a trading strategy based on Elliott Wave Theory - page 223
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...Let me remind you that Harst index(h), FAC and H-volatility(as defined in
Pastukhov's thesis), are related by obvious correlations:
FAC=1-2/H=2h-1.
Let me remind you that FAC can be defined as the difference between all co-directional price jumps (moves) and counter-directional moves, divided by the sum of all moves...
I think the equality FAC=1-2/H=2h-1 is a very strong assumption.
To put it into words, H-volatility can be defined as the sum of all H increments
(modulo) divided by the number of all increments. This is very different from your definition of FAC
. Also, I think that's not exactly how the FAC is formulated, but I'm not sure about that yet,
will have to see.
Although. For Brownian motion H-volatility =2, with H-Hurst =0.5. So
1-2/H=2h-1 holds, 1-2/2=0 and 2*0.5-1=0. The equality is true for this case
(Brownian motion).
Other cases, such as H-volatility = 1 (the so-called "saw-tooth" with a spread in H, characterized
by the fact that the general trend along such a line is zero, while the reversion of movements is absolute, that is, for every
movement "up" there is exactly the same movement "down"). If we substitute 1 for the left part,
we get -1, with H-Hurst =0 (antipersistence, also characterized by the reversion,
but in this case we cannot say anything about the overall trend and it is just as difficult to say what it is
reversion). By the way, H-volatility = 1, this is the lower bound for this parameter, there should not
be a line with an H-volatility value less than 1. For H-Hurst, I don't know if
there is such a condition.
Another case, H-volatility =4 and H-Hurst =0.75. In the simplest case, H-volatility =4
movements in one direction should be seven times larger in magnitude than movements in the other direction.
In its simplest form, this is the same saw, but with a shift in the overall trend. For the case of persistence at
H-Hurst =0.75 this cannot be said. By the way, when H-Hurst =1 H-volatility becomes
infinity at all.
I think 1-2/H=2h-1 may in some general approximation, on a very qualitative level,
describe parameter behavior but no more. This is about H-volatility and H-Hurst, I have not dealt with FAC
, maybe there are some surprises there.
2 North Wind
except in one case. Mostly a 50/50 split, give or take 2-4%.
In your thread at fxclub ForAxel gave pictures of sets which not only can be considered
sufficiently separable, but which also have distinguished centres
localization. I don't know only they reflect some real data or it is so far,
search program.
So ForAxel used other characteristics. Maybe he managed to find some that
that are reasonably well separated by the results. But there, as I recall, there was a question
of stability.
I can't seem to download it. I can see it:
File Name: USDnew.zip
Size: 4.45 MB
Description: EURUSD 2006
There is no download link. After registration and login the same thing.
Sergey, maybe you could just drop this archive to my email: yurixxx [at] gmail [dot] com
Or explain how to behave with this site.
PS
Sergei, did I understand correctly that you calculated the FAC not on the whole history, but only on the 100 renko-bar window. The result is the curve shown in the picture. If so, I must have got you wrong again. Here it is.
I understood it as a confirmation of what I said about integrating over the whole story. And the key words are, I suppose, "just like... just like the others". That is, the usual way is not to use the whole history, but a limited sliding window.
I think the equality FAC=1-2/H=2h-1 is a very strong assumption.
To put it into words, H-volatility can be defined as the sum of all H-increases
(modulo) divided by the number of all increments. From your FAC definition this is very
different. Also, I don't think that's exactly how FAC is formulated, but I'm not sure about that yet,
will have to have a look.
In the dissertation H-volatility is defined as the ratio of the sum of ALL price changes to the number of inversions or, in other words, to the number of price direction changes (see http://forum.fxclub.org/showthread.php?t=32942&page =9, post of 18.12.2006, 10:46 :-)
So, let us denote by n1 the sum of all co-directional price jumps, by n2 the sum of all counter-directional price jumps (sum of all H increments), by N the sum of all jumps (number of all increments), then for unit price increments we define
FAC=(n1-n2)/N and H=1*N/n2. Obviously, n1+n2=N.
Then, FAC=(n1-n2)/N=(n1+n2-2*n2)/N=1-2/H, which was required to prove!
I, of course, admit that I got carried away by unit amplitude increments, and correctly, in the case of a known law of distribution of increments, write:
ФАК=1-2/H/sigma=2h-1.
