Volumes, volatility and Hearst index - page 14
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Gentlemen Scientists!
I am of course "wildly sorry", but explain to me "inexperienced" reasons of "Slutsky-Yule paradox/effect".
Otherwise I cannot understand the addition of random variables.
Especially your reasoning on the subject of self-similarities.
Vita:
H = (Log(R2) - Log(R1))/ (Log(N2) - Log(N1))
So where is the standard deviation in this formula here? R2 and R1 are still the average spreads for N2 and N1. The intricacy of the algorithm for calculating Yurix does not change the layout. The algorithm still divides the log of the spread proportional to the root of N by the log of N itself. Again substitution High - Low = k * sqrt(N) works.
Yep, the substitution High - Low = k * sqrt(N) works again - for the fit. But this time the fit is really very distorted.
There is no such formula, there is High - Low = k * (N^h) and h in it is the Hurst index.
There should be no standard deviation in this formula. Unless only as a function of the spread of the RMS.
By the way, your last post, I believe, closes the question. So, I quote
The last term is a constant in theory when n tends to infinity, then k1 = k2, hence the last term is zero. In numerical calculations k1 does not equal k2, therefore in the last column you have 0.5 + error. Everything is very simple and straightforward.
For real instruments the ratio High-Low/|Open-Close|
Roughly speaking, for an average candle each shadow equals half of the body. For SB it seems to converge to two as the series length increases (based on Table 2a of Yurixx R/M). Although at low TF the deviation of real data is significant. It could be explained by a small number of ticks (as on SB with small N), but for example on h1 it should be enough. And on SB on the contrary, the ratio is approaching a double from the bottom to the top:
I'll also repeat my earlier post here
22.08.2010 13:09
I have calculated with a simple script the (High-Low)/(Close-Open) ratio on 1.5 million minute bars.
For AUDUSD on the interval from 2005.11.02 07:49 to 2010.08.20 22:59 the average (H-L)/(C-O) = 1.65539495
for USDJPY on the interval from 2006.04.11 20:21 to 2010.08.20 22:59 the average (H-L)/(C-O) = 1.72965927
for USDCHF on the interval 2006.01.24 04:23 to 2010.08.20 22:59 mean (H-L)/(C-O) = 1.69927897
for USDCAD on the interval from 2005.05.19 13:31 to 2010.08.20 22:59 average (H-L)/(C-O) = 1.62680742
for GBPUSD on the interval from 2006.02.21 23:31 to 2010.08.20 22:59 Average (H-L)/(C-O) = 1.65294349
For EURUSD on the interval from 2006.03.08 13:41 to 2010.08.20 22:59 the average (H-L)/(C-O) = 1.69371256
There is no such formula, there is High - Low = k * (N^h) and h in it is the Hurst index.
For objectivity's sake - what is written has yet to be proven. It may be true and maybe the quoting process is subject to such a power dependence, but h in this formula is exactly Hurst? Although, I may have missed something and you've already proved it. I don't remember exactly, but it seems that the initial assumption of the model was so:
The mathematical expectation of the square of the difference in the increments of the process approximates the modulus of the "number of counts" to some extent. Or so it goes. But there is some "physics" in that. And the written stuff doesn't seem to agree with that, but maybe I got it all wrong, so ignore it. "Extremes" seem to have come later, as an analysis tool and they seem to be investigated as an accumulated sum. Well hell knows - I don't remember from the move.
Yep, the substitution High - Low = k * sqrt(N) you have again works - for the fit. But this time the fit is really very messy.
There is no such formula - High - Low = k * sqrt(N) - this is the correct formula for the average spread, everything else you wrote is irrelevant to my conclusion. there is High - Low = k * (N^h) and h in it is the Hearst index. - I don't need that formula.
There should not be any standard deviation in this formula. Unless only as a function of the spread versus the RMS.
By the way, your last post, I believe, closes the question. So, and I quote - ???
So, here it is written in your own hand that in the formula High - Low = k * sqrt(N) k depends on N. - No, it doesn't say that. k is not functionally dependent on N. You're attributing it to me. So this wonderful formula finally gets a real form: High - Low = k(N) * sqrt(N). - Again, this is your formula. So there is no net 1/2 for the spread. - There's a pure 1/2, as any SB textbook points out. Which is what has been pointed out to you from the beginning. - Once again, I believe that H igh - Low = k * sqrt(N) is the correct formula, consistent with the textbook and even with Jurix's calculations, which is not the case with you. Where is your calculation consistent with the theory?All I have shown is that Jurix's formula "finds an axe under the bench", namely the theorwers dependence of the average run on the root of the steps of the run. Logarithmizing such an average run provides 1/2 stoically. But only for SB. Calculate Hurst using the Hurst formula, for any other series. I suggest you post the calculation here for rows 0, 1, 8, 27, 64, 125, ..., 1000*1000*1000. What do you get? Bullshit, not Hurst. The average of this series, alas and ah, is in no way proportional to the root of N. Jurix's formula cracks at the seams for any series where the average spread depends on the degree N>1, which means it counts anything but Hearst. Just finally give the calculation for the benchmark example, not for SB.
I think I've already explained in sufficient detail the essence of 1/2 in Jurix's formula for SB. It's not Hurst. You've gone for a second round of picking on something I didn't even write. I can imagine why it's easier to pick on than to cite Hurst's calculation of Jurix. Let's leave the scribbling aside. Calculate Hearst for the benchmark example N in a cube. Show the result to everyone so they can repeat it.
