FR H-Volatility - page 11
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Only you have constructed a probability density function (PDF) rather than a distribution function, because PDF has three properties. 1. It (PDF) is non-decreasing. 2. If x tends to infinity, then the PDF tends to 1. Naturally if everything is normalized. The SP and PDF are related by an integral (PDF is an integral of the SP).
The phrase "This graph is called a distribution curve or distribution function; the function itself is called a probability density function. " is not quite correct.
I understand what you mean - "error integral" or in another way "error function" (EF). The function that describes it is called erf(x), and is defined as follows: for a normal distribution and
for arbitrary, where f(t) is the PDF or probability density function, K is the normalization factor chosen from the condition of equality of a unit integral of the PDF over the entire definition area. So, not "FR has 3 properties. 1. It (FR) is non-decreasing. 2. If x tends to infinity, then FR tends to 1", but FO!
Another interesting property of FR is absolute value of ZZ arm without H (vector U in Fig. on the left)
If we compare the non-normalized FF for different H (Fig. right), we will see a surprising thing - the number of moves of the vector U with the amplitude of, for example, 10 points at the H=10, is greater than at H=15!!.! Although, it would seem that a high step of WP should certainly include these and some other moves... But no! It is not clear.
No, you got it wrong. It's a question of terminology. Here's a picture. And once again, here is a link to wikipedia, where the definition of FR is https://ru.wikipedia.org/wiki/%D0%A0%D0%B0%D1%81%D0%BF%D1%80%D0%B5%D0%B4%D0%B5%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5_%D0%B2%D0%B5%D1%80%D0%BE%D1%8F%D1%82%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%B9
Regarding a phase. At the point t=0 (see your figure), we kind of do not know whether the extremum at the point t=-1 has formed or not, as the vector H can reverse downwards, and this extremum will disappear (become false). It turns out we have no reliable datum H. Although I can be mistaken and I have a different zigzag indicator than yours.
As for the first point, I agree.
As for the definition of the point of formation of a Zig-Zag extremum, it is considered formed if the price deviates from its maximum (minimum) value to the left, by a value greater than or equal to H (step of division). This definition is given in Pastukhov's dissertation work and is correct.
As for the first point, I agree.
As for the definition of the point of formation of a Zig-Zag extremum, it is considered formed if the price deviates from its maximum (minimum) value to the left, by a value greater than or equal to H (step of division). This definition is given in Pastukhov's dissertation work and is correct.
One more question if not tortured: "... number of moves of vector U with amplitude e.g. ..." Does it mean motion in the same direction as vector H. If it suddenly at t=0 turns downwards also counts ?
Let's define entry/exit points for a potential TS based on ZZ prediction. Profit order should be placed at the level of predicted extremum. In case the price didn't reach this value, we close immediately at the formation of new extremum, i.e. by H below it on the price scale. Kagi strategy proposed by Pastukhov does not tell us anything about the amplitude of a certain expected movement, but it gives an integral estimate of this movement - H+-delta. Considering that we will close on a pullback equal to H - we pocket this delta as a reward! Having created a system that predicts with some probability at the point t=0 the amplitude of the expected movement U, we can estimate the expected value of delta as the difference between the centre of severity of the FF of real movements and H. If this value in absolute value exceeds the spread - the strategy will be profitable.
As an example, let's evaluate delta using this technique for the TS that opens a position at each point following the pullback from the nearest top at H and simultaneously closing the previous position, see fig. The red line shows the profitability (not including the spread) estimated according to the proposed scheme and the blue line - the profitability according to the emulation trading results. Do not be confused by the minus, in any case the strategy can be "reversed".
As they say "to pi", but for rough estimation, for want of a better one, I think it will do. You can make up variants of predicting the expected movement :-)
to Prival
Еще 1 вопрос если не замучил. ".. число ходок вектора U с амплитудой например .." Это имеется ввиду движение в том же направлении, что и вектор H. Если он вдруг в t=0 развернулся вниз тоже считается ?
Yes. In this case its move is equal to zero and we should speak about the vertex formed at the point t=0. Everything is correct. In such statement you will not find ZZ sides of absolute value less than N.
I am posting the negative result (also the result) of my research.
The figure shows the average difference between the length of the right ZZ segment and the expected value of 2H (ordinate axis) with a different length of the left segment normalized to 2H (abscissa axis). The plotting has been made on ticks for EUR/JPY, the same picture is shown for EUR/USD.
