From theory to practice - page 3
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the market is struggling with buying and selling volumes.
Not struggling. In the market, as much is bought, as much is sold. It's always a total equilibrium.
Yep...
Now!
https://www.oanda.com/lang/ru/forex-trading/analysis/open-position-ratios
Consider now the right-hand side of the Fokker-Planck equation, consisting of three terms:
1. The drift M(x,t) is a measure of the central tendency of price movements at a particular sample size. In our case it is a moving weighted average WMA, where the weight w of each tick price value is determined from the probability density of increments for a particular currency pair usingthe formula:
Probability density:
by Mikhail Dovbakh:
s^2/[2*sqrt((s^2+x^2)^3)]
The following notations apply:
X - price increment
S - scale factor (not equal to standard deviation in general).
However, it should still be said that this is an asymptotic formula, and when it comes to money, we all like precision, don't we?
Therefore, in my calculations I use exact probability density values, which I calculated for each currency pair based on historical data.
For EURJPY it looks as follows:
Here, for each value of increment in CASE blocks there are specific probability values separately for Bid and Ask, which are used as weights in calculation of the moving weighted average.
I repeat, the market has no middle ground and the trading process is chaotic.
And this theory is built precisely on the deviation from the middle
There are always more goods bought than sold in a shop!!!It is not difficult to screen out this noise at all. However, I agree that this task (sifting out tick noise) need not be addressed at all.
Lastly for today is to determine the required sample size of tick data for the analysis.
VERY IMPORTANT!
In general, this was the hardest task of all the ones I've encountered on my way. It's clear that the market is self-similar and the TS must work with any sample size. But there are some sample sizes, which are different for various currency pairs, at which the profit level reaches maximum values.
I've made a first attempt to solve this problem in the topic:
https://www.mql5.com/ru/forum/220237/page2
But it did not agree with real trading and that's it... The formula seems to be correct - but something is wrong...
The most important thing - this sample should cover almost all values of increments for a particular currency pair
I performed a series of experiments and understood that the formula for estimating the required sample size looks as follows
N=(Z^2*(S/E)^2)/2, where
Z - quantile of the distribution of increments of a certain currency pair
S - standard deviation
E - precision of measurements
For example, for the EURJPY pair, the quantile of the 0.999 confidence probability is5.337746244, standard deviation =2.99751979 and the sample size turns out to be 12.800. I checked it experimentally - the maximum profit values are indeed obtained.
I can offer the following hypothesis as an explanation of this fact:
Student's t2-distribution formed at the level of price increments NEVER disappears, it forms in one form or another around the measures of the central tendency, in particular for linear deviations of price from the moving weighted average, and reaches maximum similarity when the sample size covers the t2-distribution almost completely.
That's all for today.
Good luck to all!
Looking for a book:
Orlov Y.N., Osminin K.P. Non-stationary time series: methods of
Forecasting Methods with Examples of Financial and Commodity Market Analysis. - М.:
Book House LIBROCOM, 2011. - 384 с.
There is a material close to this theme in preprints:
http://library.keldysh.ru/preprint.asp?id=2013-3
The Student's t2-distribution, having formed at the level of price increments NEVER disappears, it forms in one form or another around measures of central tendency, in particular for linear deviations of price from the moving weighted average, and reaches maximum similarity when the sample size covers the t2-distribution almost completely.
Tell that to those who have survived the franc and the pound...
Looking for a book:
Orlov Y.N., Osminin K.P. Non-stationary time series: methods of
Forecasting Methods with Examples of Financial and Commodity Market Analysis. - М.:
Book House LIBROCOM, 2011. - 384 с.
There is a material close to this subject in preprints:
http://library.keldysh.ru/preprint.asp?id=2013-3
I was interested and searched too. I did not find the book, but found many preprints of the Keldysh Institute and other authors and co-authors. Among them doctoral dissertation "Algorithms for forecasting non-stationary time series" by Osminin, defended in October 2008 under supervision of Dr.Orlov. Orlov in 2009 published a book "Vovk V.S., Novikov A.I., Glagolev A.I., Orlov Y.N., Bychkov V.K., Udalov V.A. World industry and LNG markets: forecast modelling. - Moscow: OOO Gazpromexpo, 2009. - 312 p." and another one in 2012, coauthored with Osminin: "Orlov Y.N., Osminin K.P. Methods of statistical analysis of literary texts. - Moscow: Editorial URSS, 2012. - 312 с.". One can conclude that he and Osminin sometimes change direction, and the book we are looking for reflects results which were already in Osminin's dissertation. I therefore attach the text of the thesis.
Alexander_K, please tell me whether you and the VisSim software system you actively use take into account the inapplicability of classical probability theory to quotations, noted on pg. 4 of Osminin's thesis:
"Whereas in the stationary case there is evidential confidence in the asymptotic consistency of estimates of a particular statistic, in the non-stationary case there is no notion of a general population itself, whichmakes all the developed apparatus of modern mathematical statistics inapplicable, except when the a priori functional identity of the process model is given."
I get the impression that you gravitate towards a single identified type of probability distribution (one of the classical ones, Student's). Is there any methodological error inherent in this?
I became interested and searched too. I did not find the book, but found many preprints of Keldysh Institute and others of these authors and co-authors. Among them is the PhD thesis "Algorithms for forecasting non-stationary time series", defended in late October 2008 under the scientific leadership of Orlov. Orlov in 2009 published a book "Vovk V.S., Novikov A.I., Glagolev A.I., Orlov Y.N., Bychkov V.K., Udalov V.A. World industry and LNG markets: forecast modelling. - Moscow: OOO Gazpromexpo, 2009. - 312 p." and another one in 2012, coauthored with Osminin: "Orlov Y.N., Osminin K.P. Methods of statistical analysis of literary texts. - Moscow: Editorial URSS, 2012. - 312 с.". One can conclude that he and Osminin sometimes change direction, and the book we are looking for reflects results which were already in Osminin's dissertation. I therefore attach the text of the thesis.
Alexander_K, please tell me, do you and the VisSim software system you actively use take into account the inapplicability of classical probability theory to quotes, noted on p. 4 of Osminin's thesis:
"Whereas in the stationary case there is evidential confidence in the asymptotic consistency of estimates of a particular statistic, in the non-stationary case there is no notion of a general population itself, whichmakes all the developed apparatus of modern mathematical statistics inapplicable, except when the a priori functional identity of the process model is given."
I get the impression that you gravitate towards a single identified type of probability distribution (one of the classical ones, Student's). Is there any methodological error inherent in this?
I would also add: "And to the once-identified type of WMA mean", "And to the once-identified method of sampling a sequence of samples"...