Volumes, volatility and Hearst index - page 18
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Candid:
Для ряда Бернулли мы не можем произвольно менять масштаб потому что речь идёт о числе испытаний.
That is, a random walk at this primary level has no self-similarity, i.e. it is not a fractal.
It is another matter if we start to divide it into "bars".
There's something about your reasoning around self-similarity, Nicholas, that's a lot of confusion. :-)
What do you mean by "we cannot arbitrarily change the scale" for a Bernoulli series ? Isn't dividing a series into intervals of length N a timeframe formation ?
And what are bars in terms of a random series ? What do you work with when you work with bars ? Close, Open? How do you calculate the spread, on High-Low ? And increase by Close-Open? If so, it means that you break the initial series into non-equidistant intervals. To be precise, that's contrary to Hearst's definition procedure altogether.
And if you work with, say, only the Close series (as, for example, a mashka is considered), and already break it up into intervals, etc., then it means that you are reducing the original series to a sample. At the same time, if there are any regularities in the series, the principle of sampling may destroy them. In any case it is a rejection of some of the information. To what end ?
As for self-similarity, a tick series has it to no lesser (or perhaps greater) extent than a bar series. Unless, of course, we reduce the self-similarity (structural property) to how well it fits into Hearst's Procrustean bed.
A word or two more actually about Hirst.
You may get the impression from this thread that I think this indicator is nonsense, stupid, the wrong measure, or something like that. In fact it isn't. Hurst is quite an objective indicator, linked to other strictly mathematical measures. This alone already suggests that it is accepted by mathematics and is an objective characteristic.
However, we should still be careful about its content.
The Hurst index is a marginal measure. It is defined as a limit, asymptote to which h is tending in the known formula for the normalized spread when the number of counts in the interval increases to infinity.
A complete analogy with the Law of Large Numbers. In the limit of LNT many theorems of probability theory and statistics are proved. In this limit even all distributions tend towards normal. So why is it that the normal distribution no longer suits us in the market. And in any field, people want to know the distribution to which the process obeys now, not in the limit of the distant future.
This is why the convergence of the process comes to the fore. If it converges quickly, then limit theorems and normal distribution can be used with good approximation at early stage of statistics gathering. If not, then, imho, all results of FFT application can be framed, hung on a wall and admired at a cup of tea. And for practice it is necessary to look for something more adequate.
The historical series of quotes is short. The market is constantly changing, both as a result of changes in the financial and economic situation and the processes that shape it, and as a result of changes in market technology, its technical support (for example, the transition from 4 to 5 digits). And the TS has to be adequate to the market all the time, not in the long term. We are all going to die in the long run - that's what some famous trader said when asked about the market situation. It's hard not to agree and dangerous not to take that into account.
That's why I think that Hearst, in its classic form, is poorly suited for use in trading. It needs either to be localized somehow, or to find other, more practical measures to estimate market behavior.
Yurixx:
1. What do you mean by "can't arbitrarily change the scale" for a Bernoulli series? Isn't dividing a series into intervals of length N a timeframe formation?
2. what are bars in terms of a random series ? What do you work with when you work with bars ? Close, Open ? How do you calculate the spread, on High-Low ? And increase by Close-Open? If so, it means that you break the initial series into non-equidistant intervals. To be precise, that's contrary to Hearst's definition procedure altogether.
And if you work with, say, only the Close series (as, for example, a mashka is considered), and already break it into intervals, etc., then it means that you are reducing the original series to a sample. At the same time, if there are any regularities in the series, the sampling principle can destroy them. In any case it is a rejection of some of the information. For what purpose ?
3. As to the self-similarity, the tick series has it to no lesser (and maybe greater) extent than the bar series. Unless, of course, we reduce the self-similarity (structural property) to how well it fits in the Hearst's Procrustean bed.
1. Hmmm, I wrote the argument right away: changing the scale will lead to a change in the properties of the series. By changing the scale, we turn a tick series into a bar series. But you didn't make a bar series here, you investigated 1 bar of N ticks. Before you get indignant at this statement of mine, remember that the characteristics of this one bar are random variables, so you have quite correctly done many tests ... for 1 bar.
2. This doesn't contradict anything, there is nothing in the definition of the Hurst index about how the initial series should be formed. As already written, technically we can calculate the Hearst exponent for any series. But if we want to judge the persistence/antipersistence of our series by the Hearst ratio, we should make sure that our series has certain properties, one of which is self-similarity. So if the test shows that the bar series is self-similar, then Hearst is in our hands.
3. Where are the arguments? By the way, notice that I never claimed that bar series are a priori self-similar.
P.P.S. Thanks to Vita for the questions, which gave me the opportunity to reflect on this topic :)
You're welcome, Candid.
I was going to write - it's a pity that no one here understands what the Jurix formula counts, but now you have dispelled my doubts. Indeed, Jurix's second formula survives the Q=10R substitution. Therefore thank you too.
Unfortunately, Jurix's improved formula still doesn't count Hirst. Therefore in order to, to quote Jurix, "evaluate the correctness of Hurst's hypothesis", one needs to confirm that Jurix's formula counts exactly for Hurst. There is no such confirmation.
As a result, we have only Huricks formula: H = (Log(R2) - Log(R1))/ (Log(N2) - Log(N1)), where
N - number of ticks on the interval. The first point of the interval (initial price value) is the last tick of the previous interval and is not included in the current one. Therefore, the number of price changes within the interval is equal to its number of ticks.
