The St Petersburg phenomenon. The paradoxes of probability theory. - page 16
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Checking"how much of its distribution differs from what it would be if prices were a random walk" is not particularly valuable or useful.
Even the wording itself is wrong:"If the difference is statistically significant, then it can indicate the possibility of trading". That is, otherwise trading is impossible, according to you.
This is a deep delusion. You have accepted a false premise as an axiom without even trying to verify it.
Think about the fact that the trading process is external to the price series being traded.
The statistics of the trading process are not reducible to the statistics of the price series being traded.
Conduct an experiment:
1. Generate a SB process.
2. Apply the trading rules to this SB process.
3. Ensure that it is possible to trade successfully on this SB process.
4. Repeat steps 1,2,3 many times, recording the results of the experiments.
5. Confirm the fallacy of the postulate that it is impossible to trade successfully on the SB process.
6. Determine the statistics of the trading process.
7. Compare the statistics of the trading process with the statistics of the SB process.
8. Finally, draw conclusions.
If you dare to do such an experiment, its results, if you present them here, will help you and many others to open their eyes and get rid of the closed-mindedness artificially created and thoughtlessly accepted, like the ubiquitous theory-delusion about "market efficiency". I hope this "market efficiency" fallacy doesn't mislead you.
SO
And what program you do it in (R or not) is a different matter.
The positive results of trading in the experimenter's SB process (with the condition of having a spread, corresponding to the average volatility of a simulated trading instrument in the corresponding scale of absolute values of the current price) are possible in the presence of a profitable strategy in the SB of the experimenter. And if the experimenter does not have a profitable strategy for trading on the SB, can we say that profitable trading on the SB is impossible? - No, of course one cannot draw such a conclusion, and even less can one draw corresponding conclusions about the absence/availability of profitable strategies on real market data.
However, the expression "Trading process statistics is not reducible to the statistics of the price series on which the trade is made" at first glance, and at second glance too, does not contain logically incorrect assumptions and conclusions, imho of course.
Generally speaking, paradoxes in themselves indicate the presence of cockroaches in people's heads and nothing more, i.e. the presence of certain thought patterns which are useful in general cases and useless (and sometimes harmful) in private ones. Kudos to Starter for the topic, it's amusing.
Positive results of the experimenter's trade in the SB process (with the condition of the spread corresponding to the average volatility of the simulated trading instrument in the corresponding scale of absolute values of the current price) are possible if the experimenter actually has a profitable strategy on the SB. And if the experimenter does not have a profitable strategy for trading on the SB, can we say that profitable trading on the SB is impossible? - No, of course not. And you cannot draw corresponding conclusions about the absence/availability of profitable strategies on real market data.
However, the expression "Trading process statistics is not reducible to the statistics of the price series being traded" at first glance, and at second glance too, does not contain logically incorrect assumptions and conclusions, imho of course.
Quite right.
Absolutely right.
Prepare enlightened spirit
And experience, son of hard errors,
And genius, paradoxes friend,
And chance, the god of invention...
(C) Pushkin, who is AS.
A.S. Pushkin
A green oak tree by the Lukomorye
From "Ruslan and Lyudmila".
A green oak tree by the Lukomorye;
The golden chain on that oak:
And by day and by night a learned cat
He walks round the chain all the time;
To the right, he sings a song,
To the left he tells a tale.
There's a miracle: there's a fairy wandering around,
The mermaid sits on the branches;
There on unknown paths
The footsteps of unseen beasts;
There's a hut on chicken legs
There's a hut with no windows and no doors;
The forest and the dale are full of visions;
The waves will come in at dawn
On a sandy and empty shore,
And thirty fine knights
come out of the clear waters in a row,
And with them their uncle of the sea;
And there, the queen's man, in passing.
and there, the queen's king is captured in passing;
There in the clouds before the people
Across the forests, across the seas.
The sorcerer carries the hero;
In the dungeon there the tsarina languishes,
And the brown wolf serves her faithfully;
There's a stupa with Baba Yaga
and the wolf walks on its own,
There the tsar Kashchey woos over the gold;
There's the Russian spirit... There's the smell of Russia!
I've been there, I've drunk honey;
By the sea I saw a green oak tree;
I sat beneath it, and the scholarly cat
and the scholarly cat told me his tales.
Pushkin is certainly a genius.
Checking"how much of its distribution differs from what it would be if prices were a random walk" is not particularly valuable or useful.
Even the wording itself is wrong:"If the difference is statistically significant, then it can indicate the possibility of trading". That is, otherwise trading is impossible, according to you.
This is a deep delusion. You have accepted a false premise as an axiom without even trying to verify it.
