Volumes, volatility and Hearst index - page 19
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R is the average spread. The spread is the difference between the maximum and minimum value of the series on the interval. - For R/S analysis this is completely wrong. R/S analysis is described in Peters. Or refer to wikipedia, at least. Even the name of the analysis indicates that the series is reshuffled. R is not an average range at all. Bullshit. If you did the conversions correctly, your formula would count Hearst correctly. But you are not aware that R/S is not a formula, and you cannot calculate Hearst by dividing some R by S. Hearst can only be estimated. Which is what R/S analysis does. Analysis, not a formula. Therefore your formula is flawed from the outset. It has never and never will calculate Hearst and naturally it doesn't solve control examples and analytically you can see that an incorrect result > 1 is no problem for it. You have misdirected me to pg. 16. You have fixed your misunderstanding of R/S analysis 100%.
Once again I will point out a fact which should have alerted you from the very beginning - your formula indicates that Hurst, and consequently the fractal dimension, is the same for all series which have the same mean spreads at the same intervals. If you understood Hearst or R/S analysis you would question such naive simplicity. For it is not. Hurst and R/S analysis look much deeper than the average swing. Study R/S analysis more thoroughly, then you'll understand why your formula and work has nothing to do with Hearst.
N is the number of samples in a tterval.
S - RMS of series increments.
k - constant coefficient.
h - Hurst index.
It means that the whole series is divided into equal intervals of N counts. For each interval, the increment and the spread are calculated. On the basis of these data, the RMS of the increments and the average spread are determined. The Hurst index must be selected so that the formula is satisfied. :-)))
If Hearst was right - Hearst is right, but R is not the average spread, but your misconception starting with the very first letter of R/S analysis. and the average spread did satisfy this equation, then it would have a solution relative to h. This solution would be determined by two points
R1/S1 = k * (N1^h) and R2/S2 = k * (N2^h)
The series can be broken in two ways: into intervals of magnitude N1 and magnitude N2. Correspondingly, we obtain ranges R1 and R2, and RMS S1 and S2. Coefficient k is constant. Thus we get a system of two equations. Excluding the coefficient k we get the expression for the Hurst ratio calculation:
h = [ Log(R1/S1) - Log(R2/S2)]/[Log(N1) - Log(N2)] - V3.0, S added. But Hearst hasn't turned out yet. Will have to post the fourth version at least.
Geometrically it is the tangent of the slope of the line drawn through the two points [Log(R1/S1),Log(N1)] and [Log(R2/S2),Log(N2)]. A curve expressing the dependence of R/S on N in logarithmic coordinates has been plotted. Its graph is shown. It shows that the angle of slope changes, i.e. depends on N. This implies that the coefficient k in Hurst's formula is not a constant, that it depends on N, and that Hurst's formula is only asymptotically true for large N. As the object of research was SB, there were no problems with the amount of data, unlike the series of quotes.
I hope when you've mastered Hearst you'll post the code so it can be run on coterminous examples. I assume you realise that only then will it be possible to believe you that your work is relevant to Hearst. In the meantime you only have the same letters, but not the results of Hearst's calculations.
P.S. For all those who are too lazy to look in a book or wikipedia - R is the difference between the maximum and minimum of the rescaled series created from the accumulated sum of normalized values of the original series. Not the average. Not of the original series. Not at all the same as stated by Jurix in the first sentence of his post.
On this page is Prival's post with pictures. This is about ticks, for those who think bars are better.
Is this a joke or are you being serious?
and you can prove the opposite claim ? bars are better than ticks ?
and you can prove the opposite statement? bars are better than ticks?
So it depends on what we need to extract. Bars lose tick info, but if your trading algorithm doesn't need this lost info, then there is a gain in processing speed, testing, etc. Then bars are better as part of a particular approach :)
and you can prove the opposite claim ? bars are better than ticks ?
Let's start with this. Do ticks have the information to predict them ? :)
Let's start with this. Is there information in the ticks to predict them? :)
predict them how? If there are ticks and not a weekend, predicting that there will still be ticks :)
What's the point of Hearst, anyway? :) It's a lagging characteristic "in the frontal direction" on a continuous section. The main thing is to determine the required process in time and match it. Hurst is good only for theoretical research, not for practical trading.
Well, that's my point exactly.
But for practical trading it would be very useful to have a trend/return indicator, with a quantitative measure of this state. If, of course, it were local and moderately lagging.
to Prival
а Вы что можете доказать обратное утверждение ? бары лучше тиков ?
Of course, but a little later. I hope you are not in a hurry? :о)
to Avals
predicting them how? If there are ticks and not a weekend, I predict there will still be ticks :)
What do you mean?
Well, that's my point exactly.
But for practical trading, a trend/return market condition indicator, with a quantitative measure of this condition, would be very useful. If, of course, it were local and moderately lagging.
From my practice - for a trend it is enough to measure e.g. increment in price for a fixed time, or distance to an extremum. And such simple things prove to be more robust and profitable compared to more perverse variants. Detecting a trend or a flat is not the most important thing - it is only a filter and not the main one.
to Avals
What were you trying to say?
That prediction is too general a concept. Beginners, for example, think that they need to predict the direction of a trade for the current moment. There are a lot of things you can predict, aren't there? :)