Volumes, volatility and Hearst index - page 17
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In theory, if you calculate Hirst on some range of data, and then divide this range into a sufficiently large number of sites and on each of them to calculate Hirst, then their average value should converge to the Hirst coefficient calculated for the whole range. If this is so, the only restriction when you calculate Hirst is that N must be large enough. Judging by your studies, the accuracy at N=15 is already quite high. Therefore, perhaps this is an acceptable number of ticks on which it makes sense to calculate Hirst. And it is not necessary to average N ticks by segments - it will be more exact Hirst calculated within the whole range.
There's something wrong here. Either we don't understand each other, or there is some mistake.
How are you going to calculate Hearst over the whole range? So you have the whole range, you're not going to break it up into intervals, but what are you going to do and how to calculate the Hurst?
Tables 2a and 2b have two values N - the number of samples in the interval, and n is actually Log(N) on base 2. N=15 - this case was not considered at all. But n=15 is really the last line of the table. But just keep in mind, this line investigates the interval N=32768 counts. For reference: according to the very active year 2009, there were 15000 ticks on the average per day. That is the interval N=32768 is more than 2 days.
One such interval will give you just one value for each of the spread and increment (it is necessary to calculate S). How many more do you need to calculate averages? Just for reference, the total number of all SB trajectories that need to be averaged to get a true theoretical average is 2^N, i.e. 2^32768.
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 quantities included in it are defined. Better yet, provide the link with a scan of the relevant page. Just don't tell me that this formula is in all textbooks. - It is my hypothesis. High - Low is your R, k is just the ratio, N is your N
2 Explain what you call the value(High-Low) is your R, the average spread from your formula in this formula, what do you think High, Low are. Do all these values refer to a single trajectory, to a sample, or to the whole ensemble. Are they mean values 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 willing to use the wikipedia one.
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 the 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. Especially by artificial and meaningless rows. - And Hirst was not afraid of control examples. And I'm not afraid of control examples - upload a file, control. But you are afraid to damage your formula with artificial and meaningless series. Nice attempt to cover up the unworkability of your formula.
Pg. .10 contains an mql4-file that actually performs R/S analysis. You are welcome to check it.
There is no point in checking it. I just wanted to see how you calculate it. Since you can't simply describe the algorithm that you think is correct and that you use, you have to go the roundabout route.
Unfortunately, the code is poorly written. There are no comments. The meaning of variables and arrays is not described anywhere. The names of variables and arrays are not associated with anything and do not obey any mnemonics. I do not want to spend time deciphering them and extracting sacramental truths.
Vita, maybe you didn't write it? It can't be that the author can't describe the algorithm of the calculations he programmed.
And you can't. And you can't answer my simple questions either. How can we search for truth with you? :-))
PS
Well, at last the veil of mystery is lifted.
If this formula which you claimed that it is in all textbooks is your hypothesis, then prove it by any correct ways. And if you shout loudly that it is correct, it will hardly help.
My work was precisely to assess the correctness of Hearst's hypothesis, who postulated a more plausible formula. That is, it was the examination of a controlling example. And the result was that his hypothesis is only justified asymptotically. What about your root of N ? It doesn't even hold for SB.
And the wiki doesn't have a root, but it does have an exponent. And also a postscript like this: at n -> infinity, that is exactly what I claimed.
There's no point in checking it. I just wanted to see how you calculate it. Since you are unable to simply describe the algorithm you believe to be correct and which you use, you have to go the roundabout way.
Unfortunately, the code is poorly written. There are no comments. The meaning of variables and arrays is not described anywhere. The names of variables and arrays are not associated with anything and do not obey any mnemonics. I don't want to spend time deciphering them and extracting sacramental truths.
Vita, maybe you didn't write it? It can't be that the author can't describe the algorithm of the calculations he programmed.
And you can't. And you can't answer my simple questions either. How can we search for truth with you? :-))
It's the second attempt to cover impracticality of your formula.
Just post your code and I won't whine that your code has no comments. I'll figure it out. Do you have Hearst's code for your formula?
