Random Flow Theory and FOREX - page 70
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I propose a deal: I'll reduce variance to "almost 3" and you'll admit that random wandering "almost" is NOT stationary.
That, dear, is the difference between you and me. I don't make deals to save face by disregarding the truth. In the event that I am wrong, I admit it.
In this situation, I used the term "random walk" to refer to a process in which the values of a variable are a random variable. And in that sense I was talking about a normal distribution and all that. This is indeed a mistake. The generally accepted definition for a random walk is the cumulative sum of a random variable and for that process the distribution is certainly both blurred and the variance is time dependent - this is a known fact. So the question turned out to be a terminological one.
As for the variance for the sum of three throws, you can think of it as anything. The "financial mathematicians" seem to have their own calculations. (Help: a bill is an ancient tool for making calculations.) :-)
That, my dear, is the difference between you and me. I don't make deals to save face by disregarding the truth. In the event that I am wrong, I admit it.
In this situation, I used the term "random walk" to refer to a process in which the values of a variable are a random variable. And in that sense I was talking about a normal distribution and all that. This is indeed a mistake. The generally accepted definition for a random walk is the cumulative sum of a random variable and for that process the distribution is certainly both blurred and the variance is time dependent - this is a known fact. So the question turned out to be a terminological one.
You were right, and the fact that the variance depends on sampling time does not make the series non-stationary. It is the changing of the distribution as we get the terms of the series that makes it non-stationary. Which in the case of a monkey can be done by dividing it into series of variable length. For example, by selecting the length of the series randomly. Or changing conditions as you go along, e.g. tucking in different coins, some of which are "curved" (variable MO) or varying the result conditions (e.g. choosing new values randomly instead of +1/-1 - would be variable variance), etc.
You said it right, and just because the variance depends on sampling time doesn't make the series non-stationary. Unsteady makes the distribution change as you get the members of the series. Which in the case of a coin can be done by breaking it up into series of variable length. For example, by selecting the length of the series randomly. Or changing conditions as you go along, e.g. tucking in different coins, some of which are "curved" (variable MO) or alternately changing result conditions (e.g. choosing new values randomly instead of +1/-1 - would be variable variance), etc.
I won't interject, this is your conversation with Timbo. I'm only highlighting the key phrase of the post. It remains to be seen which row you are talking about, the row of coin values or the row of cumulative sum values.
In this situation, I used the term "random walk" to refer to a process in which the values of a variable are a random variable. And in that sense I was talking about a normal distribution and all that. This is indeed a mistake.
26 again... You were saying that you can't make money on random rambling, that it's a martingale, which is true. There is a sidebar there to make money, it's written about it in all modern textbooks, but a miracle is such a miracle. By the way, and the SB's distribution will be normal. I.e. everything is correct. Except for stationarity. Now you pretend the error is "terminological". Well, well...
A stationary random process is like two fingers on the pavement. Or who did you mean by impossibility but stationarity?
A steady-state random process is like two fingers on the pavement. Or who did you mean by impossible but stationary?
It's not entirely clear, though. Take the same series of falling out of coins (for simplicity, not kumm.sum, but the series of +1/-1). This series is stationary? What betting system d.b. to earn on this series if for example by guessing the sum is doubled, otherwise passes the opponent? of course i.e. in case of players with smaller capital loss?
You said that you can't make money on casual wandering, that it's a martingale, which is true. There is a sidebar there to make money, it's written about in all modern textbooks, but a miracle is such a miracle. By the way, and the SB's distribution will be normal. I.e. everything is correct. Except for stationarity. Now you pretend the error is "terminological".
Is it possible to make money on martingale ? Does the normal distribution have an infinite variance ? Or is it time-dependent? And what is the normal distribution in the absence of stationarity ? Why can't everyone make money from what is written in textbooks? Maybe the textbooks are secret?
Till you know variance of three shots you better not to get into more complicated questions.
...? ...? ...? ...? ...? ....?
So much for admitting mistakes. Foggy. One "terminology" question with an automatic line to drown the point... Well, well...
By the way, if you're really interested in answers to the questions posed, then get in touch - "I've got them".
It's not quite clear though. Let's take the same coin series (for simplicity, not the cumulative total, but the series of +1/-1). This series is stationary? What betting system d.b. to earn on this series if for example by guessing the sum is doubled, otherwise passes the opponent? Except of course for the option of ruining the player with smaller capital?
Good question...
The first thing that comes to mind for such a series: from the series of gambling - banal martingale - doubling bets. The player's ruin option you have 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 goes down and I make profit, or the price stays the same and I do not lose anything and I continue waiting.
Guys, you're getting into some kind of jungle. Classical random walk is an absolutely stationary process. The increments are stationary in it, because 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, you cannot "make money" on this stationary process. But on another stationary process, the same classical one, random wandering with drift, you can "make money".
What is there to argue about at all is unclear.