Random Flow Theory and FOREX - page 71
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You guys are getting off on the wrong foot here. The classical random walk is an absolutely stationary process. The stationary in it are increments, since it is possible to "wander" there only by increments and in no other way. Therefore, properties of this process are considered as properties of increments. And the fact that there appear "trends" in a number of accumulated values, etc. - this is perfectly explained by the arcsine theorem.
Yes, and most importantly, one cannot "make money" on this stationary process. But on another stationary process, the same classical one, random walk with drift, one can "earn".
It is not clear what there is to argue about.
It all depends on which series to consider. If the increments themselves or series of fixed length, then yes.
If, however, one considers the value of SB itself at each successive step (actually a series of variable increasing length), then Timbo is right it is a non-stationary process. It is denoted as I(1), which means that the first difference is a stationary process http://hometask.boom.ru/economics/econometrica/5.html
In short it's all a maze of course, closer to practice.
Good question...
The first thing that comes to mind for such a series: a series of gambling - banal martingale - doubling the bets. The player's ruin option you've ruled out, which means that the deposit is sufficient. The probability of "failsafe" series can be calculated and on the basis of their own ideas about the "impossible event" choose a bet.
The second option is to consider the process as a traded Asset, and this is the trader's aim - to find a stationary traded process, then if the current price of the Asset is 1, then I'm going downwards - sell short. After that I have two possibilities: either the price went down and I got a profit, or the price stayed at previous level, I have nothing to lose and I continue waiting.
It all depends on which series to consider. If the increments or series themselves are of fixed length, then yes.
If you consider the value of SB itself at each successive step, then Timbo is right it is a non-stationary process. It is denoted as I(1), which means that the first difference is a stationary process http://hometask.boom.ru/economics/econometrica/5.html
Anyway, it's all rubbish of course, we need to get closer to practice.
Actually, this is how the process should be viewed, in particular the coin, as an increment. This is its essence. "The very value of SB at each successive step" is the operation of the arcsine theorem. The process of price formation - may not be a coin at all, at different "investment horizons".
The link "econometric" is such specially bred in secret laboratories creatures - not economists, not bankers, not mathematicians, not traders. It is easy to recognize them, they usually with bulging eyes are talking nonsense about things they do not understand. You must never listen to them, otherwise they will zombify you, rob you of your will and freedom of movement, and take you to their lair to gobble up your brain. :)
In general, the phrase of Comrade Shyryaev, "What kind of process do you have here? - it's brilliant.
>> you've got 666 posts.
Good question...
The first thing that comes to mind for such a series: from a series of gambling - banal martingale - doubling the bets. The option of ruining the player you rejected, which means that the deposit is sufficient. The probability of "failsafe" series can be calculated and on the basis of their own ideas about the "impossible event" choose a bet.
The second option is to consider the process as a traded Asset, and this is the trader's aim - to find a stationary traded process, then if the current price of the Asset is 1, I'm going downwards - sell short. Then there are two options: either the price went down and I made a profit, or the price stayed at the previous level, I have not lost anything and continue to wait.
Oh my God, and with this f....her you were chewing, talking about sideways and about two fingers.
The "econometric" reference are such specially bred creatures in secret laboratories - not economists, not bankers, not mathematicians, not traders. It is easy to recognize them, they usually with bulging eyes are talking nonsense about things they do not understand. You must never listen to them, otherwise they will zombify you, rob you of your will and freedom of movement, and take you to their lair to eat your brain. :)
Thank you, HideYourRichess, otherwise I've already drowned in this blizzard. :-)
I'm gonna stop this silly business.
Actually, this is how the process should be viewed, in particular the coin, as incremental. This is its essence. "The very value of SB at each successive step" is the operation of the arcsine theorem. The process of price formation - may not be a coin at all, at different "investment horizons".
The "econometric" reference are such specially bred beings in secret laboratories - not economists, not bankers, not mathematicians, not traders. It is easy to recognize them, they usually with bulging eyes are talking nonsense about things they do not understand. You must never listen to them, otherwise they will zombify you, rob you of your will and freedom of movement, take you to their lair and eat your brain. :)
In general, the phrase of Comrade Shyryaev, "What kind of process do you have here? - it's brilliant.
666 messages.
Of course it all depends on what kind of series we are considering. And I agree that it makes sense for us to consider increments for obvious reasons.
At the expense of the reference, and in more serious literature sometimes consider in a similar way. Often Dickey and Fuller cannot be called pariahs of serious mathematics.
And by and large it is all unnecessary for practical trading. Just an argument about something important :)
Чего-то я не пойму, так вы всё-таки прямо связываете возможность зарабатывания со стационарностью процесса или не связываете?
Stationarity = earnings.
"If you keep stumping me with your direct questions, I will stump you with my direct answers."
1. Is there any money to be made on martingale? 2. Does the normal distribution have infinite variance ? 3. Or maybe it depends on time ? 4. What is a normal distribution in the absence of stationarity ? 5. Why can't everyone make money from what is written in textbooks ? 6. Maybe the textbooks are secret ?
1. It is common knowledge that you cannot make money on martingale, you cannot make money on random walks. It is also known that an object heavier than air cannot fly without its own thrust. However, under certain conditions it can - for example a hang glider. Similarly, under certain conditions it is possible to make money on a price that is a random walk. This does not contradict the theory.
2. Variance in a normal distribution can be anything.
3. Including can depend on time.
4. There is no need to mix the warm and the soft. A normal distribution is just a normal distribution, stationarity is not a requirement. For details about normal distribution and random walk, including cognitive pictures and formula for calculating variance, see e.g. here - https://en.wikipedia.org/wiki/Random_walk.
5. There are many medical textbooks, why can't everyone become a neurosurgeon?
6. Amazon gives out over two thousand books that talk about this theory/method, dozens of books that are solely dedicated to it, i.e. the textbooks are clearly not secret.
Stationarity = earning.
I would add - virtually guaranteed earnings. Provided that the stationary process is tradable, i.e. it can be bought and sold. There is no money to be made from stationary sound noise.