Hearst index - page 32

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Had a look at the case for February 2.

On micro 1H (you could say DC takes care of us, local extrema are not overlapped:)

On the nd account

on esn

 

So, I continue to refine the fractal theory. Earlier I proved the invalidity of the RS estimation of the spread proposed by Peters for identifying deterministic series. Nevertheless his methodology is undoubtedly a powerful theoretical pivot bringing together method and theory. Therefore, I have completely abandoned the particular RS method and developed my own non-trivial calculation of the value of "particle dispersion". At the moment I am not inclined to reveal it completely, as the method is aimed strictly at practical applications and is still extremely promising. I can only say that all calculations are based on the ZigZag indicator. This is a very plastic indicator that can efficiently work on both highly deterministic series and random data series.

So, as mentioned above, the classical definition of RS width overestimates Hearst's estimation by a significant amount. In addition, this method is very insensitive to the price data, since only two maxima and minima are chosen from the range and their difference is normalized to the standard deviation of the series for this period. As the result, the Hearst ratio was overestimated irrespective of the type of series analyzed and was always around 0.52-0.53 due to low sensitivity and wrong detrending of the analyzed period. Moreover, the R/S range of the random walk was statistically indistinguishable from the market series. All this made it impossible to use this methodology in further studies. My method does not have all these disadvantages. Unlike the old Peters method, it can work with horizons of any length (the Peters method only from 100 lag periods and higher, until then it obeys a different growth law). Besides, it is in good agreement with theory predicting runaway particle with speed T^0.5. So, I publish the graph:

What does this graph show? First, the Hurst coefficient, which specifies the linear regression angle for the random data, is fully consistent with the predicted value of 0.5. The runaway of the RTS plot is qualitatively different from the random, normally distributed wander, and is 0.53 Hurst. Compared to past calculations, this is a real breakthrough. The mathematics really works and confirms the effects predicted by fractal theory. We can say for sure that all the markets with the Hurst significantly exceeding 0.5 are trending and the market "remembers" its past state.

Now for the bad. We have found out an unpleasant peculiarity of the dependence of the estimation on the type of series distribution. This is very, very bad. In this case, we can see that the estimation overestimates results on artificial Paretto-Levy distributions (the real volume was taken and random bars were generated based on it). But even so, there is still a margin for statistically significant delta between real markets and artificially generated ones. It seems that the main problem is in volatility normalization. Apparently we will have to significantly refine methods of normalization in such a way that the distribution type would not affect the estimates of the deterministic component.

In any case, progress is evident. I managed to identify qualitative differences between the random and non-random component. In the future, I hope to bring this research to a working sample.

 
C-4:

In any case, progress is evident. We have been able to identify qualitative differences between the random component and the non-random component. In the future, I hope to bring this research to a working sample.

Extremely curious.

Good for you!

Looking forward to the sequel...

;)

 
C-4:

I wonder if the RTS comes out super-diffusing at 0.53? And on currency pairs I was getting sub (0.47-0.48) everywhere.

By way of nonsense...

Influence of medium on diffusion can be of two kinds - when interaction with it on average takes away energy from a stray particle, which leads to lower speed of dispersion, in which case we observe sub-diffusion (index less than 0.5), or when interaction, on the contrary, increases kinetic energy, and then we have super-diffusion (respectively, more than 0.5). If we take a quotient, the prevalence of stop orders on the average gives the first variant, while limit orders give the second one. How do you like this explanation?

If it is correct, we can outline a strategy: we identify the levels of concentration of the orders on the first step and set points on the continuation of movement from this level for instruments with R/S>0.5 and on the rebound for R/S<0.5

 
alsu:

If this is correct, then we can outline a strategy: in the first step, we identify the levels of concentration of orders, and bet on the continuation of the movement from this level for instruments with R/S>0.5 and on the rebound for R/S<0.5

How is it better than using, for example, charts? - The lag cannot be avoided anyway. And +-0.1...0.2 is not so big difference from the basis 0.5 that it can be useful. Imho of course.
 
joo:
And how is this better than working on, for example, mash-ups? - You can't avoid the lag anyway. And +-0.1...0.2 is not such a big difference from 0.5 basis, that you can get something useful from it. Imho of course.
R/S is a characteristic that has fractal properties (at least in theory:). This means that the R/S value calculated per hour on minute or 20-second bars can in principle be regarded as an estimate of the same figure for the hourly scale. In this way the lag can be kept to a minimum... in theory, of course))
 
alsu:

I wonder if the RTS comes out super-diffusing at 0.53? And on currency pairs I was getting sub (0.47-0.48) everywhere.

By way of nonsense...

