Do you see patterns in Random Walks?

[zedDoubleNaught]

If price distributions are not normal, with fatter tails, wouldn't that suggest "the mean" as in some sort of average is undefined and meaningless? I ask because I've learned, and currently trying to intuitively understand, "Cauchy distributions (with fat tails) averages and varinaces are undefined"; meaning each sample will give an average and a variance that never seems to tend towards a certain number. I think I've also read somewhere, price distributions are somewhere between normal and Cauchy, with kurtosis somewhere between 1 and 2 (I think those ar the right figures).
Or is that part of the step of trying to find stable distributions in the price and/or price differences?

And glad to hear your health is improving, glad to have you back.
thanks

 

[MAESTRO]

Quote from zedDoubleNaught:

If price distributions are not normal, with fatter tails, wouldn't that suggest "the mean" as in some sort of average is undefined and meaningless? ...

Good question! Yes, simple averages and some other linear interpolators become useless in the environment with the constantly changing distribution. Some higher degree polynomials are needed in this case. As you know, I am a big fan of cubic splines. They have remarkable properties that are quite instrumental in defining the mean. We have created a unique, proprietary set of those polynomials to address different market's behavioral patterns. The most important part is the "elasticity" of your mean, but that is the whole new story!

cheers,
MAESTRO

 

[intradaybill]

Quote from MAESTRO:

Two or more stochastic processes could be well correlated. The product of those two processes creates a third one that has less mean deviation than the original two if the correlation is positive. Arbitrage is based on the notion of reduced volatility of that "synthetic" security created via correlation process.

Did you mean to say "The product of those two processes creates a third one that has less mean deviation than the original two if the correlation is negative."?

I would think that for RTM startegies one would look at the sum, not the product of the processes. In this case the variance of their sum is equal to the sum of their covariances. In the case that both processes have variance s^2, for simplicity, then the variance of the mean is equal to

s^2 x (1+p)/2

where p is the correlation. We thus see that the variance increases if the processes are positively correlated and decreases if they are negatively correlated.

This is of course too intuitive. It is so intuitive that I don't think anyone can make money with such a trivial fact.

 

[intradaybill]

Quote from MAESTRO:

The most important part is the "elasticity" of your mean, but that is the whole new story!

You sound like a mechanical engineer. Splines, elasticity, etc. Are you Italian? I had an Inalian friend who called himself Maestro until he got married of course

 

[MAESTRO]

Just to answer the original question:

"Do you see patterns in Random Walks?"

Yes, of course. Everybody does. The same way we see a dog head in the pattern of clouds or mystical figures in some rock formations. The whole evolution process of us as species is based on our abilities to "see" those patterns. We cannot help it. Going further, it is actually irrelevant whether those patterns really do exist or not. Only their stability over time is relevant. There is no guarantee that we will see another dog head in the nearest future and if we do see it we tend to believe that the clouds "normally" produce patterns that look like dog heads. If see it 12 times in a row we will be more than convinced that that is a normal shape of a cloud. (Of course, we tend to forget of how many times the clouds did not form a dog head). A smart and sly shaman can convince you that if he hits the ground with his magical stick 3 times tomorrow will be rain. And if it does rain we will tell about it to our friends. Self-reinforcing positive expectations are the real reason behind all of those patterns that we see. I could go on and on, however, I have to leave and take some meds. Tomorrow is another day.

Cheers,
MAESTRO

 

[MAESTRO]

Quote from intradaybill:

You sound like a mechanical engineer. Splines, elasticity, etc. Are you Italian? I had an Inalian friend who called himself Maestro until he got married of course

My very first degree was in electrical engineering and I have 16 different nationalities evenly spread through my blood. My predecessors were players, I guess. However, there is no Italian blood in me. Oh, well, you cannot have them all ....

 

[jem]

how made trades with profits does it take to defeat the thesis of randomness?

a better question would be, do you see random walks in markets.

or do you believe markets are always random because your testing shows them to be random at times.

 

[intradaybill]

Quote from jem:

a better question would be, do you see random walks in markets.

or do you believe markets are always random because your testing shows them to be random at times.

Nobody knows what random means. Actually, there is no robust test for randomness. It is possible that the concept of randomness was invented to expalin mass multivariate phenomena that were not possible to model exactly. Everything is deterministic is this world. Randomness we call what we do not know.

 

[SrRuthenate]

Quote from SrRuthenate:

So for the exit, do you get out at the predicted mean, or try to guess the meander, or a little of both?.

MAESTRO: Do you have a link for a crash course on cubic splines for beginners?.

 

[goodgoing]

Quote from intradaybill:

Did you mean to say "The product of those two processes creates a third one that has less mean deviation than the original two if the correlation is negative."?

I would think that for RTM startegies one would look at the sum, not the product of the processes. In this case the variance of their sum is equal to the sum of their covariances. In the case that both processes have variance s^2, for simplicity, then the variance of the mean is equal to

s^2 x (1+p)/2

where p is the correlation. We thus see that the variance increases if the processes are positively correlated and decreases if they are negatively correlated.

I was wondering the same. Could MAESTRO have been wrong?