From theory to practice - page 26
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N is not the general population, right? It is a sample volume. I.e. if you plot a histogram of this sample volume, you will get the current value of variance for this sample volume and nothing else. There is no history, i.e. averaged variance for a given sample size, conventionally for a million such samples. Right?
Right, but then you write that "we'll take the average variance over all available historical data". What's that got to do with Markov or non-Markov? Markov didn't impose any conditions on the sample size.)
And what does the average variance over the entire history give you? It is a "hospital average", the current (in your terms) variance will constantly change slightly.
Then you can substitute a constant for the average variance as well.)
In terms of ticks you are currently working on - "current" is ONE last tick, and all previous ticks are history. And Bollinger works with N historical values.
If it goes without saying that there are people here who know about mathematics and programming I can offer to solve one simple problem, namely:
Take GBPUSD as an example
Count quantity and quality of ticks
1) total of 100%
2) percentage of ticks in one direction (i.e. the next tick goes in the same direction, making a combination)
2+ ticks
3+ pcs.
4+ pcs.
3) segments
2017.11.29.00.00-2017.12.01.00.00
2017.10.13.00.00-2017.10.16.00.00
Right, but then you write that "we'll take the average variance over all available historical data". What's that got to do with Markov or non-Markov? Markov didn't impose any conditions on the sample size.)
And what does the average variance over the entire history give you? It is a "hospital average", the current (in your terms) variance will constantly change slightly.
Then you can substitute a constant for the average variance)
Exactly! Here, hats off to you - you can do that too. To do this, calculate the average variance over a VERY large data archive for a certain sample size.
And not only that! You've seen from the model that trades are not captured there as soon as the price goes outside certain limits, right? This is also where nonparametric scew works. And the current value and the averaged value of history work too. You may be surprised that the historical average nonparametric scew is almost a constant. And we simply compare the current parameter with it.
In general, this topic was born as a consequence of my analysis of historical and current statistics.
Who else can tell me how to calculate the NE PARAMETRICAL coefficient of kurtosis?
Well, gentlemen programmers - I've practically covered everything. You may use it. I'm not sorry!
No, Michael - it is the time intervals between ticks that we need a histogram. Eventually we have to reduce everything to a finite-difference equation scheme with a certain sampling time T. What would be the sampling time if we read EVERY tick? The answer is none. No equation can be solved in this case. That's right!
Where do you get such hopeless answers? Is it simply because there are no variational methods in Wissim? What, now fit the data to the available solution methods, or discard them as unsuitable for the method?
Yes, the time grid will have a non-permanent step, which is death for difference methods. And it's no good or bad for variational methods. Here is the link http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=rm&paperid=8488&option_lang=rus, where you can find and download the book of 1950 "S. G. Michlin, Variational methods for solving problems in mathematical physics, UMN, 1950, vol. 5, issue 6(40), 3-51". Already the first two methods in the table of contents, Ritz and orthogonal projections, show that variational methods do not need finite differences and uniformity of the grid, but use the apparatus of scalar products, otherwise called integral sums. You wrote about a cat in Hilbert space, and this is the space (of functions) in which scalar multiplication operations are defined.
What is the problem, why do we need difference schemes?
The rest of the physics-mathematics has been described here for a better understanding of what is going on in the market. At the end of the day, in any case, the one who most accurately describes the measure of central tendency (in my view, that's WMA), variance (in my view, that's weighted variance), who most accurately handles the historical data, etc., will still have more profits.
Eh...
Not even willing to part with you... But you'll have to!
I'll see you at the trading robot tournament? :))))
Good luck, everyone!
Sincerely,
Alexander,
aka Alexander_K
aka Alexander_K2
:))))))))))))))))))))))
That's it?
Is that it?
She said she would walk to the wind )))))
The forum is karma.
Is that it?
No. I'm always sort of here as Schrodinger's cat in Hilbert space :)))))))))))
No. I'm always kind of like Schrodinger's cat in Hilbert space here :)))))))))))
What was all that sighing and shouting about?
========================================
ss
I'm '61, what year are you, Alexander?
Thanks for sharing, of course, you have interesting ideas, but to be honest, I don't really see what can be used here yet, I suspect the result will not be much better than bollinger)
Three trades in the plus is great, but you as a mathematician should understand that for more or less reliable estimate you need at least several dozens of trades? How many deals did you observe on your demo account?
And there is another detail. All drawings - both yours and Bollinger's - are coming from moving average. But you are trading not deviations from the average, but the price in its pure form. And the moving average is not a very reliable reference point, because it shifts behind the price. And if in respect to the MA, the price can go out of the channel and return to it, then it can in fact, relative to some reference level, continue going out. In practice, this means either a loss or a drawdown. Do you have an understanding of this process, can you comment on it?
Generally, the fact that the price is in some distant place does not mean that it will come back. Traders call it mean reversion, but it must be found and proved with different methods, if I am not mistaken, in terms of mathematics - conditional distributions (dependence of future price CHANGE on the previous change). Now, this dependence is indeed detectable on ticks and further on in all time scales and price derivative calculations, so it does not really matter which tool is used to exploit it. But this dependence is usually very weak and insufficient for stable earnings and covering costs. It will be all the more interesting to see what you come up with.