Influence of medium on diffusion can be of two kinds - when interaction with it on average takes away energy from a stray particle, which leads to lower speed of dispersion, in which case we observe sub-diffusion (index less than 0.5), or when interaction, on the contrary, increases kinetic energy, and then we have super-diffusion (respectively, more than 0.5). If we take a quotient, the prevalence of stop orders on the average gives the first variant, while limit orders give the second one. How do you like this explanation?

If it is correct, we can outline a strategy: we identify the levels of concentration of the orders on the first step and set the price for instruments with R/S>0.5 to continue the movement from this level and to rebound for instruments with R/S<0.5


So far, I have tested several instruments and all of them had good quality Hirst above 0.5. These were: General Electric(1965-2012), IBM(1962-2012), SP500 (1952-1912), T-Bond 30 (1970-1912). This is fully consistent with the predicted effects of FMH. Also Peters mentions that all currency pairs have a strong trend component (Hearst strongly greater than 0.5), with infinite process memory (the limit on existing history has not been identified).

Here it is more a matter of the method itself. If your method gives on Norm. Random is exactly 0,5 and on the currencies it is 0,47-0,48 - then your methodology must be carefully studied. Theoretically the markets should not divide into trendy and anti-trendy. At Peters all the markets studied had H above 0.5. Again theoretically, even different investment horizons of the same market should be fractal (self-similar) with respect to each other and thus perfectly line up. Here the degree of fractality can be estimated by the value of approximation reliability R^2 of this very line. The closer it is to 1, the more self-similar and unified the investment horizons are. I.e. it cannot be the case that one horizon is trending and the other one is anti-trending followed by the trend horizon again. But this is theoretical. Practically we see that although in the first approximation it is true, in general we observe some curious effects on small horizons (about it below) and also the divergence line is not perfectly smooth (although the data was used as much as random ones). But it is more likely to show the effect of non-stationarity, but about that also later.

What is interesting, at an investment horizon from 3 to 30 minutes since 2009, we can see a weak antipersistent component on RTS. Hearst there is just under 0.5 and yet statistically significant. Perhaps this is the same effect that ACF shows (weak negative correlation of neighbouring bars). But on the other hand, there is no antipersistence on the earlier history! It seems that something appeared on the lower RTS horizon after 2009 and it changed the market horizon structure! Maybe, it's just the same robots that work on rebound from the accumulation of large orders. Anyway, I will be in the office on Monday and I will post this interesting chart.

Limit and Stop orders - probably, they have different effects on the market. But I think that their horizon is very limited in one day. The horizon starting from one hour shows much stronger effects that make the effects caused by the pending orders statistically indistinguishable.

 
joo:
How is this better than working on, for example, mash-ups? - You can't avoid the lag anyway. And +-0.1...0.2 is not such a big difference from 0.5 basis, that you can get something useful from it. Imho of course.

Well, it's the temperature in the whole ward, and it's already as much as 0.03 degrees above the norm! And the individual cases can be even more interesting. All the more, don't forget that we're working on a power scale in logarithmic measurements. A deviation of 0.03 already gives 1.48% advantage on 100 ticks, which is not much, but it is enough to pay the spread.
 
C-4:

Well, that's the temperature of the ward as a whole, and it's already 0.03 degrees higher than normal! And the individual cases can be even more interesting. Especially do not forget that we are working with a power scale in logarithmic measurements. A deviation of 0.03 already gives 1.48% advantage on 100 ticks, which is not much, but already enough to pay the spread.
If the future looks like the past. But in this case the mash is also a beauty.
 
C-4:

Well, this is the temperature of the whole chamber, and it's already 0.03 degrees higher than normal! And the individual cases can be even more interesting. Especially do not forget that we are working with a power scale in logarithmic measurements. A deviation of 0.03 already gives 1.48% advantage on 100 ticks, it is not much, but it is enough to pay the spread.


How nice it all turns out! :-)

Can these studies be attached (supplemented) to it or can something similar (self-sufficient for the filter) be drawn for the same simple connection to a trading owl as a trend-flat filter?

Here is my signal part of the trend owl using iVAR indicator readings. 

 if  (Ask>F11 && ADX1_1>ADXOpenLevel && ADX_PLUS1_1-ADX_MINUS1_1>0 && ADX1_1<ADX_PLUS1_1 && ADX1_1>ADX1_2 && Open[1]>MA_1 && Close[1]>MA_1 &&  
      iVAR_1 < 0.5 &&                                                                                                      // тренд на основном ТФ 
   //.........................................ФИЛЬТРЫ...................................
                   (TimeHour(TimeCurrent()) >= Start && TimeHour(TimeCurrent()) <  End))   
      WmOrderSend(Symbol(), OP_BUY, Lots_New, Ask, 0, 0, "старт", MagicNumber);
    
1...252627282930313233343536373839...46
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