Think about the fact that the trading process is external to the price series being traded.
The statistics of the trading process are not reducible to the statistics of the price series at which the trade is made.
Conduct an experiment:
1. Generate a SB process.
2. Apply the trading rules to this SB process.
3. Ensure that it is possible to trade successfully on this SB process.
4. Repeat steps 1,2,3 many times, recording the results of the experiments.
5. Confirm the fallacy of the postulate that it is impossible to trade successfully on the SB process.
6. Determine the statistics of the trading process.
7. Compare the statistics of the trading process with the statistics of the SB process.
8. Finally, draw conclusions.
If you decide to do such an experiment, its results, if you present them here, will help you and many others to open their eyes and get rid of the closed-mindedness artificially created and thoughtlessly accepted, like the ubiquitous theory-delusion about "market efficiency". I hope this "market efficiency" fallacy doesn't mislead you.
SO
What program you do it in (R or not) is a matter of ten.
You are mistakenly confusing two concepts:
1) a random process
2) a finite set of its realizations (in a finite number of points in time).
The capital curve of any trading system on a random walk with no drift (no trend) will be a martingale - a random process with a zero mean. This is a strict mathematical fact, proved through the representation of this curve by Ito's stochastic integral.
But. For any particular implementation of this random walk, it is possible to come up with a profitable TS (fitting). Perhaps this TS will be profitable on several other realizations of SB. But if there are very many such profitable implementations, it will most likely only indicate the poor quality of the pseudorandom number generator used.
6H, max. deflection. So it all comes back to square one.
No, the answer must be expressed as a number between zero and one (probability)
Do you know the Hearst distribution law for a random walk (Wiener process)?
Hearst has been studied up and down.
Clearly, it's a cakewalk.
...
The capital curve of any trading system on a random walk with no drift (no trend) will be a martingale - a random process with zero mean. This is a strict mathematical fact, proved through the representation of this curve by Ito's stochastic integral.
...
A strong statement. Strong enough to create the fact of the statement itself a need to provide pruphs.
It is interesting to see that brave theorist who was able to describe in general terms the mataparatum of "any trading system", confirming private cases as well, without exceptions.
Checking"how much of its distribution differs from what it would be if prices were a random walk" is not particularly valuable or useful.
Even the wording itself is wrong:"If the difference is statistically significant, then it can indicate the possibility of trading". That is, otherwise trading is impossible, according to you.
This is a deep delusion. You have accepted a false premise as an axiom, without even trying to verify it (here is the paradox).
Think about the fact that the trading process is external to the price series being traded.
The statistics of the trading process are not reducible to the statistics of the price series at which the trade is made.
Conduct an experiment:
1. Generate a SB process.
2. Apply the trading rules to this SB process.
3. Ensure that it is possible to trade successfully on this SB process.
4. Repeat steps 1,2,3 many times, recording the results of the experiments.
5. Confirm the fallacy of the postulate that it is impossible to trade successfully on the SB process.
6. Determine the statistics of the trading process.
7. Compare the statistics of the trading process with the statistics of the SB process.
8. Finally, draw conclusions.
If you dare to do such an experiment, its results, if you present them here, will help you and many others to open their eyes and get rid of the closed-mindedness artificially created and thoughtlessly accepted, like the ubiquitous theory-delusion about "market efficiency". I hope this "market efficiency" fallacy doesn't mislead you.
SO
What program you do it in (R or not) is a moot point.
You are mistakenly confusing two concepts:
1) a random process
2) a finite set of its realizations
The capital curve of any trading system on a random walk with no drift (no trend) will be a martingale - a random process with zero mean. This is a strict mathematical fact, proved through the representation of this curve by Ito's stochastic integral.
But. For any particular implementation of this random walk, it is possible to come up with a profitable TS (fitting). Perhaps this TS will be profitable on several other implementations of SB. But if there are very many such implementations, it would probably only indicate the poor quality of the pseudorandom number generator used.
1) No, no, I'm not mixing these two notions, I'm just suggesting that you make an experiment, but I see that you don't intend to do that, and in vain.
2) Please give me a link to this rigorous mathematical fact, so that together we can look and see the full picture, and not just the dry residue, but also see and understand the conditions of its derivation and application. I would not be surprised if in this proof it turns out that the trading system is described as a Wiener process. After all, otherwise the application of Ito's stochastic integral is, to put it mildly, incorrect. I hope you're not going to deny that a trading system must not be a Wiener process. Quite the contrary ;))
3) Well, everything here is very familiar in general (label fitting, etc.)... That is, if the facts don't fit the theory, so much the worse for the facts(???)... well, and the necessary "base" will be summed up by any...