By the way, the fact that at "absolute saw" (no opposite price movements) the Hurst index (h) is equal to zero, isn't strange, if we remember that this index defines dependence of the standard deviation on the TF: sigma(TF)= sigma(t0)*(t/t0)^h.
That is, as the TF increases, the "absolute sawtooth" spread does not increase. Which is obvious.
to Yuryxx
I have sent an archive with ticks by a parcel to your address :-) Please wait.
As for the Hurst index I told you, I INTEGRATE over the whole history to calculate the standard deviation for the selected timeframe. To calculate the FAC, I sum it up in a sliding window. The length of the window is 100 bars.
Here is an example for FAC:
And here is an example for Hearst:
I can't seem to download it. I can see it:
File Name: USDnew.zip.
Size: 4.45 MB
Description: EURUSD 2006
There is no download link. After registering and logging in, the same thing.
You have to find the following phrase in the middle of the page and click on it:
Download for free with FileFactory Basic
You will see 1 advertisement page, Click Skip, and then on the next page click again on Download....
Hi Sergey.
Now I am a bit distracted from the forum threads and absorbed in my research, especially since we have temporarily moved away from the topic of trend detection. I must confess that I am not particularly interested in kagi, renko and H, although I give the author his due. It's rare to find such a well-founded and interesting work in this area. But perhaps I am jumping to conclusions regarding the use of the approach outlined.
But trend detection is really interesting to me, especially as it forms the basis in my strategy.
Basic objectives of time series analysis.
The basic objective of statistical time series analysis is to follow the available trajectory of that series:
....
After reading this post I realized that you are outlining the theoretical base, but I didn't find any useful information for myself. It's interesting that, while rightly insisting on building the right model beforehand, you've already found the trends:
Sergey, pay attention to the picture from my previous post. The moving window size there is 100 renko-bars, so the phase delay due to the averaging procedure on historical data does not exceed half of this value, i.e. 50 bars. The characteristic period of market volatility (see fig.), is about 300-400 bars! Thus, we can state the fact of REAL identification of the trend (deterministic) on the time series with the use of renko-construction! With the classical time series of currency tools this has never been possible, and on all TFs FAC, it was not reliably positive.
And rightly so, that you found them. And what, the whole model is in the use of renko-building? By the way, I have a question, just about the trend: how do you define it in your picture? With your permission, I've stained it a bit. The big trend is between the two thick red lines. How, or what is the correct way to read, the FAC chart to understand that it is obviously there.
Addendum: So if I give you a separate FAC chart without price, can you find trends on it?
I categorically reject the use of a data sliding window in any manifestation of that idea. Why do you have it 100 counts and not 137, 76 or 7? And how long would the period of market volatility be if you chose a window of 7000 bars?
Let me remind you of my search for a trend. Reading clever books on this direction, for example, only frustrates me. Everything comes down to the fact that it is either difficult or impossible to find them, and therefore everything that is found is not a trend. I decided to correct the formulation of the task. I do not need to find all trends that appeared and disappeared during the whole history of quotes. I set myself a more modest task - to find the starting point from which the correlation level between samples ("strength of connection"), moving from the current reference point in the history, falls to the minimum value from which it is considered that the connection from the current bar (reference point) is completely lost. For this purpose I chose autocorrelation (but there are other ideas). Hence, I have:
Statistics - autocorrelation values (Ro)
Criterion - range [0:Ro=y]
I had to rework autocorrelation a bit. By logic (of course), the closest bars should have the strongest correlation. The function of this strength, should gradually (but not necessarily uniformly) converge to some value (including 0.0). Concentrating on my approach, I continue my research on optimal criterion selection. The point is that this criterion can find (of course, not always) very "long links" and I very much want to shorten them in some clever way.
And what are your statistics and criteria for identifying a trend based on renko-building?
Glad you're continuing in your chosen direction.
What you marked in the image as a trend is actually a "stochastic trend" - it looks like a directed price movement but its essence is a random, Brownian motion. It is impossible to earn on it in principle. And what distinguishes FAC, going into the area of positive values, is a deterministic trend, one can and should earn on it. Also one can and should earn on the pullback market - when FAC goes to the area of negative values. The criteria for identifying the trend and the flat on the rennco-building are the same as for the normal time series. And it is logical because we're looking for the laws of relationship between the cause (disturbance) and consequence (market reaction) and the laws should be the same for any view of the time series.
