Distribution of price increments - page 4
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Thanks for the links! Interesting enough.
It seems that the creators of these GARCH models are very close to the solution.
Do people using the GARCH models have bad results? And where can we read these trading results? I can suppose that their situation is bad - they don't know exactly for which currency pair a t-distribution must be used, because although for all currency pairs a t2-distribution must be used, for each pair there is a different scale factor, different from 1. This adds complexity to calculations.
Sincerely,
Alexander_K
You're welcome. I can provide many such tables - for any currency pair whose quotes are provided by a broker.
I interpret zero increments on a mundane level - as if a currency exchanger had increased the buy price and left the sell price the same as it was the previous day.
You don't need a lot of tables, it's the methodology of analysis that counts.
Having read the wikipedia"Student's distribution", I did not notice a single example where the histogram of frequencies had a dip to zero in the middle. I note that you weren't talking about any joint distribution of two random variables at all. In the first post you talked about analyzing two different series, Bid and Ask.
If you leave only meaningful data about changes in Ask rate, which are not zero, there is a dip in the middle of the histogram of frequencies of occurrence. The width of the gap for your data is two five-digit points, while in the 4-digit DC there will be twenty five-digit points. Does this have any effect on the fact that it is the t-distribution of the Student with 2 degrees of freedom that will be most appropriate? This is a no-nonsense inference, it means that there is no variance in the increments... I wouldn't draw such a serious conclusion based on "mundane" additions to the histogram of frequencies. How do you justify your conclusion about the type of distribution?
You don't need many tables. What's important is the analysis methodology.
After reading the wikipedia "Student's distribution", I didn't notice any examples where the histogram of frequencies had a dip to zero in the middle. Note that you weren't talking about any joint distribution of two random variables at all. In the first post you talked about analyzing two different series, Bid and Ask.
If we leave only meaningful data on changes of Ask rate, which is not zero, we will have a dip in the middle of frequency histogram. The width of the gap for your data is two five-digit points, while in the 4-digit DC there will be twenty five-digit points. Does this have any effect on the fact that it is the t-distribution of the Student with 2 degrees of freedom that will be most appropriate? This is a no-nonsense inference, it means that there is no variance in the increments... I wouldn't draw such a serious conclusion based on "mundane" additions to the frequency histogram. How do you justify your conclusion about the type of distribution?
Yes, that's a question that must surely be answered - so I'm back for a while :)
1. I don't see any dips in the Ask increment histogram - look at the "pockets" of values to the left of the histogram. Everything is quite nice and rigorous. At zero is the maximum value, and then in descending order. The same will be for Bid. If you use any combination of Ask and Bid, the histogram will lose its shape.
2. Most importantly. Here are the formulas:
Distribution function: F(x) = (1+(x/sqrt(s^2+x^2))/2
Probability density: P(x) = 1/sqrt((s^2+x^2)^3)
Quantile function: Q(p) = 2*s*(p-1/2)*sqrt(2/a), where a=4*p*(1-p)
The following notations apply:
X - price increment
S - scale factor (not equal to standard deviation in general)
Check it yourself for the EURUSD pair, for which s=1.647.
3. These formulas are a special case of the non-standardized t-distribution and can be found in the literature on the Student's distribution with 2 degrees of freedom.
4. I have obtained many different distributions using random number generators, but this is the one that most accurately describes price increments. Once again, it is the same for all currency pairs, just a different coefficient s for each currency pair.
5. And now I want to know what to do with it. They advised to study the GARCH model, and I will do that in the nearest future.
Sincerely,
Alexander_K
Thanks for the links! Interesting enough.
It seems that the creators of these GARCH models are very close to the solution.
Do people using the GARCH models have bad results? And where can we read these trading results? I can suppose that their situation is bad - they don't know exactly for which currency pair a t-distribution must be used, because although for all currency pairs a t2-distribution must be used, each pair has its own coefficient of scale, different from 1. This adds complexity to calculations.
Sincerely,
Alexander_K
Well, in general, this model is studied even in universities, it's kind of common and there's nothing wrong with it. I look from the point of view of an individual trader. Probably some organizations with great experience and base are benefiting from it, at least they can estimate risks for portfolios and etc. But in terms of forex speculation I have not seen examples of effective use, again, as you have noted, maybe because of the complexity of statanalysis and the models themselves. I.e. there are no examples, maybe someone has them and will throw in some links. SanSanych suggested something, I will have to look into it.
Well, in general, this model is even taught at universities, it's kind of universally accepted and there's nothing wrong with it. I am looking at it from the point of view of an individual trader. Probably some organizations with great experience and base are benefiting from it, at least they can assess risks for portfolios and so on. But in terms of forex speculation I have not encountered examples of effective use, and again, as you have noted, perhaps due to difficulties in statanalysis and the models themselves.
Good day Maxim!
I have an old Soviet education, when this was unheard of. My daughter simply asked me to analyze these increments, so I did it.
At the moment I simply have no idea - how to apply these beautiful formulas and graphs in practice. Now I'm going to study GARCH - if there is a really solid theory proved by practical results, I'll provide my daughter with money for this game :)))
Regards,
Alexander_K
Good afternoon, Maxim!
I still have that old Soviet education, when this was unheard of. My daughter simply asked me to analyse these increments, so I did it.
At the moment I simply have no idea - how to apply these beautiful formulas and graphs in practice. Now I'm going to study GARCH - if there is a really solid theory proved by practical results, I'll allocate money for my daughter for this game :)))
Regards,
Alexander_K
Here's more notes from a practicing trader http://www.quantalgos.ru/?s=garch who has a serious grasp of the mathematical apparatus and models.
His blog is interesting in general. I myself don't know and haven't mastered a lot of things.
Yes, this question must definitely be answered - so I'm back for a while :)
1. I don't see any dips in the Ask increment histogram - look to the left of the histogram for "pockets" of values. Everything is quite nice and rigorous. At zero is the maximum value, and then in descending order. The same will be for Bid. But if you use any combination of Ask and Bid, the histogram will lose its shape.
I didn't just ask you to comment on the second picture at https://www.mql5.com/ru/forum/218475/page2#comment_5989670. It shows that the frequency of price increments in the Bid series was much lower than in the Ask series. This is in reality. You, on the other hand, when inserting the illegal values of price increments to zero in cases where the change was in the other row, the total number of price increments for the two different rows is always the same. This is a sign of falsification of the data. The object of analysis is substituted, the events that took place in the other series are inserted into the Ask series of increments.
The analysis by your methodology of Ask series is not possible if there is no Bid series. It does not make sense as a row analysis technique, it requires two rows at once.
Great.
Simply speaking, a certain value of price increment corresponds to a certain value (see the probability density formula in my posts above) of the probability of occurrence of such increment (the so-called weight), knowing that the increment distribution is a t2-distribution with coefficient s. Thus,for the real price Bid or Ask, for a certain sample size, we can obtain a conditional estimate of mathematical expectation Bid or Ask as weighted average and conditional estimate of price variance as weighted di
Further, treating that sample size as a dynamic FIFO-type series and averaging the weighted variance, we obtain for our moving average of the mathematical expectation a certain conditional mean variance.
If this conditional variance is exceeded, a trade can be executed.
But this reasoning still has some weak links - the uncertainty of the necessary sample volume (in fact - the choice of timeframe) and the uncertainty of the volume of history tick data (the averaging should be performed for 1000000 tick history data or more?)
I will read further. If anyone has any ideas - write them down.
There is a reason I asked you to comment on the second figure in https://www.mql5.com/ru/forum/218475/page2#comment_5989670. It shows that the frequency of price increments in the Bid series was much lower than in the Ask series. This is in reality. You, on the other hand, when inserting the illegal values of price increments to zero in cases where the change was in the other row, the total number of price increments for the two different rows is always the same. This is a sign of falsification of the data. The object of analysis is being substituted, the events which took place in the other series are inserted into the series of Ask increments.
Analysis by your methodology of Ask series is not possible if there is no Bid series. It does not make sense as a row analysis methodology, it requires two rows at once.
Once again, I was collecting data from a randomly selected broker (I'm not even going to say which one, so as not to advertise) from a demo NDD account.
Perhaps, the demo server gives out part of the wrong data or vice versa - I will not argue. But still, from a practical point of view, I can't demand more accuracy from a broker (probably this is a futile way), and worked with what I have.
Great.
Simply put, a particular value of the price increment corresponds to a particular value (see the probability density formula in my posts above) of the probability of that increment occurring (the so-called weight), ...
If anyone has any ideas - write them down.
I suppose that taking bare increments and working with them is not very effective. Gradients should be tied to some context (filter, events, conditions). It would be more correct to differentiate (divide) the time series into components and process them separately. Such features can be: