Random Flow Theory and FOREX - page 66
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The fact that the distribution is normal does not say that you can make money on it, nor does it say that you can't. NR is not characterized by returning to the mean (it does not say anything about the presence of memory in the series). The recurrence to the mean (or vice versa) is called persistence and is measured in Hursts for example. The fact that the series with the normal distribution of increments or stationary series form a flat is also wrong. Remember at least the Arxinus theorem.
SB can be generated by stationary series of increments as well as non-stationary ones. You can with a coin - the eagle/dash series is stationary and incidentally normal if you take the increments from a significant fixed number of throws. SB is a fiction, an abstraction. It is impossible to make money on it by definition if we base it only on previous values of a series because it has no memory by definition. The fact that a series is normal or abnormal, stationary or non-stationary does not classify it as a SB. Moreover, there is no test that says that the series is SB.
Just before you say anything, we need to find out the properties. And we (at least to me) do not know them.
So the answer was purely hypothetical, just like the statement "You can't make money from this process - that's the mathematical result", which is simply nonsense and the result of an incorrect statement of the problem.
Before asserting anything you should at least understand it. Moreover, it is not recommended to call something nonsense without sufficient grounds.
Martingale is known to be a game with zero mathematical expectation. Regardless of the form and properties of the distribution of events in this game. The mentioned mathematical result is obtained exactly for the martingale. Any other questions ?
Personally, I've had enough of the normal distribution so far, although fellow wrestlers are actively wooing me with stable. Naturally, these are special cases, and as far as I know, there is no general solution.
Now I see what you mean. It's a fractal distribution that Peters writes about in his "Fractal analysis of financial markets", for example. It, too, has no explicit closed-form expression in the general case.
Well, they have their own problems, I will not go into details. All the more so because it is the distribution not of the price itself, but of its returns. And its parameters also seriously drift with time.
P.S. To be honest, after a certain period of interest I have cooled down to this topic - it seems finally. Of course Peters' researches are interesting, but they are tightly bound to a given way of representing information - the usual, standard bars on which 95% of traders trade. You can study the peculiarities of world perception through a fly's eye indefinitely, but we will not have a serious shift in our understanding of the world until we realise that there are also other living beings who perceive the world differently.
There are options for making a steady income from the occasional wandering price process as well. Two men received a Nobel Prize for this idea,
I make a steady 10-20% per month on this "miracle" of the amount of capital raised (not to be confused with the deposit).
Timbo, it's good to have you back here again. I remind you of my request for the names of these two men and a link to their work.
You're a stickler for evidence and specificity. Now, if you'd be so kind as to back that up. I'm not talking about your income, I'm talking about Nobel laureates.
Keep in mind that 97% of probability theory and statistics formulas refer to normal distribution of a random variable. If its distribution differs in any way from the normal distribution or from the "standard dozen", the formulas simply do not work. But before applying the robust one (there is not much of it yet) you should have the distribution function at hand, and I would ask you to clarify - how do you or anyone else know the distribution of our price series and if there is such a thing as "probability distribution" for a currency series?
I am shocked at the difference between the two and everything stops working at once.
The fact that the distribution is normal does not mean that you can make money on it, nor does it mean that you can't.
It's more likely that you can than not, or rather, you should.
The chart shows the price per share, it is not the first difference, it is the sum. The standard deviation is 35 cents. There are tails - these are gaps at the holidays. It is well seen how the volatility at the end decreases, it is not difficult to calculate it. ACF = -5-20%, which increases the return even more.
You can rather than can't, or rather should.
The chart shows the price per share, it is not the first difference, it is the sum. The standard deviation is 35 cents. There are tails - these are gaps at the holidays. It is well visible how the volatility decreases at the end, it is not difficult to calculate it.
I was talking about the cumulative sum, not just the distribution of the increments.
By the way, your distribution graph in the previous post doesn't look like HP. What is the sigma?
Z.I. And volatility is indeed quite predictable. Especially FX intraday. There are also its good mathematical models like GARCH. It was awarded a Nobel for it, maybe Timbo meant it
The fact that a series with a normal distribution of increments or a stationary series forms a flat is also incorrect. Think at least of the arcsinus theorem.
And this is correct.
The GSC with a normal distribution and the standard deviation equals EUR.
Timbo, it's good to have you back here again. I remind you of my request for the names of these two men and a link to their work.
You are an advocate of evidence and specificity. Now, if you'd be so kind as to back that up. I'm not talking about your income, I'm talking about Nobel laureates.
I told you right off the bat it would remain the ninth wonder of the world. Keep trumpeting about "stationary random wandering".
I told you straight out that for you it would remain the 'tymbic ninth wonder of the world'. Keep prattling on about "stationary random walk".
The standard example with a coin and its cumulative sum is an example of a stationary series ideally forming a SB