FR H-Volatility
I read Shiryaev's materials and Pastukhov's dissertation in summer. I think the theme is very interesting, but I always lack time and knowledge. Your and Yurixx's developments are impressive, but they are mainly on EUR. I would like to use my own hands to develop this theme for other currencies on MT4 as well. Who has such knowledge and experience? First of all I am interested in the calculation of N from h. Unfortunately, I'm not good with cads yet.
Remind me again what is N and how do you plan to use it?
of the cagy-zigzag segments ... constructed for H=10.
If possible, a little more detail about these concepts. Unfortunately I don't know the terminology. I would really like to understand what kind of BP you are analysing ? how does it come out ? to understand what you have on the chart here.
Remind me again what is N and how do you plan to use it?
".......I, for example, looking at this picture - right here I have it written that if N from h is greater than two, then we buy at the appropriate moments. I.e. in this case we act in the same direction as the market moves. If N is less than two, then we should do the opposite. Even if prices are rising, we should still sell. ....".
Although both in the picture and in Pastukhov's dissertation everything is different every time (well, that's nothing). The essence of the method is clear. I do not understand the physical sense of R(H) and therefore I am not confident that I will calculate it correctly. Therefore, I want to ask you how it all is calculated. Perhaps, it would be clearer if someone has already done it in MQL4.
In fact the graph is mirror-symmetric about the ordinate axis, I took the modulus of the difference for better statistics. Obviously, this distribution is not normal. As I understand it, all your reasoning is based on the postulate of normal distribution of cagy zigzag segments... Please formulate the question again.
P.S. By the way, if we find the average value (not maximal, but c.t. ) of FR, it equals 19.3 for the given partition, which is <2H and does not contradict anything.
Yes in general the question was about constructing an experimental FR. I did the same as you, and implied that for obvious reasons the ZZ segment > 0. I did not take into account the sign. Therefore I relied on the area of definition [0,∞] and zero value of FR at zero. From all this there was a conclusion that the normal distribution is not suitable even as a model function.
Now, of course, I realized that taking into account the sign gives a symmetric FR. That leaves only the dip in zero. But that too is a dark question. When the price doesn't change, no new quotes are translated - no point. So we have only (or almost only) non-zero differences in the data stream.
Your picture (if I understand it correctly) is a new argument. On a logarithmic scale you get almost a straight line. This means that the exponent is in the first degree, not the second. This is already interesting.
And as for the value of H-volatility for the Wiener process, I've figured it out. Whatever position the price is at, the probability that it will pass H upwards from that point is equal to the probability that it will pass H downwards. And it doesn't depend on the current price value, nor on previous price values, nor on H. And from this, you can eventually get an explicit view of the FR. We need to see what the distribution for Brownian motion is derived from, probably the same. The 2H value for the mean is also, as far as I understand it, a result of this provision.
But, by the way, there is another relation for the Wiener process, which can be used as an arbitrability criterion. Since for the Gaussian distribution the value of the mean and the sko is explicitly calculated, we have sko/mean = root(pi/2). And this is also true for any H partition parameters. It is interesting to check what we actually have, for example, for that distribution in your picture.
That's an opinion:
I am not interested in the strategy of kagi, etc. But R(H) itself as an independent characteristic of the instrument in question. I would like to investigate it. I think there is something in it?
".......И, например, глядя на эту картинку – вот тут вот у меня написано, что если N от h больше двойки, то мы покупаем в соответствующие моменты. Т.е. мы в этом случае действуем сонаправленно с движением рынка. Если N меньше двойки, то поступать надо наоборот. Даже если цены растут, то надо тем не менее продавать. ...."
Everything is clear, this is the definition of H-volatility (Hv). It can be shown that for the Time Series obtained by integrating a random variable with zero expectation (Wiener process or one-dimensional Brownian motion), H-volatility is identically equal to 2. In other words, the average cage spread with step H tends to 2H (Hv=2H/H=2). On the other hand, the return of any Trade Strategy (TS) BP of Wiener type tends to zero. That is why the difference between Hv and 2 can be regarded as possible arbitrability of TS: s=(Hv-2)*H - average return of TS per one transaction in points, as a function of H. Moreover, if s<0, we have a counter-trend TS, if s>0 - a trend TS.
Rosh wrote (a):
There is such a thing:
Yes we have known for a long time that on all instruments, and for all H-partitions, the dreprofitability of the TS, in the long run, lies inside the spread. Besides, it can probably be proven that H-partitions are the asymptotic limit on returns for all sorts of arbitrage strategies.
But by the way, there is another relationship for the Wiener process which can be used as an arbitrability criterion. Since the Gaussian distribution has an explicit mean and sko, we have sko/mean = root(pi/2). And this is also true for any H partition parameters. It is interesting to check what we actually have, for example, for that distribution in your picture.
For symmetric FRs it is true: sko=SQRT(Sum[(M-x)^2]/[n-1]), mean=Sum[(M-x)]/n), then sko/mean != root(pi/2).
Explain, what do you mean by that?
- Free trading apps
- Over 8,000 signals for copying
- Economic news for exploring financial markets
You agree to website policy and terms of use
This thread is a continuation of the conversation about kagi splits.
Yura, let's look at the FR of the cagy zigzag segments for EURJPY 10^6 ticks BP, plotted for H=10.
The graph is actually mirror-symmetric about the ordinate axis, I took the modulus of the difference for better statistics. Obviously this distribution is not normal. As I understand it, all your reasoning is repulsed by the postulate of normal distribution of cagy-zigzag segments... Please formulate the question again.
P.S. By the way, if you find the average value (not maximum, but t.t. ) of FR, it is 19.3 for this partition, which is <2H and does not contradict anything.