Number of Pos	43547
Total Num	65532
Ratio	0.664515

>> Nonius >> Thank you for your answer. I think I kind of get your arguments. Reading some Frédéric Laupies under the defintion of "cartésianisme", he points out that "a result without a theory and proof is useless". If I understood you correctly, this is why you are sceptical about trend-following HF's.

On the other side, if there is a mathematical model that perfectly describes a process e.g. the relationship between two assets (as in NOKI SEK vs NOK1V EUR), every trading opportunity/"arbitrage" you might see is probably something that you have missed- As the game evolves, you find less "straight" relationships that offer opportunities and you go on finding more complicated models that try to describe the phenomena you're watching:

In 1995, BS in London could still make profits trading the index-basket against the OMX-future by actually calling a broker in Sweden over the phone and ask them to do the trade even though both the equity-market and the derivatives market were electronic. A few years later, people talk about pairs trading and define mathematical models that should hold given this and this and that. Finally, it gets to the point where Vidyamurthy publishes "Pairs Trading" and all "opportunities" are gone ( I don't imply any causality there :-) )

I think what I'm trying to say is that most people want to hear a good investment/HF story based on cartesian thinking; i.e. a trading model that you can put in nice mathematical formulation and that sounds intuitively right. That's why invetsors keep on throwing money into "long/short" funds and market-"neutral" vehicles.

In a world like that, a guy saying "well we're buying because it has gone up" or "selling because it has gone down" freightens most investors. So they try to sugar-coat the story with quasi-finance speak (like the nonsense: everything is in the price and therefore we buy because it HAS gone up). But ultimately investors are uncomfortable with the lack of theory. And I also think that this is the reason why even a guy like Patrik Brummer, who has incubated a number of  hedge funds directly from start chose to buy a call in Lynx (their TF futures fund) rather than back it from the beginning, watched the performance for 3 years (with only 15mEUR in AUM) before he decided he was comfortable with their type of money management. Today, it has over 400mEUR in management and cannot be compared in sophistaction to the things their sisterfund Nectar is doing, "but it still works"...

(I'm skating on real thin ice and its already spring...)