Distribution of price increments - page 13
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Again I suggest you to comment on the tick increments shown in the just taken picture in the market overview window (USDJPY) and in the trade opening window (EURUSD). Now from the perspective of the three hypotheses quoted above. The account is real.
Don't you want to analyze groups of consecutive changes by one point back and forth? What is their quantile function?
Good afternoon Vladimir!
I think manually trading on tick charts based on visual data is a futile exercise. The distribution function and the quantile function - see t2-distribution Student's distribution.
I've written repeatedly that you need to analyse historical data before analysing the current state. You're following a Markov chain - trying to figure out everything here and now. Since linear deviations of the price increment distribution in a Markov process have the geometric probability density with p=0.5, you can only say here and now - price will go up or down with the probability 0.5. This is exactly the classic game.
I am now modelling the process on the basis of 1.000.000 historical ticks. It is an amazing picture - I cannot believe how price behaves similarly near some boundary conditions. Of course, there are rare and seemingly inexplicable deviations - it means that the boundary conditions must be chosen more strictly. Just think about it - this distribution has only 99 percent of values around 7 sigma and that 1 percent gives everyone a light. But I think it can be handled as well.
Respectfully,
Alexander.
All indicators in the terminal set assume that price formation is not morphic, i.e. the developers of the terminal (any terminal with technical indicators) are already aware of the presence/absence of morphality.
There is a theoretical assumption that markets are fractal, on small TF one may observe the same processes as on large ones - it has not been argued yet, may be it is worth to argue? (humour) https://ru.wikipedia.org/wiki/Фрактальный_анализ_рынка . I.e. someone has already thought about it and proved the non-morkiness of price formation, at least since the appearance of candlestick analysis, when the "tick" waited for a week or a month - figuratively, no carrot.
Good evening, dear traders and just fans of statistics!
I have not indulged you with interesting results of my studies for a long time - I will show them now.
So,the theoretical assumption that markets are fractal and one can observe the same processes on small TFs as on large ones can be practically proved.
It was not an easy task. I needed to find a certain invariant statistical parameter that wouldn't change when increasing/decreasing the sample volume of tick data. This parameter turned out to be nonparametric asymmetry coefficient (nonparametric skew). Perhaps there are some others, but it is enough to prove it.
A dynamic FIFO-type tick data buffer was used in calculations. EURJPY was analyzed on the general data set of 1,500,000 quotes i.e. in fact 1,500,000 sequential samples with 1 quote difference were analyzed. We have received the following results for the average value of skew taken modulo for different volume of samples.
0.186043748375457
0.18560474492056
0.184953481402386
0.184985234902438 etc.
Simply put - for any sample size of tick data, the non-parametric asymmetry coefficient remains constant.
The conclusion is as follows: indeed, small TFs show the same processes as large ones, and a trading system operating on one TF will operate on the other and vice versa.
But what is interesting is that we obtain a quite mystical thing - it turns out that some distribution with a strange mean (I emphasize - mean) nonparametric coefficient of skewness = 0.185 (modulo) "walks" in Forex. I personally do not know such a distribution... Maybe someone can help me determine it?
I.e. in a simple way - at different moments of time this distribution is like "born", "formed" and "dies", and the process starts all over again. At different points in time this distribution has different skew, but on average this distribution is skewed with coefficient = 0.185 and it is invariant.
Until I understand what this distribution in its average form is, there's no point in exploring it further...
Respectfully,
Alexander.
Alexander, your observations are interesting. It would be great if you could write an article on the results of your study inMQL5 Articles on Data Analysis and Statistics.
Alexander, your observations are interesting. It would be great if you could write an article on the results of your study in the "Articles on Data Analysis and Statistics in MQL5" section.
Yes, thank you. I like the results myself - it's fascinating. It's very beautiful.
Methodological question. Why don't you do outliers clearance before fitting an allocation - outliers detection?
And I don't have time to write an article - I'm working and I don't have much time. It turns out to be like a hobby. Maybe someone will get interested and, for example, defend a doctoral thesis - I do not feel sorry for that. And maybe someone will get interested and create a super-trading system - that's fine too. I am still very far away from real programming - let people use it.
Methodological question. Why don't you perform outliers cleaning before fitting the distribution - outliers detection?
Strangely enough, but for most currency pairs the distributions of net increments without processing are t2-distributions, and only for some there is an "under-distribution" of ticks at zero, i.e. when there was trading and Ask and Bid prices remained the same, then no tick comes. I don't know why and I don't work with such pairs (like AUDCHF).
I must not have asked the right question. I downloaded the ticks you posted. So, if you clean up the outliers (very large and very small values in the sample) there, it will be a different distribution :-)
I must not have asked the right question. I downloaded the ticks you posted. So, if you clean the sample from outliers (very large and very small values in the sample), it will be a different distribution :-).
But you shouldn't do this - then you won't get the invariance of skew either. And I say - all very beautiful and as if one follows from another, but to comprehend this depth to form a general picture I can not yet.
But, um, it's standard procedure. To find out how the system behaves in most cases and not in rare ones... By the way, what's the point of taking the whole population? Imho, you have to work with a sample.