R is the average price spread over K intervals.
0. Please note that Jurix tries to calculate Hurst on the basis of two averages and two quantities of steps, on which these averages are formed. This is already nonsense to anyone who has ever delved into Hearst. But, god forbid. Suppose that the genius of Jurix simplified Hearst's complex algorithm to the ratio of the difference of the two averages to the difference of the two intervals. Let's look at what Jurix has provided us with as evidence of the fact that his formula counts Hearst:
1. the analytical derivation of his simplified formula from any Hearst calculation known to us or accepted before Jurix is NOT PROVIDED;
2. Confirmation that his formula counts Hearst on controlled examples is NOT PRO VIDED ;
3. Code for Yurix to calculate his H so that everyone can check if he counts Hearst - NOT PR ESENTED ;
4. Any confirmation that 1/2 in Jurix's formula for Jurix's series is not a fit - NOT PR ESENTED;
5. The control example that my Hearst calculation code fails to cope with - NOT PR ESENTED;
I, in turn, have posted for general judgment:
1. analytical calculation of how the Jurix formula converges to 1/2 for SB and without Hurst - PRESENTED;
2. Confirmation of my analytical calculation by the results of Jurix's calculation and prediction of convergence to 1/2 from above - PRESENTED;
2. My hypothesis that for SB in the limit the mean |Open - Close| = k * (High - Low) - PRESCRIBED;
3. my hypothesis is even supported by the actual price range, thanks to the forumers for the redundancy - PRESCRIBED;
4. A code that counts Hurst according to R/S analysis and anyone can check it - PRESENTED;
5. Analytical calculation according to Hurst's formula for the control series N in cube:
H = (Log(N2* N2* N2) - Log(N1*N1*N1))/ (Log(N2) - Log(N1)) = 3 - which contradicts Hurst by definition. Jurix's formula is wrong. - PROVIDED;
Please also note that the incorrectness of my calculations and arguments does not add anything to Jurix's formula. It remains unsupported because Jurix cannot support it with anything. At the moment the most important thing NOT PROVIDED by Jurix is the courage, the courage to admit that his Hearst formula does not hold that his work has nothing to do with Hearst.
But the question remains unanswered:
Curious to know your version of what the Hearst figure is for your own example.
Another question has come up:
What definition of the Hearst figure do you use?
Don't link to it, either write it in your own words, or give a snippet of the source here.
But the question remains unanswered:
Curious to know your version of what the Hearst figure is for your own example. - After Q=10R? The same as for R. I pointed it out by saying that the second Hurst formula survives the substitution Q=10R; For N in a cube? H=3. Cite the question if I haven't guessed it.
Another question has matured:
What definition of the Hurst index do you use? - A measure of persistence, an estimate of how long a series retains the memory of its previous members.
Just don't link to it, either write it in your own words, or give a snippet of the source here.
Vita, you are either a very lazy person or very stupid. I want to think well of you, so I choose the first option. But laziness also has to have its limits. Not asymptotics, but a limit beyond which a person still picks himself up and deals with what seems incomprehensible to him.
On pg. 16 of this thread I replied to Prival, and gave a detailed description of all variables, procedure and derivation of the formula to which you have such claims. If you are incapable of solving a simple system of 2 equations with 2 unknowns, then you don't belong here, but on a school bench.
Vita, go to page 16 and read my post Privalu as many times as it takes to understand the groundlessness of your claims.
1. hmm, I wrote the argument right away: changing the scale will change the properties of the series. By changing the scale, we turn a tick series into a bar series. But you didn't make a bar series here, you investigated 1 bar of N ticks. Before you get indignant at this statement of mine, remember that the characteristics of this one bar are random variables, so you have quite correctly done many tests ... for 1 bar.
Explain, plz, what the scale is and what the change in scale is. And tell me plz how you work with a bar - as an interval or just a row of only one of the 4 prices.
If all your bars are different, then your statistics are also trivial - for each instance of the object under study (i.e. for each bar) you have only one dimension. Isn't that so ? And can this provide at least minimal validity to the result ?
2. It doesn't contradict anything, in the definition of Hurst index there is not a word about how the initial series should be formed. As already written, we can formally calculate the Hearst exponent for any series. But if we want to judge the persistence/antipersistence of our series by the Hearst ratio, we should make sure that our series has certain properties, one of which is self-similarity. So if the check shows that the bar series is self-similar, then Hearst is in our hands.
Technically there are no claims. :-) However, still, in order for me to understand you, explain your methodology of using bars.
And it's much worse with self-similarity. So you're saying that before we can count Hearst and draw any conclusions we have to establish the presence of self-similarity ? Is that in Hirst's definition? Or in some of his other theoretical positions ? Then legitimate questions arise - in what way are you going to establish the existence of self-similarity ? is there any justification for this method ? does SB not have the property of self-similarity ? etc.
Actually I assumed that for any series one can calculate the fractal dimension and hence the Hurst exponent. So is this naive ?
3. Where are the arguments? By the way, notice that I never claimed that bar series are a priori self-similar.
I didn't ask about arguments. The questions I asked were only about clarifying your position. They were also about trying to explain the reasons for my doubts. I'm not disputing your point of view, I just want to understand.
Bragging is bad, but I couldn't stand it. There's a branch here that remembers that from level to level... with small stops. 16 figures ... pyramiding ...
https://www.mql5.com/ru/forum/126769/page429
This page is Prival's post with pictures. This is about ticks, for those who think bars are better.
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, but not for practical trading.