Discussion of article "Calculating the Hurst exponent" - page 3

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СанСаныч Фоменко:

For example, the FGN package with the function HurstK(z), which produces a nonparametric estimate of the Hurst coefficient that gives a much more accurate value.

Replace the phrase"Hurst coefficient" in the highlighted phrase with" Pearson'sCorrelation Coefficient" and, for example," Pearson's Correlation Coefficient". for example, with "Pearson Correlation Coefficient" and then, perhaps, you will feel the absurdity of the highlighted statement.
 
fxsaber:
Replace the phrase "Hurst coefficient" in the highlighted phrase with "Pearson correlation coefficient", for example, and then perhaps you will feel the ridiculousness of the highlighted statement. For example, replace the phrase "Hirst coefficient" with "Pearson's Correlation Coefficient" and then you might feel the ridiculousness of the highlighted statement.

I won't substantiate, as all my posts were actually directed at the author of the article.

I looked at his profile and my impression is that the man tends to provide a certain level of his reasoning and actions. On the example of Hirst's calculation I tried to convey to the author of the article that the level of the article can be provided ONLY taking into account already available results in the relevant field. And this level, the point of reference, the stove from which one dances, is exactly what R gives. It is possible to take another system, for example, Python, other paid..... But in any case one should not pretend that this is the first word on the topic in this article.

I was not interested in everything else.

 
СанСаныч Фоменко:

I won't substantiate, as all of my posts were in reality directed at the author of the article.

Read my comment above. If Pearson is inserted into the phrase, it becomes ridiculous for some reason. If we put Hearst in it, it doesn't. What does that have to do with it?

Apparently it's because Pearson is a clear-cut algorithm for calculations. And Hearst is every bit as cheesy.

There is Hearst-DmitriyPiskarev, there is Hearst-R and there are many others. The funny thing is that it is impossible to compare them, because there can be no comparison criterion when there is no clear definition.

That's why it's funny to hear people say that one Hirst variant is more accurate than another. They are simply different values, which because of a historical mishap people call the same thing - Hearst.

 
The article is of interest, if only for the simple reason that there is very little information on this topic. But unfortunately the author's research vector was chosen incorrectly. In particular, the so-called R/S method is described in detail, which is so dense and crude with respect to H estimation that it is not even serious to talk about it. Simple experiment, try to calculate H on the generated white noise by pre-integrating it into the random walk I(1). You will get the same numbers around 0.54-0.58. I.e. R/S is not really applicable to processes whose characteristics are close to random walk, which are all markets. Of course, on some Nile spills where H is greater than 0.7 R/S will show something, but not on real markets.
 
fxsaber:

Read my comment above. If we put Pearson in a sentence, it becomes ridiculous for some reason. And if we put Hearst in it, it doesn't. What does that have to do with it?

Apparently it's because Pearson is a clear algorithm for calculating. And Hearst is every bit as cheesy.

There is Hearst-DmitriyPiskarev, there is Hearst-R and there are many others. The funny thing is that it is impossible to compare them, because there can be no comparison criterion when there is no clear definition.

That's why it's funny to hear people say that one Hirst variant is more accurate than another. They are simply different values that because of a historical mishap people call the same thing, Hearst.

I absolutely agree with you that the Hirst thing is extremely vague both in terms of calculation algorithm and interpretation

I am writing about something completely different: if a person gives an algorithm, he should justify this algorithm. A code that implements an incorrect algorithm will also be incorrect.

If you look specifically at the algorithm given in the article, it uses linear regression estimated by MNC. This piece of the article has no relation to reality at all, because the estimation of linear regression coefficients by ISC is an ASSESSMENT of two random variables: displacement "a" and slope angle "b". If the author had used, for example, the lm() function from R, he would have seen surprising things, that not necessarily the value of "b", which he considers as the value of the Hurst coefficient, exists on paper, but in reality it may not exist at all, because the standard lm() function, besides the value of "b" itself, gives its variance and the confidence level of this value. Quite often, when using linear regression, the confidence level is much lower than 90%.