Here it should be noted: what is a trend in a given TF or RN, in another TF or RN, may be a pullback. This should be remembered, rather than trying to make a decision about the current nature of the market by looking at the time series chart. This is the rare case where human intuition is powerless. Chaos reigns supreme here, with its own specific laws which are alien to the common mind.
Well done. Take another step towards the truth!
...So let us denote by n1 the sum of all co-directed price jumps, by n2 the sum of all counter-directed price jumps (sum of all H increments), by N the sum of all jumps (number of all increments), then for unit price increments we define:
FAC=(n1-n2)/N and H=1*N/n2. Obviously, n1+n2=N.
Then, FAC=(n1-n2)/N=(n1+n2-2*n2)/N=1-2/H, which was required to prove!
I, of course, admit that I got carried away by unit amplitude increments, and correctly, in the case of a known law of distribution of increments, write:
ФАК=1-2/H/sigma=2h-1.
By the way, the fact that at "absolute saw" (no opposite price movements) the Hurst index (h) is equal to zero, isn't strange, if we remember that this index defines dependence of the standard deviation on the TF: sigma(TF)= sigma(t0)*(t/t0)^h.
That is, as the TF increases, the "absolute sawtooth" spread does not increase. Which is obvious...
Let's try to sort out the terminology, for starters. I suggest
the following:
H - value, characterizing the size of change of price value at which
is considered to be a real change of price value. As
any size can only be positive.
Price change - the interval at which the price value changes
to the value H, positive or negative, depending on the sign
difference of price values, at the end and at the beginning of the interval. It is calculated as
=(Price value at the end of the interval - price value at the beginning of the interval)/H, therefore
therefore can only take values 1 or -1.
A positive price change is a price change with a positive sign.
A negative price change is a negative price change.
Price movements are plots of consecutive price changes with the same sign,
greater than or equal to one change in price. This value is countable.
Thus, H-volatility is defined as
=(Num of Positive price changes + Num of Negative price changes)
/total number of price movements.
Now, I want to understand what you mean by co-directional and counter-directional price movements.
and counter-directional price movements?
No parcel, no parcel post, not even a receipt. :-))
Check if it came back. If so, there is a mistake in the address. Most likely a lost 'x'.
Likewise. You're a tough nut too. :о)
It is logical, because we are looking for the laws of the relationship between cause (disturbance) and effect (market reaction), and the laws should be the same for all time series representations.
Sergey, I don't agree with you here. Not only me, but also Mr Peters, with his treatise on market fractality. Market participants, never react the same to the same market change (hence what we all generate together - the price series), hence its fractality. Everything is different for everyone, both the deposit and the forecast horizon and the allowable losses... The market, as you correctly noted, is Chaos, and it cannot react to the same thing in the same way. If, for example, you enter a dense forest, the local "investors" will react differently to the "disturbance".
It is that rare case when human intuition is powerless. Chaos rules here with its own specific laws, which are alien to the ordinary mind
Apparently I am getting old, or stupid, but more and more I am inclined to think, there is no greater order than Chaos.
And what is singled out by FAC going into the area of positive values is a deterministic trend.
Now let's take a close look at your graph, specifically the 1600 to 2000 countdown section. In it the FAC, moving from 1600 reference, reaches 0 (1700 bar to the eye) and goes into its positive region. It remains there until 1900 (as far as the eye can see). Hence, it is a deterministic trend. Good. I look at the price movement and what do I see? A trend? I don't see a trend. So far I trust my eyes and intuition more than the FAC (especially with such an acronym :o)
By the way, FAC shows pretty little of the deterministic trend areas. And mostly where there are none to the eye at all. And clarify if FAC+ series is deterministic and if FAC-, which one?
What you see in the picture as a trend is in fact a "stochastic trend" - it looks like a directed price movement, but in essence it is a random, Brownian motion.
I'm totally confused about determinism, trendiness, stochasticity, etc. :о) And I'm not at all worried about it. I've understood, or rather read in smart books, that I will never see a trend. But I also realized that I do not need it. The model that I am working on now may be conditionally called evolutionary fractal-wave analysis (I've never encountered any analogues). All that's needed is an estimate of the strength of the relationship between the samples. By the way, I also summarise multidirectional movements in the same way, and how can it be stochastic if I use essentially the same FAC and the same sums as you do? All I've done is to "raise" it up a bit.
Good for you. Take another step towards the truth!
Thanks. Stepping confidently towards it. :о))))
Good luck