It may be noted that there is no statistically significant dependence between the sides of ZZ! You have to dig somewhere else.
I think that statistical methods will not give statistical advantage in our case - arbitrariness appears unexpectedly in the market (at least for me), and disappears unexpectedly. We all know what we would do with it if we could track it, but how do we detect it?
I am convinced that statistical methods will not give us a statistical advantage in our business - arbitrariness arises unexpectedly (at least for me) and disappears just as unexpectedly. We all know what we would do about it if we could track it, but how do we detect it?
There can be two options that correspond to two opposing assumptions.
1. Arbitrariness emerges instantly (i.e. in a flash) and just as instantly disappears. It is impossible to predict when it occurs or when it disappears.
(2) Arbitrability has inertia and, therefore, its emergence, presence and disappearance are a market process that takes a certain amount of time. Consequently, arbitrability cannot emerge or disappear instantly. It is impossible to predict the moment of its emergence, but the moment of its disappearance can be predicted on the basis of its dynamics.
Which of these two statements do you prefer? I mean, which one do you think is fair and corresponds to reality?
If neither, then offer your version. Or offer it in addition to one of these two.
Until recently, the answer for me was not that unclear, but looking at the results of the Automated Trading Championship 2007 we have to admit the presence of arbitrage or (the same thing) market inefficiency, in fact! I agree with you that "The moment of occurrence of arbitrage cannot be predicted, but the moment of its disappearance can be predicted on the basis of its dynamics", the only question is which analysis methods to use, which toolkit to consider as adequate. BP analysis methods are based on the assumption of a cyclical process, the a priori presence of trends (herd effect). This is applicable to the analysis of sales volumes of a large company, but does not work at all for currency series.
Thus, the 2nd statement is accepted. We can take it as an axiom and dance from there.
The following questions arise:
What is arbitrability? What are its mathematical peculiarities, what are the mathematical characteristics of a series of quotes, and how is it reflected?
What is the best measure of arbitrability ? Obviously, we can construct many values to measure it. H-volatility is one example. It is, however, as we have seen, not very attractive and not very effective. It would be good to build a mathematical characteristic, which would be a measure of arbitrage at any behavior of quotes series: both at trend and flat periods.
It is clear that the process is cyclic. The possibility for arbitrage appears and disappears. But this cyclicality can never be stationary or even quasi-stationary. Therefore it is possible to investigate periods of stationarity intervals, it is even possible to construct their FR, but it will not lead to anything constructive. IMHO.
It seems to me that if one constructs an adequate, dynamic, local measure of arbitrability, then one can also investigate the properties of its inertia and, independently, track its changes to identify entry and exit moments. That is, consider an arbitrability indicator. And to do this, we need to solve the two questions posed: the first, to understand the nature (at least mathematical) of arbitrability, and the second, as a result of solving the first, the correct construction of the value itself.
Until recently, the answer for me was not that unclear, but looking at the results of the Automated Trading Championship 2007 we have to admit the presence of arbitrage or (the same thing) market inefficiency, in fact! I agree with you that "The moment of occurrence of arbitrage cannot be predicted, but the moment of its disappearance can be predicted on the basis of its dynamics", the only question is which analysis methods to use, which toolkit to consider as adequate. BP analysis methods are based on the assumption of a cyclical process, the a priori presence of trends (herd effect). This applies to analysis of sales volume of a large company but does not work at all for currency series.
I do not agree with you.
1. Regarding arbitrage, here is an interpretation of arbitrage from Wikipedia: "Broker A puts in an order to buy 100 shares of some company for 18 cents, and broker B puts in an order to sell 100 shares of the same company for 17 cents. If the speculator notices both bids at the same time, he can accept both and make a profit. This is what is called arbitrage." That is, arbitrage either exists or it doesn't. The time of its emergence and disappearance does not matter (the main thing is to make two deals). Although we may understand arbitration differently, because I do not understand the phrase market inefficiency in fact.
2. The methods of analysis of BP (time series) do not work? The MA does not work, the correlation coefficient does not work too, etc. The methods of BP analysis are a wagon and a small cart and they all do not work. BP prediction with NS Better also does not work?
3) Looking at the results of the Automated TradingChampionship 2007, could you clarify your conclusions?
Regards Privalov