FR H-Volatility - page 13
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We are even - I am already afraid of your criticism!
Prival, I interpret the concept of FR and use the term correctly - as it is taught at university and used in scientific articles published in peer-reviewed publications, physicists. That is, the term is well-established! The concept of "Efficient Market" and "Arbitrariness" is introduced and exploited in his two-volume work by econometrician A.N.Shiryaev, "Fundamentals of Stochastic Financial Mathematics". Equidistance means the uniformity of something, in this context we are talking about price values in equal time intervals, e.g. after one hour. Speculation is also a commonly accepted term and means to make certain bodily movements in order to make a profit without producing material goods. As for "efficiency", I agree with you.
1) Shiryaev has clear definitions of EVERYTHING - and you don't. I should know, I used his books to pass probability theory at the Faculty of Mechanics of Moscow State University and he is my friend's researcher.
2) Do not confuse science and trading. They are two very big differences - what clever people do in theory is not applicable in practice by 90% (experience of mechmate + currency trader in a major bank)
3) Shiryaev is not a meter "econometrics", he is a meter in probability theory.
4) Uniformity is also from the "on the fingers" series. If you know, Mathematical Analysis defines uniform convergence of an integral not "but it is such an integral that converges uniformly".
5) >> I interpret the concept of FR and use the term correctly - as it is taught at university and used in scientific articles published in peer-reviewed publications, physics. That is, the term is well-established!
Yes, among physicists. Who sit on low salaries at universities and teach nerds (for which they are honoured and respected, by the way - true). But not among traders who really trade )))). And what do you want - to trade or to defend a dissertation, let's make up our minds?
6) >> Speculation is also an accepted term and means doing certain gestures for the purpose of making a profit without producing material goods.
Here we go again with the problem of definitions. Your definitions are lousy, comrade! According to your definition, armed robbery of a bank is "speculation". Why, it all fits :-D
Sergey, you are my namesake. You yourself have agreed, that on your pictures it is not FR, but a probability density function (see pp. 1, 10 and 11 of this thread). And in the university it should have been taught correctly too, I am telling you as a former head of the Information Technology Department. For the rest of the terms I will not vouch, I am not an economist, but something is wrong in them from my humble point of view. References to authoritative dissertations, not an argument (better a book that has survived several editions on statistics, let's say B.R. Levin). I will be very happy to chat via Skype, that would not litter the forum. I am waiting privalov-sv. I even made a special gift for when you get in touch.
Prival, honey. It's hard to argue with the head of the department, even a former one. But I'll allow myself to slightly interfere.
As written in Bulashev, "Statistics for Traders", there are two kinds of representation of a CB distribution law: integral and differential. The integral law is actually called the SP probability distribution function, and you are absolutely right. The differential law is called the probability density function, or the probability density function (loosely speaking). Neutron and I have long since figured this out amongst ourselves, so I suggest you drop the terminology debate and get into a substantive discussion.
Arbitrage is the property of the market to produce a statistically valid return. It can be caused by e.g. stationarity of non-zero values of autocorrelation function, presence of deterministic or stochastic trends or whatever. The main thing is that the arbitrage market allows selecting the situations with the probability of some outcome stably differing from 0.5
The speculations are operations on the market, the essence of which is just "bought cheaper, sold dearer" or first "sold dearer", then "bought cheaper". Arbitrage, as a market operation, consists of the simultaneous buying and selling of the same asset on different markets, but at different prices. This is the classical definition. Recently, there have been attempts to call speculative transactions arbitrage as well. After all, what is the difference between simultaneous buying on different markets or selling on the same market at different times? The main principle is the same.
Concerning Pastukhov's thesis dispel your doubts - it is a good work. The mathematics there is elementary, and the main content of the work is the proof of theorems, which actually justify the method. For someone who wants to look at the market from a statistical point of view - very useful experience. For me, a total ignoramus of mathematical statistics, this work has brought me to a level where I know what I'm talking about. :-))
Equity may, of course, be an indicator of arbitrage (if it steadily increases :-), but it may never be an indicator of it. The essence of the indicator is a qualitative and quantitative reflection of some property, an aspect. Regardless of the TS, trader, broker, weather and other things. And equity, in the presence of arbitrage, may not grow.
I understand you that we can only talk about something if we agree on the concepts and the same language. Therefore, if something seems incorrect, unclear or wrong to you - speak up, ask and we will sort it out. As long as it gives constructive impetus to the work of all of us.
>> Arbitrage is the property of the market to produce a statistically valid return. It can be caused, for example, by the stationarity of non-zero values of the autocorrelation function, by the presence of deterministic or stochastic trends or anything else. The main thing is that an arbitrage market allows to distinguish the situations with the probability of some outcome stably not equal to 0.5
Concerning the question of definitions - you probably want to say the following: "A market is arbitrage when at least one profitable TS exists in it.
A couple of questions then:
a) Is insider trading a TS?
b) Is it a TS on the news?
c) And on technical analysis (but this you certainly call a TS, fact - but in "a" and "b" I am not sure).
If you read Shiryaev's books thoughtfully, you can understand that it fits into the following, already quite strict definition:
"A market is Arbitrageous if it is NOT a martingale relative to a *** flow of sigma algebras". Where *** is substituted depending on what you want to consider a working TS of a,b,c - and what is not.
No, I'm not a maths maniac - it's just that you're discussing seemingly clever things for 12 pages here, but in fact there's no clarity ))) If you play, you'd better play to the full :-D
>> Concerning Pastukhov's thesis dispel your doubts - it's a good work. The mathematics there is elementary, and the main content of the work is a proof of theorems, which actually justify the method. For a person who wants to look at the market from a statistical point of view, it's a very useful experience. As a total ignoramus of mathematical statistics, this work took me to a level where I know what I'm talking about. :-))
Did this work make you any money?
to Prival.
I do not agree with you.
1. About arbitrage, here's an interpretation of arbitrage from Wikipedia: "Broker A puts in an order to buy 100 shares of a certain 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 all do not work? BP prediction with NS Better also does not work?
3) What is the result of the Automated Trading Championship 2007 that leads you to such conclusions?
For the first point. I cannot give the link - I cannot remember where I looked, but I assert that the term "arbitrage" applies to the act of buying one currency and simultaneously selling another with the goal of selling the first and buying the second at different times on the same market to make a profit from the expected instrument price difference. The efficiency of the market by definition postulates the impossibility of making speculative profit on it (except for the exploitation of insider information) - it is impossible to forecast the market.
On the second point. How to evaluate the performance of a method? If we talk about the possibility to forecast BP, then it is possible! The same "correlation coefficient" perfectly predicts the future price value on any TF. In this sense "BP analysis methods of which there are a wagon and a small cart" do work. But if we estimate prognosticating ability of these methods, the required value is much less than the commission charged by DC for each transaction. In this sense "it turns out that MA does not work, correlation coefficient does not work either, etc." turns out that it does.
On the third point. We may have misunderstood each other here. I assert that the analysis of trading results on the Automated Trading Championship 2007 allows us to say with certainty about the possibility of arbitrage trades at Forex, taking into account the current commissions of brokerage companies! This is a strong statement of principle! Indeed, in our time we went into this business without being fully convinced of the positive outcome of this event. I'm not talking about the mentally ill people who "just for luck" put thousands of quid into Forex hoping to get rich, at best by attending a couple of "trading courses" organized by brokerage companies. No, first of all, before we start spending our years to develop a profitable strategy, we should be sure in the basic solvability of the task. Otherwise we should be in an asylum. Unfortunately, all of the above methods of analysis do not give a clear answer to this question, but fortunately Better answered it for us :-) At least for me the goal is now clear and attainable.
>> Market efficiency by definition postulates the impossibility of
There is efficiency in a weak and a strong sense, and in general there is a lot of complexity there really )))) Just a lot is tied up in the attitude towards insider...
>> I claim that the analysis of results of trades on the Automated Trading Championship 2007 allows to say with confidence about the possibility to conduct arbitrage operations in the Forex market, taking into account the current commissions of brokerage companies!
It does not. This is just a demo, alas. And even super-mega-smart system of modeling requotes will not simulate the market for you. The sad fact is that even BANKS (attention, BANKS - not poor physicists) close the limits on each other with motivation "you trade too well, we do not have time to cover you, sorry".
>> but luckily Better answered for us :-)
Don't make an idol of yourself. Though, of course, quite entertaining! I personally don't believe in neural networks, sorry. I think the simpler the better. But if Better has actually found something - I'm genuinely happy for him. But I have my doubts.
Look at the logic - Renaissance Technologies (the world's most successful hedge fund - http://www.rentec.com/, https://en.wikipedia.org/wiki/Renaissance_Technologies) has a 60% annual return before commissions. And it's SUPER cool - the whole industry is licking its eyes and thinks they've sold their soul to the devil. Batter's returns are at least 200 times higher. Yes, Batter is smart, BUT - Renick has 50 PhDs in mathematics, a bunch of programmers psychologists. I'm sorry, I still think that in terms of aggregate capabilities, this mega is more powerful than Batter. No, maybe Batter will be a second Simons (founder of rentech, Ph.D. in maths - https://en.wikipedia.org/wiki/James_Harris_Simons)- but 2 things
a) Forget about the returns we see in the championship.
b) The DCs are best forgotten too. Too far from the real market - trade currency futures, why trade spot with predatory swaps?
kniff, request to you, since by Shiryaev's books terwer passed: you explain to me, also an amateur, on my fingers, what is this theorem of Dub(Doob), which so like to mention particularly advanced. What is this theorem about martingale proved, which supposedly implies that a profitable TS can not be built on a martingale?
Prival, thank you very much for the excerpt from Tikhonov's article. I found something there that interested me.
There are many of them, by the way - about the frequency of sub-martingale band crossing, Dub's nerve, Dub's theorem about the convergence of sub-martingales, etc.
And why doesn't the TS on a martingale work? Well in the discrete case it's a trivial fact (you can check with your hands) - after all TC is just some random variable measurable on a stream of sigma algebras with some conditions (conditions on the fingers are that it "doesn't see" the future).
And in general, the fact that a profitable TS cannot be built follows from the fact that the Stochastic Integral of any martingale function has a mean zero (in the discrete case the stochastic integral turns into a sum and this fact is checked simply by the definition of the martingale).
And finrez of any strategy is, if you think about it, the Stochastic Integral of any function (implementing the strategy) on the price process.
Ask Amir if you want details )))) He's not just a martingale, he's a disciple of Shiryaev himself ;)
Don't make an idol of yourself. Although, of course, it's quite entertaining! I personally don't believe in neural networks, sorry. I think the simpler, the better. But if Batter has actually found something - I'm genuinely happy for him. But I have my doubts.
Look at the logic - Renaissance Technologies (the world's most successful hedge fund - http://www.rentec.com/, https://en.wikipedia.org/wiki/Renaissance_Technologies) has a 60% annual return before fees. And it's SUPER cool - the whole industry is licking its eyes and thinks they've sold their soul to the devil. Batter's returns are at least 200 times higher. Yes, Batter is smart, BUT - Renick has 50 PhDs in mathematics, a bunch of programmers psychologists. I'm sorry, I still think that in terms of aggregate capabilities, this mega is more powerful than Batter. No, maybe Batter will be a second Simons (founder of rentech, Ph.D. in maths - https://en.wikipedia.org/wiki/James_Harris_Simons)- but 2 things
a) Forget about the returns we see in the championship.
b) The DCs are best forgotten too. Too far away from the real market - trade currency futures, why trade spot with predatory swaps?
Let's assume for a second that you are wrong after all. Let's just say.
Let's assume that a technology has appeared on the market that shows a return of approx. 100% a month at low risk. What do you think are the consequences of this phenomenon?
....The DC is also best forgotten. If you are too far from the real market - trade currency futures, why trade spot with predatory swaps? ...In general, the fact that you cannot build a profitable TS follows from the fact that the Stochastic Integral of any martingale function has a mean zero (in the discrete case the stochastic integral turns into a sum and this fact is checked simply by the definition of the martingale).
If I understand you correctly, the only way to make a long-term income in the market is by accumulating swaps. That is the only (except for insider) source of income for a psychologically healthy person. Right? If so, then how can one explain the profitability of the Championship leader's strategy. After all, the number of transactions carried out by him, and therefore the result obtained by him can be considered statistically significant. Of course, one can say that the bettor happened to hit a lucky streak in the market condition, but it shows the presence and duration of such streaks... Or everything is determined by greenhouse conditions created at the championship - a kind of non-trivial PR campaign from Forex.
So I understand that I communicate with you on a public forum, and you are not a member of the Higher Attestation Commission who has been thrust into consideration a topic from this forum instead of the expected dissertation work! Then I do not understand your reaction to what is happening, which borders more with a process of narcissism than with the search for a constructive dialogue. I can see that you know a lot of useful things that we can all benefit from. So let us ask questions and you answer them!
In general, the fact that a profitable TS cannot be built follows from the fact that the Stochastic Integral of any martingale function has an average of zero (in the discrete case the stochastic integral turns into a sum and this fact is checked simply by the definition of the martingale).
And finrez of any strategy is, if you think about it, the Stochastic Integral of any function (implementing the strategy) on the price process.
P.S. If TC is a random process that depends on the price itself, then it is much more complicated...