From theory to practice - page 350
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the idea of coming up with some distribution of time intervals, superimposing it on real ticks and getting a Laplace distribution?
Of course, every idea has a right to exist, but I don't think it's going to work because it's all artificial.
I don't think if you impose artificial time intervals on a process without memory, you can make it a process with memory.
https://www.mql5.com/ru/forum/2973/page4#comment_43164
You can analyse the relative price increment - the result is the same. If you take the logarithm of the relative increment - well, try it, it's an interesting curve). This is what Alsu writes.
"Here is a relative increment with a lag of 8
and here is the distribution of the logarithm of relative increment.
Just don't start trying to convince me that it's normal. Here the left tail is much thicker and longer than the right one anyway. It looks more like a gamma, albeit unfolded along the x-axis, well, or something quite exotic. Peaks in the left wing are a consequence of quotes quantization (the left part corresponds to very small changes of Close, and they, as you know, can differ by no more than a Point, hence the observed noise), so they can be easily smeared on the slope, making the left tail even fatter.
Any TF is a ready conversion of BP with uniform thinning over astronomical time. What do we see? An exponential distribution, also if you take the increments close with a minimum lag, the (bilateral exponential)Laplace distribution comes out.http://blog.quantquant.com/blog/statistics_and_probability/317.html
Even exponential reading for ticks is not enough to get rid of "heavy tails" as indicated by several other distributions with high positive kurtosis, including general hyperbolic as a class (combining Laplace, Student, Hyperbolic, Gamma distributions, etc.) A transformation method is needed to obtain stable statistical characteristics of normal distribution. Would like feedback from those who are working in this direction.
Haven't seen it. Can I have a word in private?
the guy took the eurgbp pair and his synthetic eurusd/gbpusd (i.e. the same instrument)
and genuinely wondered why arbitrage hft between the same instrument does not work
philosophy begins with wonder! :)))
I don't think that if you impose artificial time slots on a process without memory, you can make it a process with memory.
Interesting reading:
"The distribution of time intervals between price changes gives us important information about the market." The Weibull distribution is often used to model time intervals in the financial markets
Sony Bank uses a trading system in which foreign exchange rates change according to a first-passage process. Namely, the Sony Bank USD/JPY exchange rate is updated only when the reference market rate fluctuates by more than or equal to 0.1 yen [8]. As a result, in the case of the Sony Bank rate, the average duration between price changes is longer, passing from 7 seconds to 20 minutes .......... ""
https://arxiv.org/pdf/0808.0372.pdf
Why is it so important to achieve a stable distribution of the increments?
Clear as day - then all the known mathematical power for Gaussian processes, Levy processes, etc. - are at your service.
Until such a known distribution of gradients is obtained (and it's impossible to achieve it with uniform readout IMHO), any Golden Grail is out of the question.
There will be a wooden Grail (on the basis of Shelepin's theory, with 1 deal a week, like mine) and nothing more. But, we literally want to rip cash from the tree of life every second, don't we?
There's money for fish again.)
The fact that the noise distribution is known only tells us about the stability of the expectation and variance on average over multiple measurements in the past . It gives no information about further price movements, because the vector of price movement is exactly in the expectation, while it is artificially filtered and reduced to zero.
That is, mathematically such a way of thinking is absurd, and a student who declared such a thing would have been instantly expelled).
Conclusion: it is necessary to look for more scientifically grounded explanation about the Grail, and not something else.) At least for their own peace of mind if everything suddenly works by magic.)
On the other hand, even if mathematically such an explanation is pure illiterate nonsense, but on this point there is another Russian proverb, "the fools are happy", i.e. the Grail, which does not offend anyone, but it is not good to abuse proverbs, because they are based on the practical experience and confirmed statistically by all the rules of mathematical science. ))
There's money for fish again)).
The fact that the noise distribution is known only shows the stability of expectation and dispersion on the average of many measurements in the past . It gives no information about further price movements, because the vector of price movement is exactly in the expectation, while it is artificially filtered and reduced to zero.
That is, mathematically such a way of thinking is absurd, and a student who declared such a thing would have been instantly expelled).
Conclusion: it is necessary to look for more scientifically grounded explanation about the Grail, and not something else.) At least for their own peace of mind if everything suddenly works at will.)
On the other hand, even if mathematically such explanation is pure illiterate nonsense, but on this there is another Russian proverb, "the fools are happy", i.e. the Grail, no offense to anyone, but it is not good to abuse proverbs, because they are based on practical experience and confirmed statistically by all the rules of mathematical science. ))
I do not agree with everything, but it may be taken as a basis. On first reading.))
More money for the fish).
You, uncle, need to finish the first grade of school, for starters. You should only go there with coins, throwing them in different directions. Studying, so to speak. In many years you'll share the results :))).
In general, children with years of experience in white noise should be kicked out of here. They won't let them pull the Grail out of the Russian soil with their teeth. Neither Kolmogorov nor diffusion equations... Pattalom :)))
And sago, consumed inappropriately, can cause harm. (Kozma Prutkov.) Similarly, mathematics).
:))) Yuri, yes I am literally pissed off and pissed off by Teachers. And maths, as you know, I don't have much and it works. It's the diffusion equations in all their glory. But, I've decided to move on - to confirm or disprove Kolmogorov's theory of predicting stationary sequences. Just have started on this path and some obscurantists immediately, interrupting each other, prove that it is impossible. Are they smarter than Kolmogorov? What other experience? Experience of shame? Ugh...