For objectivity's sake - what is written, has yet to be proven.
Just to reiterate my earlier post here
22.08.2010 13:09
I have calculated with a simple script the (High-Low)/(Close-Open) ratio on 1.5 million minute bars.
For AUDUSD on the interval from 2005.11.02 07:49 to 2010.08.20 22:59 average (H-L)/(C-O) = 1.65539495
For USDJPY on the interval from 2006.04.11 20:21 to 2010.08.20 22:59 average (H-L)/(C-O) = 1.72965927
For USDCHF on the interval from 2006.01.24 04:23 to 2010.08.20 22:59 average (H-L)/(C-O) = 1.69927897
For USDCAD on the interval from 2005.05.19 13:31 to 2010.08.20 22:59 Average (H-L)/(C-O) = 1.62680742
For GBPUSD on the interval from 2006.02.21 23:31 to 2010.08.20 22:59 Average (H-L)/(C-O) = 1.65294349
For EURUSD on the interval 2006.03.08 13:41 to 2010.08.20 22:59 Average (H-L)/(C-O) = 1.69371256
Yes, it's the same on the minutes. Apparently the same effect as on SB with small N values. On the minutes there are many bars with small tick volume
Of course it is not clear with the tick volumes themselves. For example, here is the distribution of probabilities of the tick volume of minute bars EURUSD of one DC (though not for a very long period)
Some strange falling out in the area of tick volume = 2 and 3. And burst in values 11 and 21. Well 21 is understandable - a point :) The impression is that some bars with volume d.b. 2 or 3 complemented to 11 and 21.
Vita, stop being a cliché. Know how to keep your tone in the discussion. If, of course, you want to find the truth. If you have come to demonstrate your deep understanding of mathematics, then don't bother so much, everyone has already figured it out. Try to imagine that I really want to find common ground with you and try to answer a couple of constructive questions.
1. Give me the exact link to the book and the page in it where the formula High - Low = k * sqrt(N) is given, and the values included in it are defined. Even better, provide the link with a scan of the relevant page. Don't tell me that this formula is in all textbooks.
Explain what you call the value(High-Low) in this formula, what do you mean by High, Low . Do all these values refer to a single trajectory, to a sample or to the whole ensemble. Whether they are averages or local values.
3. Give a definition of the Hearst exponent. Explain where and how it comes from, how it is calculated and what it means.
I am very grateful to you for explaining the essence of 1/2 "in the Jurix formula". Unfortunately, the central point in this thread is quite different - the lack of 1/2 even for pure SB. But there is no need to explain the essence of absence. So far. So far we haven't found an understanding on the questions cited. Better answer them.
And until then no one will calculate any control examples. All the more on artificial and meaningless rows.
All I have shown is that Jurix's formula "finds the axe under the bench", namely the theorwers dependence of the average run on the root of the steps of the run. Logarithmizing such an average run provides 1/2 stoically. But only for SB. Calculate Hurst using the Hurst formula, for any other series. I suggest you post the calculation here for rows 0, 1, 8, 27, 64, 125, ..., 1000*1000*1000. What do you get? Bullshit, not Hurst. The average of this series, alas and ah, is in no way proportional to the root of N. Jurix's formula cracks at the seams for any series where the average spread depends on the degree N>1, which means it counts anything but Hearst. Just finally give the calculation for the benchmark example and not for SB.
I think I've already explained in sufficient detail the point of 1/2 in Jurix's formula for SB. It's not Hurst. You've gone for a second round of picking on something I didn't even write. I can imagine why it's easier to pick on than to cite Hurst's calculation of Jurix. Let's leave the scribbling aside. Calculate Hearst for the benchmark example N in a cube. Show the result to everyone so they can repeat it.
I have run out of arguments.
I can only recommend to remember some basics. If k for N1 is k1 and for N2 is k2, this is called the dependence of k on N. It is synonymous with the formulation: k is a function of N. Formally it is written as k = k(N). So I just translated Vita's phrase into stricter language.
I simply did not understand the passage about problems with calculation of the Hurst exponent for series other than SB. For a moment I had a wild idea whether the author thinks that for any series the Hearst exponent must be 1/2, but I immediately dismissed it.
For series High - Low = k * (N^3) Hearst exponent will be equal to 3.
For the example of Vita 0, 1, 8, 27, 64, 125, ..., 1000*1000*1000 let's take for certain points with N=2 and N=3 (numbering from 0).
So, h=(ln(8)-ln(27))/(ln(2)-ln(3)) = 3*(ln(2)-ln(3))/(ln(2)-ln(3)) = 3.
research on the spread distribution https://www.mql5.com/go?link=http://www.mathnet.ru/php/getFT.phtml?jrnid=sm&paperid=3245&what=fullt&option_lang=rus There seems to be a formula 2.14 for first and second momentum, but something doesn't seem to add up :)
S.I. https://www. mql5.com/go?link=http://83.149.209.141/php/getFT.phtml?jrnid=sm&paperid=3415&what=fullt&option_lang=rus continued
Thanks for the articles. Very interesting. Wanted to see a theoretical approach to calculating the spread a couple of years ago. I'll try to figure it out.