a trading strategy based on Elliott Wave Theory - page 225
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Besides, instead of the "straight" formula to calculate H-volatility you seem
Instead of the "straight" formula you seem to use your own one which is wrong and that's why your result is wrong too.
You are right!
I have acted incorrectly introducing a new definition of H-volatility.
In my excuse, I can say that if we normalize the H-volatility, we get a great indicator that characterizes the market as a trend or flat one and it is not connected with the amplitude of price movements.
ZZY. I will count the series you suggested after sleep.
...New definition of H-volatility...
In a good way, we need a new name for the new method.
...I can say that by normalizing H-volatility we get an excellent indicator, which characterizes a market as trendy or flat, and which is not bound to the amplitude of price fluctuations...
I don't argue with that, but first we need to investigate its properties.
Another row, e.g. 3,-1,3,-1, etc. I argue that FAC would be =-1, H-volatility =2.
H-partitioning is done at h=1. No differences need to be taken, the series is pure.
By the way, another interesting example of a series, 1,2,-3,1,2,-3. What do you think will happen?
Go for it.
For series 3,-1,3,-1, etc.
The series is stationary, not centered. We perform the centering procedure by subtracting expectation m=1 from each term of the series.
For series 1,2,-3,1,2,-3 etc.
The series is stationary, centered. The distribution of amplitudes of price jumps is not symmetric to the ordinate axis. We will use a more general expression for FAC:
as with FAC=-1 there should be H=1 and with FAC=-0.5 there should be H=4/3.
Did I understand the summary correctly ?
I'm not so much interested in the relationship of H-volatility to FAC as I am in their relationship to the Hurst index.
In the case of series 3,-1,3,-1, etc. we get:
from FAC=-1 follows h=0, which is incorrect, and from H=2 follows h=0.5, which is also incorrect because the spread in this case grows as T and not as sqrt(T) and should be h=1.
In the case of series 1,2,-3,1,2,-3 etc. we get:
from FAC=-0.5 it follows h=1/4, which is wrong, since here the spread is not time-dependent at all and should be h=0. From H=3 it follows h=2/3, which is also wrong.
More precisely, the identity FAC=1-2/H is true for a renko partition with step 1, which generates a time series with normally distributed (or close to normal distribution) first differences. If the partition step is m, then it is true: FAC=1-2*m/H. For Kagi partition, it is true: FAC=1-2*sigma/H, where sigma is standard deviation. The identity FAC=2h-1 is true for ALL integral time series (typical forex) with normally distributed (close to normal distribution) first differences.
The examples of artificial series we consider (3,-1,3,-1, etc.) have distribution laws that are far from normal. Not surprisingly, the results look strange too.
...More precisely, the identity FAC=1-2/H is true for a renko partition with step 1, which generates, a time series with normally distributed (or close to normal distribution) first differences. If the splitting step is m, then it is true: FAC=1-2*m/H. For Kagi partition, it is true: FAC=1-2*sigma/H, where sigma is standard deviation. The identity FAC=2h-1 is true for ALL integral time series (typical forex) with normally distributed (close to normal distribution) first differences.
The examples of artificial series we consider (3,-1,3,-1, etc.) have distribution laws that are far from normal. Not surprisingly, the results look strange too.
It is more correct to write FAC=1-2/H as FAC=1-2/H=-1
equality is true only for this case, it does not work for other cases.
The algorithm is identical to the one described by Northwind on http://forum.fxclub.org/showthread.php?t=32942&page=8 post: 12.12.2006, 15:44
The question of interest was: What value the price would pass relative to the previous movement, after the formation of the next extremum. In other words, the threshold value was subtracted from the right side of the imaginary triangle constructed by three extrema and the resulting difference was divided by the full value of the left side. This is what we got for EURUSD 2006 tick quotes for the threshold of 2 points. The abscissa axis represents the value of the aspect ratio and the ordinate axis represents the relative amount of such movements. The integral of the obtained distribution function is 1, which is obvious.
What can we say when analyzing the obtained result? Probably, the only thing that the price will most likely turn around after the formation of the next extremum and go in the opposite direction without giving any chance to make profit. This situation is typical of a wide range of thresholds for EURUSD, EURCHF, EURGBP. Which in turn allows us to characterize the market as a "non-trending" one. Indeed, otherwise the price would have probably continued the move once it had started...
To Northwind
For example, for a series of ticks EURUSD 2006:
You can see that the value -0.512=FAC=1-2*sigma/H=-0.51 with an accuracy of at least 1%.
I got hooked on the highlighted words. What are the conditions for the formation of an extremum? Isn't the move backwards by at least the threshold value ? If so, your summary can be clarified a bit by removing the stamp of pessimism from it.
The formation of an extremum means that the price has already reversed and moved in the opposite direction by at least the threshold. In the distribution graph the cases when the price has passed the distance<=threshold+previous movement lie in the interval [0,1] and amount to 95% (by eye). This would seem to indicate the absolute dominance of returns in the market. However, there is another way of looking at it.
According to my own observations, the average tick rate (MQ-demo) is about 4 ticks per minute. According to Neutron's archive it is about 5. According to GainCapital archive - about 5.5
And how long do short-term price movements last for which there is an opportunity for trading? Well, not much, if we remember what happens during news releases and abruptness of price movements on the market. What will the rest of the time the price does if the ticks follow with such a speed.
5% of the time that remains for the trends according to Sergey's calculations is quite good, in my opinion. It is more than an hour every day! The only question is the formulation of the problem. There appear to be several possible solutions.
1. Identification of the emerging trend. I think it is closest to the discontinuity problem, which North Wind wrote about . What criteria are needed to be able to say that the stationarity of the return price movement has broken down?
2. Conventionally speaking - "market betting" . While the price is languishing, you can enter at any time. The market will itself determine the direction of the trend at the right moment. The only thing you need is to correctly set a stop with a reversal, which again requires an appropriate criterion or the skillful use of MM that exploits this same reversibility.
3. The actual use of reversion in the price movement. For this purpose, we need to determine the frame (ticks ? times ? H- ?), on which this rebound is most clearly seen. Your post, Sergey, after reading Pastukhov's thesis, perfectly demonstrated that it is possible and how to do it.
I think there can be many more constructive approaches.
I understand that your pessimism is ironic. You weren't going to make money on every tick movement, were you? ? :-)) And if that's the case, then maybe you could shift your focus somewhat in researching market statistics ? What I mean is this.
Large, directional movements occur rarely, but they are what we are interested in. Maybe we can distinguish them from the general trampling and statistically investigate their structure. For example, those cases which on your distribution correspond to the 0 abscissa point (94% of all cases) means that price has passed exactly the threshold in the opposite direction. If it has passed 2 thresholds in the original direction, then the sum of the two moves is already a threshold and after another reversal price moves in the original direction again. It would be interesting to see the statistics of the 3rd zigzag knee under the condition of the 1st knee >> 2nd knee.
I've actually been fiddling with the tick zigzag for a long time too, trying to investigate market structure. However, my lack of education in mathematical statistics imposes certain limitations even on the problem statements I make. I think in completely different categories to you statisticians. That's why it would be very interesting to discuss both problem formulations beyond the study of two adjacent zigzag knees and the results of their solutions.
...
My H-volatility, for this series, has always come out very close to 2, yours is 1.35.
The number 2 turns out the same for many other people who have calculated this parameter.
Also, for H-volatility you should not use a, but b,
then it would really be H-volatility, otherwise it is something else again.