Hearst index - page 25
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Obtained a curious summary graph of the three measured quantities:
We can see that the real results, although by their nature they tend to inflection after 1.8 - 1.9, can be too well approximated by a graph of a random walk of a normally distributed value. At the same time the ramp plot itself is practically ideal straight line without visible kinks (good result). Compared to the Peters' benchmark calculation, the Hurst value is underestimated by about 0.10 and amounts to 0.68 in its peak against 0.78 for Peters. At the same time, the character of the slope of the lines after the inflection (moment of memory loss) is more similar to each other.
At the moment the results are still too much different from those announced by Peters and it is too early to talk about a stable identification of non-random series by this indicator.
P.S. The difficulty also lies in the fact that we have to work with very small values. Insignificant deviations of several percents give very different slope angles. Half a step to the left, half a step to the right - and the series is already indistinguishable from random wandering.
P.S. Another difficulty is that you have to work with very small values. Tiny deviations of a few percent give very different slope angles. Half a step to the left, half a step to the right - and the row is already indistinguishable from random wandering.
The error and correctness of the application to the Hearst's market have to be considered.
The whole conclusion begins with well-known Einstein formula for SB which says that the mean deviation of a wandering particle from the origin increases in direct proportion to the root of time. If per tact of time a particle moves +1/-1, then R=SQRT(N), where N acts as time, or number of increments. But in fact we rarely deal with processes with two discrete increments +1 and -1 and it follows, that in general case R=sko*SQRT(N), which has sense if distribution has sko=constant, i.e. distribution is stationary. Hence R/sko=N^0.5 for random walk. Then 0.5 is substituted for the variable and it is calculated through logarithms. In order to use accumulated rather than average increment (because for average increment much more statistics are needed) an empirical correction factor is introduced. The value of the Hurst index for market data is highly questionable, as the distribution is non-stationary and it changes rapidly and depends on its previous values. There is no theoretical basis for the validity of using this indicator for nonstationary data. I.e. it can be applied, but the results can be trusted :)
There is still a problem with the error and correctness of application to the Hearst market in general.
The whole conclusion starts with the well-known Einstein formula for SB which says that the mean deviation of a stray particle from the origin increases in direct proportion to the root of time. If per tact of time a particle moves +1/-1, then R=SQRT(N), where N acts as time, or number of increments. But in fact we rarely deal with processes with two discrete increments +1 and -1 and it follows, that in general case R=sko*SQRT(N), which has sense if distribution has sko=constant, i.e. distribution is stationary. Hence R/sko=N^0.5 for random walk. Then 0.5 is substituted for the variable and it is calculated through logarithms. In order to use accumulated rather than average increment (because you need much more statistics for average increment) an empirical correction factor is also introduced. The value of the Hurst index for market data is highly questionable, as the distribution is non-stationary and it changes rapidly and depends on its previous values. There is no theoretical basis for the validity of using this indicator for nonstationary data. I.e. it can be applied, but the results can be trusted :)
Hurst's statistics is designed in such a way that neither the type of distribution, nor its non-stationarity, can confuse it. At least that is what Peters himself says. On the contrary, it can be used to reliably determine whether the studied series is stationary or not, whether the increments in it are dependent on each other (the memory effect), to calculate the cycle length of the process under study (I think it is not necessary to explain why) and to determine whether the series is trendy or counter-trendy. One snag - it is extremely difficult to repeat Peters results, and so far I don't know why this is the case. As for the s.c.o. - it is here only for normalisation of the spread, so that one can compare series of different non-comparable systems.
The file does not stick. You'd better read it.
OLGA STANISLAVOVNA GULYAEVA
CURRENCY RISK MANAGEMENT ON THE BASIS OF FRACTAL METHODS OF CURRENCY RATE PREDICTION ANALYSIS
Google it. It's easier . Maybe someone will make an indicator.
The file does not stick. You'd better read it.
OLGA STANISLAVOVNA GULYAEVA
CURRENCY RISK MANAGEMENT ON THE BASIS OF FRACTAL METHODS OF CURRENCY RATE PREDICTION ANALYSIS
Google it. It's easier . Maybe someone will make an indicator.
Maybe someone will ... And, in my opinion, you are spamming the purchase of not only a dissertation, but also an abstract (complete mayhem) by an unknown author on a dubious topic.
For some time I had to be distracted by other concerns - my daughter was 18 - I had no time for fractals ;))).