Here is an example of a standard linear regression estimation table with many variables

Coefficients: (5 not defined because of singularities)
                    Estimate Std. Error z value      Pr(>|z|)    
(Intercept)       -338.88337  152.55692  -2.221      0.026327 *  
rsi_eurusd           0.01237    0.01363   0.908      0.363934    
macd_eurusd         13.94972    4.36041   3.199      0.001378 **
trix_eurusd       -741.34816  148.31309  -4.999 0.00000057768 ***
sig_eurusd        1118.41702  212.31435   5.268 0.00000013811 ***
trix_eurusd_trend         NA         NA      NA            NA    
trix_gbpusd        407.84268  131.29586   3.106      0.001895 **
sig_gbpusd        -918.57282  202.12341  -4.545 0.00000550361 ***
trix_gbpusd_trend         NA         NA      NA            NA    
trix_eurgbp        264.59572  115.74195   2.286      0.022249 *  
sig_eurgbp        -795.43634  159.17763  -4.997 0.00000058180 ***
trix_eurgbp_trend         NA         NA      NA            NA    
trix_usdchf        -76.32606   27.15637  -2.811      0.004945 **
sig_usdchf          14.28410   31.35889   0.456      0.648747    
trix_usdjpy          5.42010    8.93393   0.607      0.544059    
sig_usdjpy          65.28629   11.08181   5.891 0.00000000383 ***
trix_usdjpy_trend         NA         NA      NA            NA    
trix_usdcad         32.76774   21.62655   1.515      0.129731    
sig_usdcad         -25.12268   25.27109  -0.994      0.320161    
trix_usdcad_trend         NA         NA      NA            NA    
fit.eurusd         -72.05260  149.20763  -0.483      0.629166    
fit.gbpusd        -304.38920  121.47457  -2.506      0.012218 *  
fit.eurgbp         253.58306  132.96820   1.907      0.056508 .  
fit.usdchf        -387.54743  100.37962  -3.861      0.000113 ***
fit.usdjpy           1.82458    0.41496   4.397 0.00001097684 ***
fit.usdcad        -133.88962   81.83316  -1.636      0.101813    
fit.eurusd.2        25.03730  160.94619   0.156      0.876377    
fit.gbpusd.2       423.37220  143.07774   2.959      0.003086 **
fit.eurgbp.2      -227.97261  192.34022  -1.185      0.235916    
fit.usdchf.2       426.74965  101.14174   4.219 0.00002450374 ***
fit.usdjpy.2        -2.15458    0.42133  -5.114 0.00000031587 ***
fit.usdcad.2       321.48459   86.36230   3.723      0.000197 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Only the values marked with asterisks can be trusted with the specified confidence level. The rest are just a fiction, the figure is there, but in reality it is not!

That's what this is about. It is about accuracy and careful attention to each result of calculations.

 
fxsaber:

Read my comment above. If we put Pearson in a sentence, it becomes ridiculous for some reason. And if we put Hearst in it, it doesn't. What does that have to do with it?

Apparently it's because Pearson is a clear algorithm for calculating. And Hearst is every bit as cheesy.

There is Hearst-DmitriyPiskarev, there is Hearst-R and there are many others. The funny thing is that it is impossible to compare them, because there can be no comparison criterion when there is no clear definition.

That's why it's funny to hear people say that one Hirst variant is more accurate than another. They are simply different values, which because of a historical mishap people call the same thing - Hirst.

Hirst is not a calculation algorithm, it is a characteristic of the process. Accordingly, this characteristic can be calculated in different ways. That's why there's nothing special about it. The main thing is that the final calculation should coincide with other recognised algorithms of calculation, otherwise the obtained value will not be Hirst, but something else.
 

СанСаныч Фоменко:

Например,  пакет FGN с функция HurstK(z), в которой производится непараметрическая оценка коэффициента Херста, которая дает гораздо более точную величину.

fxsaber:
Replace the phrase "Hurst coefficient" in the highlighted phrase with "Pearson correlation coefficient", for example, and then perhaps you will feel the absurdity of the highlighted statement. for example, to "Pearson Correlation Coefficient" and then, perhaps, you will feel the absurdity of the highlighted statement.
SanSanych is absolutely right here. I don't understand why the R/S method is called non-parametric, although it is based on the standard deviation S, which is even reflected in its name.
 
СанСаныч Фоменко:

I absolutely agree with you that Hirst's thing is exceptionally vague both in terms of calculation algorithm and interpretation

My point is quite different: if one gives an algorithm, one should justify this algorithm. A code that implements an incorrect algorithm will also be incorrect.