Give me test examples, give everyone a chance to replicate your result. Otherwise you are a charlatan and your Hearst calculation is a sham.
There's something wrong here. Either we don't understand each other, or there is some kind of error.
How are you going to count Hearst over the whole range? So you have the whole range, you are not going to divide it into intervals, but what are you going to do and how are you going to count Hurst?
Tables 2a and 2b have two values N - the number of samples in the interval, and n is actually Log(N) on base 2. N=15 - this case was not considered at all. But n=15 is really the last line of the table. But just keep in mind, this line investigates the interval N=32768 counts. For reference: according to the very active year 2009, there were 15000 ticks on the average per day. That is the interval N=32768 is more than 2 days.
One such interval will give you just one value for each of the spread and increment (it is necessary to calculate S). How many more do you need to calculate averages? Just for reference, the total number of all SB trajectories that need to be averaged to get a true theoretical average is 2^N, i.e. 2^32768.
Yes, I've got it, I need intervals. By the way, here is how Naiman talks about the same https://www.mql5.com/go?link=http://capital-times.com.ua/dobavit-novost/view-30.html. He roughly defines trendiness/flatness there - through the rule of three sigmas. He also picked up the unknown coefficient experimentally.
Vita, drink some cold water and rinse your mouth out. There is too much mud coming out of it.
I described the algorithm in great detail, with all the formulas. I disproved my own hypothesis, by the way. The results of calculations of the test example are very detailed. Anyone who knows a bit about mql4 can repeat everything I've done. I can also post the code, it won't bring anything new to me.
Since you don't answer the questions, you can't describe the algorithm of your (?) code, you have already admitted your innocent mischief - your hypothesis is a trivial formula from a textbook, and in addition you are ready to use definition of Hurst from Wikipedia, which I used initially, so what to talk about?
Do with your (and it is yours, not the one accepted by all) Hearst what you want. I have no desire to dissuade you and look for your mistakes. And you have failed to convince me that I have some mistakes - you simply have no arguments on the contrary.
Yes, I've got it, I need intervals. By the way, here is how Naiman talks about the same https://www.mql5.com/go?link=http://capital-times.com.ua/dobavit-novost/view-30.html. He roughly defines trendiness/flatness there - through the three-sigma rule. He also picked up the unknown coefficient experimentally.
Interesting, I will take a look. But it is a big job, not today. I liked the statement in the preface "it takes at least 21 observations to detect a trend". :-)
1. h = 3 means that the formula is rubbish, the author is ignorant.
2. I suggest you do a substitution of 1 old pips = 10 new pips. Q=10R.
Compare the results of the formula for both cases. I'm sure the results will be different.
1. I'm curious to know your version of what the Hearst ratio is for your own example.
2. Multiplying a value by a constant in logarithmic coordinates gives a constant offset, i.e. has no effect on the slope. Therefore, h will not change from changing the scale. You can do the calculations yourself.
Another thing is if we start dividing it into "bars". As can be seen from Yuri's calculation, with increasing "timeframe" (i.e. with increasing N) the Hurst exponent will reach a constant, i.e. the Bernoulli process generated series will as if gain self-similarity, but will finally gain it only at N equal to infinity.
The moral here is simple: the Hurst exponent will be constant only for series with self-similarity property. It means that formally we can calculate it for any series but substantive conclusions will be obtained only for series with self-similarity property.
P.S. Here is the answer to the dilemma - for bars or for ticks you must calculate the Hurst index. It turns out that the proximity of a tick process to a Bernoulli process deprives it of self-similarity properties, at least for small N. It means that the value of the "tick" Hurst ratio will not give us any information.
But the degree of informativeness of the "bar" Hearst figure will be determined by the degree of self-similarity of the series on this timeframe.
P.P.S. I express my gratitude to Vita for questions that give reason to think upon this subject :)
For real instruments, High-Low/|Open-Close| ratio
Roughly speaking, for an average candle each shadow equals half of the body. For the 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: