FR H-Volatility - page 22
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Neutron
A little more detail on both the X and Y axes, confused by the negative values on the Y axis if this is p.d.f.
Yes, these are the indicators of the degree of ten:-)
Neutron
I apologise for answering as I was not the one asked. But I will try to comment on what I see from this figure. This allocation is beautifully huge amount of work, only one thing is that it is difficult to use it in any way for the construction of TC. It was already said here about these independent increments that prevent us from using it. Earlier I posted a picture - how to build TS by knowing the parameters of the distribution law, but there everything is simple, there can=sonstante. Here, due to the fact that the increments are independent it (can) shifts all the time and is unknown where. That is why in reality you don't know where the 0 point is (the stove on which to dance=set thresholds).
I think that's it, although I may have commented differently from what you wanted to hear. The right question is 2/3 of the answer.
Here's another place where you can get a 10 second story (packs of 10k and free...though I haven't checked the quality)
...maybe someone needs...
http://www.dukascopy.com/swiss/english/data_feed/csv_data_export/
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"?
Yes, of course, I'd even say at present only such strategies are possible, and I never cease to be amazed at stockpickers who beat the index in the long run.
Regarding the ticks: Sorry, I'm not in Moscow now, I promise when I arrive - to repeat statistical computations and then we will discuss exactly. Tics on the picture above - geinkapital, maybe it plays a role ....
a) If I understand correctly, by SP you mean all infinite set of realizations of series 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. You several times stressed the 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 the field, can get something useful for himself here.
a) mmm I unfortunately don't really understand certain phrases like "infinitely variable CB". What we're talking about (or rather what I said, maybe I misunderstood you) is when NE takes a value in numbers, like 5, 10, 20, and not the whole trajectory of the process. The trajectory is also from the mathematical point of view NE, just as if I did not talk about it, the trajectory FR has no (well, only in the sense of a set of finite-dimensional distributions, but so deeply you probably do not dig).
In short, I really understand what you need, you just need to know what is the average maximum deviation one can observe at the price in en steps, i.e. what is the maximum of difference between the initial value and the maximum in en steps (ticks, minutes...). This also counts, but unfortunately is not as easy as in the last time. I can tell right away the result in a particular case, if the price is assumed to be a Brownian motion (in the short run it's not a bad first approximation), then this max. deviation will be distributed like a Brownian motion, and the mo max. deviation will be proportional to the root of the number of steps. By the way, it is very useful to know that the Brownian motion (and the price it simulates) grows as the root of time (it is not clear in which direction :)).
b) Yes, it's a FR, but it's not the case that interests you, you consider cumulative amounts, while I talk about specific realizations of the same CB, taking values in numbers.
c) Well, how can I tell you, the situation here is not simple. There are specific effects that emphasise the dependence of increments. For example: after strong movements you should expect strong movements, after slack you should expect slack. Mathematically, volatility is persistent, and there are also (non-trex related) effects such as the leverage effect (if price falls, volatility rises). There is no model that takes all this into account, but martingian theory does not prohibit such behavior and therefore it can be used rather than corresponding results for a usual process with independent updates. That is, the conditions imposed on the process are very weak and do not unambiguously describe the behaviour of the process.
Actually I understand what you need, you just need to know what is the average maximum deviation possible for the price in en steps, i.e. what is the maximum of difference between the initial value and maximum in en steps (ticks, minutes...). This also counts, but unfortunately is not as easy as in the last time. I can tell right away the result in a particular case, if the price is assumed to be a Brownian motion (in the short run it's not a bad first approximation), then this max. deviation will be distributed like a Brownian motion, and the mo max. deviation will be proportional to the root of the number of steps. By the way, it is very useful to know that Brownian motion (and the price it simulates) grows as the root of time (it is not clear which way it goes :)).
Yes, I think you understood me correctly. The NE I am referring to is not a price, but its series is related to the price series (in a sense you could say it is an indicator) and it is the average maximum deviation in N steps that interests me.
The results relating to Brownian motion are known to me and I am not satisfied. The question was posed as follows: I know the SP distribution for this series (or FR). How on this basis to calculate the average maximum deviation in N steps ?
c) Well, it's a complicated situation. There are specific effects that underline the dependence of increments. For example: after a strong movement you should expect a strong movement, after a lull you should expect a lull. Mathematically, volatility is persistent, and there are also (non-trex related) effects such as the leverage effect (if price falls, volatility rises). There is no model that takes all this into account, but the martingian theory does not prohibit such behavior and therefore it can be used rather than the results for a usual process with independent updates. That is, the conditions imposed on the process are very weak and do not unambiguously describe the behaviour of the process.
This effect: "Mathematically: volatility is persistent" - is it a market phenomenon or to some extent a mathematical result ?
c) Well, how can I tell you, there is a tricky situation here. There are specific effects which emphasise the dependence of increments. For example: after strong movements you should expect strong movements, after a lull you should expect a lull.
It is not clear if the lull is about the price, then we won't come out of the calm or something else. I thought that the lull is followed by a strong movement. Thank you.
c) Well, how can I put it to you, there is a tricky situation here. There are specific effects which emphasise the dependence of increments. For example: after strong movements one should expect strong movements, after slack one should expect slack movements.
Could you please elaborate on that, it's not clear if the lull is about the price, then we won't get out of the silence or something else. I thought the lull was followed by a strong move. Thank you.
You keep looking at the market deterministically and that is not very right. Yes, after the lull it is more likely to calm down, but it doesn't mean that volatility cannot suddenly jump up. It's just that periods of low and high volatility are indeed distinguishable, both on small timeframes and globally (for example, we have now come out of a multi-year low volatility cycle and entered an equally multi-year high volatility cycle, see the VIX chart).
In short, I actually understand what you need, you just need to know what is the average maximum deviation that can be observed at the price in en steps, i.e. what is the maximum of difference between the initial value and maximum in en steps (ticks, minutes...). This also counts, but unfortunately is not as easy as in the last time. I can tell right away the result in a particular case, if the price is assumed to be a Brownian motion (in the short run it's not a bad first approximation), then this max. deviation will be distributed like a Brownian motion, and the mo max. deviation will be proportional to the root of the number of steps. By the way, it is very useful to know that Brownian motion (and the price it simulates) grows as the root of time (it is not clear which way it goes :)).
Yes, you can assume that you have understood me correctly. The CB I am referring to is not a price, but its series is related to the price series (in a sense you could say it is an indicator) and it is the average maximum deviation over N steps that I am interested in.
The results relating to Brownian motion are known to me and do not suit me. The question was posed as follows: I know the distribution of SP for this series (or FR). How on this basis to calculate the average maximum deviation in N steps ?
c) Well, it's a complicated situation. There are specific effects that underline the dependence of increments. For example: after a strong movement you should expect a strong movement, after a lull you should expect a lull. Mathematically, volatility is persistent, and there are also (non-trex related) effects such as the leverage effect (if price falls, volatility rises). There is no model that takes all this into account, but martingian theory does not prohibit such behavior and therefore it can be used rather than corresponding results for a usual process with independent updates. That is, the conditions imposed on the process are very weak and do not unambiguously describe the behaviour of the process.
This effect: "Mathematically: volatility is persistent" - is it a market phenomenon or to some extent a mathematical result ?
On the last point: this is a market phenomenon.
Regarding the max deviation: in general it is non-trivial. That is, what are our assumptions, the values of the indicator at different moments are independent? or are the sums of independent values? or neither? In the general case there is no single algorithm, we must look specifically.