From theory to practice - page 624
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Alexander_K2:
then we would really have a direct analog of the Ornstein-Uhlenbeck process with a return to the average.
So there is no average in forex, i.e. there is no constant mathematical expectation. So there is nothing to return to initially... We may return to the waving as an average, but it does not necessarily help...
Accordingly, the deviation from the average is also a fiction...
Can anyone tell me what distributions with very large kurtosis, similar to Laplace, are symmetric?
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From Theory to Practice
Alexander_K2, 2018.09.28 00:03
Something I'm interested in is this distribution as a model for returnees:
https://en.wikipedia.org/wiki/Skellam_distribution
It is extremely similar to the real incremental distribution and its values are, come to think of it, by difference of two values with Poisson distribution.
If so, one could argue that the price itself has a Poisson distribution relative to the expectation in the sliding window. And Poisson distribution tends to normal with a large sample size...
So, do what you want with me, but the theory of Gaussian, Wiener processes such as Ornstein-Uhlenbeck process with return to the mean has not been fully exhausted.
I suspect we must increase the time intervals between reading tick quotes (specifically - work in high order Erlang's flow) and in a sliding window at least twenty-four hours.
I run my TS with 60th-order Erlang's flow (read once a minute on the average) and window = 24 hours - it will be interesting to compare my quotes later with OPEN/CLOSE M1...
Let there be rare trades (God be with this fact, I'm ready to be patient), but grainy ones.
P.S. I also don't forget about autocorrelation - let's see on longer times whether it is exponentially decreasing as required by Ornstein and Uhlenbeck.
Skellama.
If we consider price as a sum of increments with origin at 0, instead of some initial value, then obviously the current and previous price belong to different Poisson distributions shifted by 1 increment in the sliding window. Expectations of such distributions are always somewhere around 0. The excess is prohibitive.
I think the ancestor of the double geometric distribution (Laplace distribution) we see in Erlang flows is the Skellam distribution.
So there is no such thing as an average in forex, i.e. a constant mate expectation. So there is nothing to go back to initially... You can go back to the waving as an average, but it's not sure it will help either...
Accordingly, the deviation from the average is also a fiction...
I'm getting tired of publishing this picture:
In the second graph - expectation = 0 always and forever...
I'm getting tired of posting this picture:
In the second graph - expectation =0 always and forever.
It's hard to guess what's in the picture again, alas, I can't follow your research, even though I try )))
what is it ? closing price increments on M1 ?
It's hard to guess what's in the picture again, alas, I can't follow your research, even though I try ))))
what is it? closing price increments on M1 ?
I don't really remember... I got confused by the Erlang flows... Drowned...
But the gist is the same - it's the sum of the increments in the sliding window.
I'm getting tired of posting this picture:
In the second graph - expectation=0 always and forever.
And I'm tired of exposing your ignorance.)
You have to trade on the price, not on the second chart. If TC would give out "the second chart" instead of the price - another matter)
In the second graph, expectation=0 always and forever.
Well, if you average over a thousand years, it might be a zero price, but I don't think you will live long enough to wait for that zero).
And I'm getting tired of exposing your ignorance)
You have to trade the price, not your second chart. If the DCs would give you a "second chart" instead of the price - that would be different)
Familiarise yourself with the subject:
http://inis.jinr.ru/sl/vol2/Physics/Динамические%20системы%20и%20Хаос/Федер%20Е.,%20Фракталы,%201991.pdf
OK, the market is fractal. Hearst has been counted. What next? How does this help forecasting?