If you look specifically at the algorithm given in the article, it uses linear regression estimated by MNC. This piece of the article has no relation to reality at all, because the estimation of linear regression coefficients by ISC is an ASSESSMENT of two random variables: displacement "a" and slope angle "b". If the author had used, for example, the lm() function from R, he would have seen surprising things, that not necessarily the value of "b", which he considers as the value of the Hurst coefficient, exists on paper, but in reality it may not exist at all, because the standard lm() function, besides the value of "b" itself, gives its variance and the confidence level of this value. Quite often, when using linear regression, the confidence level is much lower than 90%.

Here is an example of a standard linear regression estimation table with many variables

Coefficients: (5 not defined because of singularities)
                    Estimate Std. Error z value      Pr(>|z|)    
(Intercept)       -338.88337  152.55692  -2.221      0.026327 *  
rsi_eurusd           0.01237    0.01363   0.908      0.363934    
macd_eurusd         13.94972    4.36041   3.199      0.001378 **
trix_eurusd       -741.34816  148.31309  -4.999 0.00000057768 ***
sig_eurusd        1118.41702  212.31435   5.268 0.00000013811 ***
trix_eurusd_trend         NA         NA      NA            NA    
trix_gbpusd        407.84268  131.29586   3.106      0.001895 **
sig_gbpusd        -918.57282  202.12341  -4.545 0.00000550361 ***
trix_gbpusd_trend         NA         NA      NA            NA    
trix_eurgbp        264.59572  115.74195   2.286      0.022249 *  
sig_eurgbp        -795.43634  159.17763  -4.997 0.00000058180 ***
trix_eurgbp_trend         NA         NA      NA            NA    
trix_usdchf        -76.32606   27.15637  -2.811      0.004945 **
sig_usdchf          14.28410   31.35889   0.456      0.648747    
trix_usdjpy          5.42010    8.93393   0.607      0.544059    
sig_usdjpy          65.28629   11.08181   5.891 0.00000000383 ***
trix_usdjpy_trend         NA         NA      NA            NA    
trix_usdcad         32.76774   21.62655   1.515      0.129731    
sig_usdcad         -25.12268   25.27109  -0.994      0.320161    
trix_usdcad_trend         NA         NA      NA            NA    
fit.eurusd         -72.05260  149.20763  -0.483      0.629166    
fit.gbpusd        -304.38920  121.47457  -2.506      0.012218 *  
fit.eurgbp         253.58306  132.96820   1.907      0.056508 .  
fit.usdchf        -387.54743  100.37962  -3.861      0.000113 ***
fit.usdjpy           1.82458    0.41496   4.397 0.00001097684 ***
fit.usdcad        -133.88962   81.83316  -1.636      0.101813    
fit.eurusd.2        25.03730  160.94619   0.156      0.876377    
fit.gbpusd.2       423.37220  143.07774   2.959      0.003086 **
fit.eurgbp.2      -227.97261  192.34022  -1.185      0.235916    
fit.usdchf.2       426.74965  101.14174   4.219 0.00002450374 ***
fit.usdjpy.2        -2.15458    0.42133  -5.114 0.00000031587 ***
fit.usdcad.2       321.48459   86.36230   3.723      0.000197 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Only the values marked with asterisks can be trusted with the specified confidence level. The rest are just a fiction, the figure is there, but in reality it is not!

That's what this is about. It is about accuracy and careful attention to each result of calculations.

Before making any conclusions, it is necessary to understand from what data the regression is calculated.

San Sanych, I'm sorry, but you're really fed up with your "expert judgements". From your side you can't see anything at all except the eternal sticking of some R. At least put some MQL code somewhere so that it would be clear that you understand something.

 
In defence of San Sanych I can give you this story/example:
An old teacher says to a young one - if it seems to you that some student is always asking you stupid questions and annoying you, think - maybe this is the only student in your class who listens attentively to you.<br/ translate="no">
 
Dmitriy Piskarev:

Maxim, thank you for your comment!

Yes, you are right, of course the calculation of Hurst coefficient is just a base to get at least a slightest idea about the application of some kind of matrix statistics in the study of time series. I support your remark and I also think that it would be naive and wrong to use only coefficient analysis for forecasting market dynamics. Of course, it is necessary to build a strategy on the basis of aggregate indicators and using various indicators and sources.

In the next article I will definitely show you my correct understanding of fractal analysis.

Thanks again for your comment.

P.S. I was asked to do a review of the MT5 tools for such analysis. I took the opportunity to promote it.

Super, we are waiting... the topic needs development )
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