But such a switch - this is the first time I notice it - led to clear vision of the unsolved yet unsolved fractal problem.
Well, as soon as I come to my senses, we are going to solve this problem ;)
tara:
Вы спаммите покупку не только диссертации, но и автореферата (полный беспредел) никому не известного автора на сомнительную тему.
You should learn how to use the internet. Then read it, and then draw conclusions. In the meantime, you're digging through the manuscripts of .....Newton.
There is still a problem with the error and correctness of application to the Hearst market in general.
The whole conclusion starts with the well-known Einstein formula for SB which says that the mean deviation of a stray particle from the origin increases in direct proportion to the root of time. If per tact of time a particle moves +1/-1, then R=SQRT(N), where N acts as time, or number of increments. But in fact we rarely deal with processes with two discrete increments +1 and -1 and it follows, that in general case R=sko*SQRT(N), which has sense if distribution has sko=constant, i.e. distribution is stationary. Hence R/sko=N^0.5 for random walk. Then 0.5 is substituted for the variable and it is calculated through logarithms. In order to use accumulated rather than average increment (because you need much more statistics for average increment) an empirical correction factor is also introduced. The value of the Hurst index for market data is highly questionable, as the distribution is non-stationary and it changes rapidly and depends on its previous values. There is no theoretical basis for the validity of using this indicator for nonstationary data. That is, it can be applied, but the results cannot be trusted :)
I thought for a long time about what you have said - all these are serious and valuable remarks. But you must agree, that to check all this, firstly, it is required a verified methodology of calculations, secondly, it is required some experiments really proving theoretical statements and calculations. Besides, the experiment will help to adjust calculation methods and synchronize them with theoretical calculations (if this is possible at all). Only after that it will be possible to reliably judge whether the method is suitable for analysis of real financial series. I must admit that I have as many doubts as you do. But the only way to answer all these questions is to work on the subject.
With this in mind, I will start with the very basics, namely Einstein's formula for SB R=SQRT(N):
1.0 I will generate a pure normally distributed SB +1/-1 without any AR effects or volatility clustering.
1.2 I will test the hypothesis of R=SQRT(N). If there will be some deviations, then most likely it is about the PRNG generation algorithm. We can try it with numbers from random.org. The main thing is that at this, the lowest stage, we have to have a superreliable SB that is 100% consistent with the theory.
1.3 Hearst check on the generated SB. This is a special, very important moment. Here he should pass the SB, so he could be allowed to more complex formations.
1.4 Generation of SB with Paretto-Levy distributions, based on volatility of real instruments. Theoretically, Hurst should show the same as before, on a normal distribution. If it is not so, we should analyze why it happens and if further investigation is meaningful.
1.5. Adding AR effects to the SB. We must carefully study how short-term linear dependencies can distort (in theory distort) the indicator readings, and how to properly account for these effects, etc.
1.6 In parallel, I would like to develop the cyclic topic and experiment with artificial primitives like y=Cos(x) and more complex Weierstrass function. Theoretically, the V-statistic should correctly determine the lengths of cycles in these processes.
2.1 If the first stage is passed, the fractal method can be allowed to work on real financial series. At this stage we will already be absolutely sure of the correctness of the methods it provides, and therefore it will be possible to correctly interpret the results.
P.S. It should be noted that most of the TA indicators, such as RSI or MA, will not pass even the very first test on the SB. RSI for example will show overbought and oversold zones, and the SMA will change its direction.
P.P.S. I wonder if the time during which the RSI will be in the overbought and oversold zone for the SB will be approximately equal to the time for real financial series or not?
Still, what fascinates me about this whole topic is that fractal statistics is positioned as a reliable method of separating the chaff (SB) from the grains (real markets). To the eye, the charts of the SB and markets are indistinguishable, they all appear in the technical analysis, and all TA indicators work on both the SB and the real markets. So if a pattern appears where it cannot occur a priori, may it mean something?
The file does not stick. You'd better read it.
OLGA STANISLAVOVNA GULYAEVA
CURRENCY RISK MANAGEMENT ON THE BASIS OF FRACTAL METHODS OF CURRENCY RATE PREDICTION ANALYSIS
Google it. It's easier . Maybe someone will make an indicator.
Yeah, I looked it up. There is a slightly different method there. But so far I am more interested not in how to count (that is known), but in the representativeness of the results and how to reconcile theory with practice.