Do you see patterns in Random Walks?

Quote from MAESTRO:

May be we should agree on something first. Do you accept that any deterministic system has to have less complexity than the tools we use to measure it in order to be certain that it is in fact a deterministic system? If a system is more complex than the tools we have to understand it then there is always a part of this system that cannot be explained within the set of available to us tools. (Gödel's incompleteness theorem and Ashby's principle of requisite variety). if that is the case then there is always a process that is too complex for any available set of tools to describe it with any predetermined degree of accuracy. Thus this process is random within this set of observation tools.
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Looks like you want to discuss of deep and subtle concepts and topics using a rather approximative language. Maybe here on ET this kind of approximation is tolerated, but in a specialized forum you would be severely reproached.
It's more or less like a surgeon who wants to make a precision surgery using a rusty chainsaw.

What has the concept of "complexity" to do here ? What "complexity" are you talking about? And what has it to do with Gödel's incompleteness theorem ? (http://mathoverflow.net/questions/3...ness-theorem-and-the-complexity-of-arithmetic)

Looks like you are throwing out arguments pretty "randomly". Also you appear ("this process is random within this set of observation tools") to conceive "randomness" as a state of ignorance. This seems real "randomness" in your sense. ;-))

A "random process" is just a mathematical object with a precise definition. "Probability" needs not to "exists" (provided that we could ever define "existance"), we just proceed from the axioms (Kolmogorov): http://en.wikipedia.org/wiki/Probability_axioms

Just like a "line" does not need to "exists", but it is actually a set of math properties (http://userpages.umbc.edu/~rcampbel/Math306/Axioms/Hilbert.html)

The only "link" of the mathematical construction with the so called "reality" is created by human "intuition".

Tom
 
Quote from MAESTRO:

May be we should agree on something first. Do you accept that any deterministic system has to have less complexity than the tools we use to measure it in order to be certain that it is in fact a deterministic system? If a system is more complex than the tools we have to understand it then there is always a part of this system that cannot be explained within the set of available to us tools. (Gödel's incompleteness theorem and Ashby's principle of requisite variety). if that is the case then there is always a process that is too complex for any available set of tools to describe it with any predetermined degree of accuracy. Thus this process is random within this set of observation tools.
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I do not agree with this conjecture. I find a very loose connection between complexity and randomness. An airplane of today would be an extremely complex, even incomprehensible system for people 500 years ago. Today it is established technology.

I am still waiting for you to present a process that is fundamentally random and whose evolution cannot be described using deterministic principles.

The market is a deterministic process. It is our lack of initial conditions (transactions) that does not allow full prediction.

In the futures pits of the past, locals had a very good understanding of initial conditions because they could see order flow. They could predict the market direction and profit from it.

If you know order flow, predicting the market is an easy task of an algorithmic trader. The problem is lack of data. Not that the market is random.
 
A random process, is the counterpart to a deterministic process (or deterministic system). Instead of dealing with only one possible reality of how the process might develop under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths may be more probable and others less so.

In the simplest possible case (discrete time), a stochastic process amounts to a sequence of random variables known as a time series (for example, Markov chain). Another basic type of a stochastic process is a random field, whose domain is a region of space, in other words, a random function whose arguments are drawn from a range of continuously changing values.

One approach to stochastic processes treats them as functions of one or several deterministic arguments (inputs, in most cases regarded as time) whose values (outputs) are random variables: non-deterministic (single) quantities which have certain probability distributions.

Random variables corresponding to various times (or points, in the case of random fields) may be completely different. The main requirement is that these different random quantities all have the same type (Mathematically speaking, the type refers to the codomain of the function).

Although the random values of a stochastic process at different times may be independent random variables, in most commonly considered situations they exhibit complicated statistical correlations.

Familiar examples of processes modeled as stochastic time series include signals such as speech, audio and video, medical data such as a patient's EKG, EEG, blood pressure or temperature.

Examples of random fields include static images, random terrain (landscapes), or composition variations of a heterogeneous material.
 
