FR H-Volatility - page 5

 
Let me get this straight. Are you talking about integral PDF or probability density function? In principle they are both quite "integral", but for clarity of understanding ...

I'm talking about a curve describing a probability density function.

Regarding AR-models of different order, TCs built on their basis do not overlap existing commissions :-(

By the way, I want to share one observation. Below I present an indicator that displays Cagi constructions (red line) with a Zig-Zag that generates them (blue line) in a separate window. Moreover, the constructions are not bound to a timeline (step - edge). It seemed to me that it is easier to identify the peculiarities of BP behavior in terms of H+ or H- arbitrability.

Perhaps it makes sense to impose restrictions on the applicability of Cagi-strategy. This will increase the number of profitable passes and, consequently, the excess of arbitrage over the value of the transaction.

P.S. The indicator is raw!

Files:
 

Sergey, I don't understand a bit.

for (i=Start; i>=0; i--) { hh[i]=Bid;  YY[i]=Bid;  XX[i]=0; }

In this line you assign the current value of Bid to all elements of arrays hh, YY ? Even if so, it's still incorrect. The size of these arrays is 5000 and Start=10000.

Can you just explain in words what it does ?

As for the applicability of FR for TC, my opinion, it is unsuitable for this, because it is an integral characteristic of the system and, as a consequence, it misses a lot of interesting things from the point of view of arbitrage.

By the way, what is interesting from an arbitrage point of view? I confess that I am completely uneducated in this respect. I just can't imagine what means of statistics can be useful for arbitrage. Or you mean something else? Explain anyway.

 

The vector lengths YY, hh are equal to the number of Zig-Zag breaks, which is not known in advance and must be less than the value declared in the variable description (5000). After the vector elements are defined, the remaining undefined elements are filled with zeros automatically. Because of this, when scaling a picture, you sometimes get a situation where there are Kagi elements and zeros in the window at the same time. As a consequence, you can't see anything. So, I prepopulate the whole vector with numbers close to the expected ones. I have developed this indicator from the similar chart indicator without any artificial thinking. That's why it is overloaded with unnecessary details.

Below is the link to the improved version:

Yura, I don't know the answer to your second question!

Files:
 
I think the Cag plots for opening prices are more correct compared to High-Low extrema.
Files:
 
It's hard for me to say anything about it. I'm not used to this kind of zig-zag, so I don't see what I can get out of it. Besides, I got hooked on this statistical topic and nothing else comes into my head now. :-)
 
Not used to this kind of zigzag, so I can't see what I can get out of it.

Yes, it's in the ready-made "Merrill patterns". Compare: http://www.bollingeronbollingerbands.com/subscribe/login.php?ref=patterns/library. php:-)

Besides, I got hooked on this statistical topic and nothing else comes to mind now. :-)
What's the theme?
 

Thank you, you've enlightened me. I admittedly didn't know or hear anything about it. I'll see if there really is something interesting there.

And this topic is exactly what we've been discussing lately: real process FR, no arbitrage, effectiveness of Pastukhov's strategy and H-volatility. And the central point of all this is the actual measure of market arbitrage - where is it ?

 

Here is what I think about the arbitration indicator: Pastukhov in his work introduces the concept of H-inversion (ratio of the sum of absolute price increments by the value more than H to the number of Zig-Zag breaks composed of these increments) as a measure of market arbitrability, proving that for nonarbitrage market this value tends to 2H. Essentially, this boils down to comparing the absolute values of the lengths of the sides of the Zig-Zag to 2H. Pastukhov, integrates this value over some window and shows a steady, for some instruments, difference between it and 2H.

Here I thought that if one were to link not to this integral characteristic, but to the absolute value of the Zig-Zag side without 2H, calculated at each step of construction... In essence, this is nothing more than the size of the profit in pips that you would take if you were to open "on the move". From this point of view, arbitrage is a dependency in the alternation of the sign of the lengths of the sides of the Zig-Zag without 2H. One can dream of beating the market quickly and accurately.

In Fig., the blue histogram shows the lengths of the sides of a Zig-Zag without 2H; the red line shows the autocorrelation coefficient averaged over the window between adjacent bars in the histogram.

We need to investigate this feature for robustness.

 

I've been zigzagging in this direction for quite some time. By the way, the FR study is part of this research. For the kagi I did at all H=1 ... 50. For H=1, 5, 10, 15, 20 the obtained FR was posted in this thread. But I did the same for zigzags built without limitation of H value. The view of phd is completely identical.

However, I did not try ACF. I do not know what it can give. After all, when calculating the ACF a fixed time lag is taken between the current count and the count from the past ? If so, it is unlikely to do any good. Fixed lag is too rigid a relationship for a number of CBs. I liked your experiment with ACF better, which I have already mentioned. I even found that post of yours. It is on page 111 of the famous thread. There you've built ACF not by time lag (an integer number of equidistant time samples), but by price delta (i.e. candles were drawn as equidistant counts of price changes). In my opinion, he even built a TS based on it.

Are you watching the championship? Are you watching the leader? What can you say now about how arbitrage-free the market process is ? :-)I wonder how you rate the statistical advantage that Better's system provides ?

 
Yurixx писал (а): Or maybe a Wiener ? :-)
A Wiener process is, by definition, an integral of Gaussian white noise, and a returns process is not Gaussian at all.
Reason: