FR H-Volatility - page 21
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Sergei, there is a process on which in principle one cannot make money in the long run. I'm talking about the Venusian process obtained by integrating a normally distributed SV with zero MO. So, whatever TS you invent, in this case it is doomed to failure. Even theoretically such a TS cannot be created! Let us call such VR EFFECTIVE. As you see, efficiency is a property of this BP, not of a particular TS. I think the analogy made is transparent and intuitively clear?
Thank you, there's finally a stove to dance from. I'm just cutting out the words "in principle, you can't" from here. Let's start taking the process apart :-). 1 A Wiener process is a process with independent increments. Does this curve always have this property ? I think not, and you'll agree that there are areas where the increments are dependent - the task is to detect this fact as quickly as possible and trade in the direction of the increments within the correlation time. The second way is "any process with independent increments is Markovian, go there. We need to determine the transition probability matrix, since the set of price values is discrete and countable, it is theoretically possible
to Prival
Since this is my assertion, I'll add a little more. My conclusion is based only on common sense, not on the concepts of "martingale" and "efficiency". Moreover - I don't even know what those concepts mean and moreover - I don't want to know. But this ignorance doesn't bother me at all, just a different approach, a different outlook... :о)
I do not use these terms in my research either, as I do not understand them. And I consider mathematics as applied, just need to understand what mathematics and where to apply it :-).
Concerning that "the system's aspiration to occupy a steady state gives no advantages for forecasting", I understood correctly and showed you in pictures that this property may be well used or not I failed to convince. If not explain this idea in more detail, I always try to stay within the bounds of common sense too.
So there is complete unanimity on the first question. :-)) Great.
2. I understand, in general terms, what you are talking about, but I also understand that this is beyond my mathematical capabilities and maybe even my more specific understanding. :-(
3. Yes, this view of TC is indeed trivial, you don't need to know the FR to do it, just have the mo. I understood it from the beginning. So the question can be formulated in another way: does explicit knowledge of FR give any advantage compared to the elementary case of knowing mo, sko ? Well, and, if so, can it be used in some way.
Example. SP has asymmetry (as opposed to Gaussian, which is symmetric), though still mo=0. Can something be extracted from the shape of the curve or is it pointless ?
But this is interesting: "mathematics in money management is much more adequate from the point of view of the fact that there are correct and clear algorithms of action". Can we discuss these algorithms in more detail? That is, what is meant and where can it be found in an accessible form.
4. I am not interested in a qualitative comparison, but in a quantitative one. It is not a logical condition of TC. :-) To be precise, I want to normalize the spread over a sample so that it does not depend on the size of that sample.
I understand the calculation algorithm, but explain pls,
(a) By "each random variable" is meant that each sample of a SV series is a separate variable which has its own distribution ? This assumes that all such variables have the same distribution F(x) ? If not, what does "every random variable" mean ?
b) What is G(x) ? Why do we have to increase F(x) to the power of n and what does this have to do with the sample maximum ? Sorry, as a physicist I need to understand what I am doing.
The mathematics of money management and more exactly, risk management, has been described in many works and many results have been obtained. Some results are known to all (the Sharp Ratio/Sortino or V@R), others are more related to the common trading knowledge (such as Kelly's rule), others are beyond practical use in the nearest future (the coherent and convex measures of risk). All of these results are constructive, each saying "do this and that to limit risk with this and that". In practical terms there is a book I think by Vince, "The Mathematics of Capital Management" or something like that. If I'm not mistaken - it's about money management. I have not read it myself, only glanced through it, but it seems to be without nonsense and shamanism.
4. So, by the way, I just now understood that you probably want to look for the maximum not in a sample, but in the implementation of a process with independentincrements. This is a slightly different (more complicated) loop. I'll answer as I wanted to answer, exactly for sampling, if you need other you can ask me again.
a) This version assumes that the values of the series are independent equally distributed (with distribution function F) random variables. Eagle-Rash (1-0) is there, or whatever. The values themselves, not their sums.
b) G(x) is actually a maxima distribution function. The proof is simple: the probability that the maximum is less than x is equal to the probability that each s.v. is less than the suit (taptology) and this equals the product of the probabilities of events like "een value is less than x". Since the probabilities of all such events are equal, and equal to F(x), we get that G(x) = F^n(x).
1 A Wiener process is a process with independent increments. Does this curve always have this property? I think not, and you will agree that there are areas where the increments are dependent - the task is to detect this fact as quickly as possible and trade in the direction of the increments within the correlation time. The second way is "any process with independent increments is Markovian, go there. We need to determine the transition probability matrix, since the set of price values is discrete and countable, it is theoretically possible
Disagree! by convention - the increments are INDEPENDENT. Any local dependence is random (stochastic), therefore it will end as unexpectedly as it started and therefore this property cannot be exploited. About the second variant I do not understand. In general, the attempt to build a profitable TS using a random process (as defined above) is nonsense! Sergey, I've emphasized that "it is impossible in the long run" and I don't exclude variants to win locally. That doesn't contradict anything. The important thing is that on average, over a BIG history, the TC's return (the ratio of total profit to the number of trades made n) tends to zero as 1/SQRT(n).
to kamal
Based on your practical experience in the stock market, is it currently possible to use a strategy other than "buy (sell) and hold"?
3. In the case of independent increments - no, it does not, because in the case of independent increments and mo=0 the advantage cannot give anything - the market is efficient (according to the martingale criterion that I gave above). Otherwise there can be nothing better than the buy and hold rule. All this, I emphasize, for independent increments.
The mathematics of money management and more exactly, risk management, has been described in many works and many results have been obtained. Some results are known to all (the Sharp Ratio/Sortino or V@R), others are more related to the common trading knowledge (such as Kelly's rule), others are beyond practical use in the nearest future (the coherent and convex measures of risk). All of these results are constructive, each saying "do this and that to limit risk to this and that". In practical terms there is a book I think by Vince, "The Mathematics of Capital Management" or something like that. If I'm not mistaken - it's about money management. I have not read it myself, only glanced through it, but it seems to be without nonsense and shamanism.
4. So, by the way, I just now understood that you probably want to search not for a sample, but for the implementation of a process with independentincrements. This is a slightly different (more complicated) loop. I'll answer as I wanted to answer, exactly for sampling, if you need other you can ask me again.
a) This version assumes that the values of the series are independent equally distributed (with distribution function F) random variables. Eagle-Rash (1-0) is there, or whatever. The values themselves, not their sums.
b) G(x) is actually a maxima distribution function. The proof is simple: the probability that the maximum is less than x is equal to the probability that each s.v. is less than the suit (taptology) and this equals the product of the probabilities of events like "een value is less than x". Since the probabilities of all such events are equal, and equal to F(x), we get that G(x) = F^n(x).
Well, the second question has been dealt with as well, thank you. Special thanks for Vince, I'll be sure to find it. One last question remains.
a) If I understood correctly, by SP you mean all infinite set of realizations of series of SP, each of which is a special case of infinite series of this SP. In this case it is possible to talk about a distribution function for a single element. Correct me if I'm wrong.
And by "SP" I meant that very series (may be infinite) the finite part of which I have on my computer in the form of a fragment of quotes history. And I called a sample a part of this history, which I directly use in my calculations. Does it change the question? If so, what does it change? And what then is a sample ?
b) About the maximum and degree I understand, thank you. This is a different, more interesting view. I based my calculations on other assumptions. As far as I understand it, the result is a distribution for the maximum. And it is exactly FR, not SP. And further on it is clear.
If you're not bored yet with this literacy, I would like to ask one more question. Several times you emphasized independence of increments as a significant limitation which separates theory from practice too much. You also mentioned that theory has been able to go a step further. Could you please elaborate on this theory, at least enough to give a first idea of these steps, and also to understand how a person who is not too far from mathematics (like me :-), but not an expert in this field, can get something useful for himself here.
With this phrase I wanted to lead you to the idea that it is more probable to place a bet on the trial leader falling into range 2 than into range 3 (4 heads in a row), you can also place a bet into range 1 (4 tails), see figure.
This is completely wrong.
This is a clear demonstration of a typical mistake made by players in sports lotto, roulette, etc. games. They honestly believe that they have to place their chips on the playing field more or less evenly (or you can think of your own system), but some specific combination, from their point of view, (e.g. all reds) seems unlikely to them. And they will never put all their 17 chips on all red (or all black).
Your example with the picture can also be easily misleading. The reasoning is: if you get 357 eagles in a row (wow!), then bet on tails, you can't go wrong. This is wrong.
I suggest the doubting users consider the variants (it is supposed that the coin is of a correct form, there is no wind, the coin is not magnetic, and the experiment is absolutely clear from the technical viewpoint):
1. There was no flip. What is the probability of tails on the next flip? The correct answer is 50%.
2. There were 100 tosses. There were 95 times when heads fell out. What is the probability of tails? The correct answer is 50%.
3. There were 100 tosses. The history of the eagle-tails toss is unknown (well, the long-legged secretary wrapped a herring in it). What is the probability of tails? The correct answer is 50%.
Obviously, in this example, the history of events is irrelevant.
Practically, it means that if a coin is tossed 4 times in a row as heads, it means absolutely nothing. It also means that if the chart (not the real financial market, but the chart of this stupid coin flip) went up in a steep trend, then:
- it does not at all mean that the probability of a chart rollback is greatly increased;
- it just means that there was that trend in the last story.
It is impossible to predict a random process.
You can draw a normal distribution curve. You can write some words. You can think that the result is just around the corner.
But it is impossible to predict a random process, because that is its essence - it is random.
Only such processes in which a certain regularity is manifested, can be predicted. For example, there are reasons to believe that the financial market is not completely random.
However, outwardly random and non-random graphs are very similar.
If you make an eagle-shear chart (you can flip a coin, write down the results and then enter them into a PC as incremental quotes), you will find it difficult to distinguish from a market quote chart. This is what makes it confusing. In fact the eagle-sheets are in principle impossible to predict, while the market ones, to a greater or lesser extent, can.
The task of the researcher-programmer-builder-TC comes down to identifying the patterns that allow making forecasts, i.e. to determine the difference that distinguishes one chart from another - to identify a useful signal.
If I would like to buy from the market I will see that it is not correct to cut the market and use an example with a coin, and I will not explain the different martingales in those examples as well. SK is not a coin, but a random variable. Analogously let's say the mains voltage is 220 volts, in which case it may be 220 instead of 0 (not crucial). But then no one would want to play this game with me, if I bet that the voltage will be within 220V + 3sigma, against the other hypothesis.
I'm just tired of asking efficiency fans what they mean by that, I was hoping they would see it and want to play, because according to them the market is efficient all the time striving for its equilibrium state and so the visitors can't win.
Calling anyone to play by the rules described above.
SK Thanks again for seeing this
Edit: with all you have written above I absolutely agree, although here I am defining a random variable it has two regularities can and variance=const. That explains why I beat anybody. Unfortunately the market is not as simple as we would like it to be.
And to crown it all, in order not to act only as an "ideas killer" I'll tell you a very simple idea, which I used to push in my article here at mql4.ru, and which grew in importance as I gained practical trading experience: the standard Gaussian model of geometrical random walk can be saved from all problems by rethinking only one parameter: time. This idea has already been mentioned here, but it's not a sin to repeat it again: look at the tickframe! And the effects like "heavy tails", like "volatility", and many other things will disappear.
Have a look too: the figure below shows in red the number of calculations of the first difference of TP EUR/USD ticks expressed in pips and falling in the interval of the value set on the abscissa.
So where are the missing effects in the form of"heavy tails"? We could still do a"volatility" chart, if you suggest its correct definition to "see" how"a lot is missing"
Where did the ticks come from?
Concerning the volatility - to a large extent what I am saying is taptology, because the price variability (volatility) is directly related to the activity of transactions (the number of ticks) and considering the tickframe you devolalue the chart, go to the so called operational time. Since the data about the traded volatility are closed for us (i.e. someone will find short expiration options - you are welcome, but even the minutiae of them are not freely accessible), so it is difficult to check my statement "directly", only the speculative construct above.
Not exactly, Neutron. We need to build bars with equal tick volume in them (equivolume). And look at their p.d.f. already. (probability density function). This idea was expressed a long time ago, almost a year and a half ago by Amir in "The Principle of Substitution of Time in Intraday Trading".
I noticed the article at the time, but I wasn't yet hooked on p.d.f., and I haven't seen any trading application of these ideas. Even now I do not see too much use for trading, but on the other hand I clearly understand what the author wrote in the beginning of the article (emphasis added): I will dare say that few of system developers - beginners, as well as some "experienced" ones - think that even the simplest indicators of the moving average type, being related to time, are actually different units at different times of day. Of course, there are also systems formulated in terms of price, but not time. A typical example is the renko and kagi systems, but they are in the minority. Most of them, I repeat, are "tied" to the time, most often indirectly through the indicators. This is exactly right: the appearance of the classical continuous indicators greatly changes after such a conversion. Those who try to use this in their TS, just have a look at envelopes and Bollinger Bands applied to this chart. I suspect that along with the disappearance (or significant thinning) of thick tails and stabilisation of variance (volatility) these indicators will show much more reasonable entries/exits. You won't get a grail, but dealing with simpler processes will also be easier.
Personally, I'm only interested in this chart conversion because the chart itself could potentially become much closer to a Wiener process - with p.d.f. increments very close to those described by Bachelier (+-1 tick at any point in time, regardless of the past). What to do next is the second question.
SK., I understand very well that the tick volumes on Foreh is too dependent on the data provider and its filters. But you can try, right?
I apologise for the huge quote, but it will allow to reconstruct the course of the topic under discussion.
Look at the fig. it shows the distribution of price increments in bars by 1 tick, 10, 20, 40, 80 ticks.
I.e. what is required - "bars with equal tick volume in them (equi volume)". data is given for EUR/JPY Alpari 2007 ticks. It is clear that even for TF=80 one can speak about distribution normalization only with great reservations (compare solid red line and red line with circles).
Maybe you, kamal and Mathemat, can comment on this situation.