Quote from MAESTRO:

A random process, is the counterpart to a deterministic process (or deterministic system). Instead of dealing with only one possible reality of how the process might develop under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths may be more probable and others less so.

In the simplest possible case (discrete time), a stochastic process amounts to a sequence of random variables known as a time series (for example, Markov chain). Another basic type of a stochastic process is a random field, whose domain is a region of space, in other words, a random function whose arguments are drawn from a range of continuously changing values.

One approach to stochastic processes treats them as functions of one or several deterministic arguments (inputs, in most cases regarded as time) whose values (outputs) are random variables: non-deterministic (single) quantities which have certain probability distributions.

Random variables corresponding to various times (or points, in the case of random fields) may be completely different. The main requirement is that these different random quantities all have the same type (Mathematically speaking, the type refers to the codomain of the function).

Although the random values of a stochastic process at different times may be independent random variables, in most commonly considered situations they exhibit complicated statistical correlations.

Familiar examples of processes modeled as stochastic time series include signals such as speech, audio and video, medical data such as a patient's EKG, EEG, blood pressure or temperature.

Examples of random fields include static images, random terrain (landscapes), or composition variations of a heterogeneous material.
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Thanks for letting us know what wikipedia says

(http://en.wikipedia.org/wiki/Stochastic_process)

you must be really bored... to spend your time teasing people ... ;-))


Tom
 
Quote from fullautotrading:

Thanks for letting us know what vikipedia says

(http://en.wikipedia.org/wiki/Stochastic_process)

you must be really bored... to spend your time teasing people ... ;-))


Tom
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I have tried many times posting the link to this definition, however, short of retyping it I really do not know what else I can add. This really summarizes my point of view. That is all. I cannot say it any better. Also, if you read who contributed this definition to Wikipedia (not "vikipedia") you might understand why I quoted it.
 
Quote from MAESTRO:

I have tried many times posting the link to this definition, however, short of retyping it I really do not know what else I can add. This really summarizes my point of view. That is all. I cannot say it any better. Also, if you read who contributed this definition to Wikipedia (not "vikipedia") you might understand why I quoted it.
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I am happy to see you read and understood "derailing for dummies"
http://www.derailingfordummies.com/

"vikipedia" is good enough to respond to your level of approximation. In your, case i could even say: "vikicacca"

Or do you expect people bother check the spelling to respond to any troll throwing around random arguments and pasting from the web ?

If you have so much time in your hand, i just have something for you to help me and to use your time in a more constructive way ;-))


Tom
 
Quote from fullautotrading:

I am happy to see you read and understood "derailing for dummies"
http://www.derailingfordummies.com/

"vikipedia" is good enough to respond to your level of approximation. In your, case i could even say: "vikicacca"

Or do you expect people bother check the spelling to respond to any troll throwing around random arguments and pasting from the web ?

If you have so much time in your hand, i just have something for you to help me and to use your time in a more constructive way ;-))


Tom
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You are right, of course! What was I thinking! I should not waste my time. Thank you so much for your timely advice. Being a "troll" I completely forget sometimes that for any speaker there should be at least one listener. I shall indeed focus on something more productive.

Cheers,
MAESTRO
 
Quote from MAESTRO:

You are right, of course! What was I thinking! I should not waste my time. Thank you so much for your timely advice. Being a "troll" I completely forget sometimes that for any speaker there should be at least one listener. I shall indeed focus on something more productive.

Cheers,
MAESTRO
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Right, infact <b>MAESTRO</b> (which means "teacher" or "master") is evidently just a perfect nickname for one who wants to humbly listen and learn, and not instead professorially educate us, poor ignorant rednecks, who evidently know nothing about trading... ;-))

Tom
 
IMO let us refrain from ad hominen attacks, direct or indirect, and agree to the fact that randomness and determinism are metaphysical issues and as far as logical thinking goes red herrings.

The practicle issue is whether simplicity can predict/model complexity and to what extend.
 
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