FR H-Volatility - page 12
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1. About arbitrage.Here is the 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 market, 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.
Thus, the 2nd statement is accepted. It can be taken as an axiom and be relied upon.
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.
Correctly posed questions are a noticeable part of the volume of tasks that need to be accomplished in order to achieve the goal.
Without pretending to absoluteness, I will tell on the basis of personal experience and operating experience on the given theme:
1. For currency series on the Forex market Arbitrage - the act of buying an instrument with the purpose of selling it on the same market at different times for the purpose of gaining profit from the expected price difference. Arbitrage or market ineffectiveness is characterized by the occurrence of significant (in the sense of excess of possible longterm profit over commissions) dependences between past price increments and expected movements.
2. Price increments can be searched at equidistant time intervals, or at any other way of breaking down the BP. Without evidence, I argue that the natural, optimal way to partition BPs is a price scale partition, because for us as speculators, only the absolute value of the price increment is of interest, and the time over which this increment occurred is not an issue. Thus, there is an optimal breakdown (in the sense of maximum possible profitability) of a price series, the Kagy structure. It also gives an opportunity to define the arbitrage value for the trend (H+ strategy), as well as for the flat (H- strategy).
On the basis of Kagi (Renko) constructions it is possible to realize an arbitrage indicator of the market - the transaction line (red colour in Fig. ) or its derivatives.
I think this is the most effective indicator of market arbitrariness. Its properties should be studied. But how to be sure that I am not mistaken. Is it possible to prove this statement strictly?
Neutron
I am still amazed at you, you introduce new concepts with such ease, and then interpret them well. I'm already afraid to ask you. For example, what is the difference between the concept of speculation and your interpretation of arbitrability? Or what is "equidistant time intervals" and "market arbitrage"?
If all these concepts are taken from the dissertation to which you are referring, and there the author confuses the distribution function with the probability density, which we discussed with you earlier. Then throw it out, it is called scientism in simple human language. The aim for the dissertation candidate is clear - "to put a fog, that nobody understood, and hopefully I will be protected". You are carrying out real research and the fog only hinders.
Concerning the H-volatility, you are trying to find a pattern using a nonlinear transformation (H-partitioning, Kagi, Renko) to a nonstationary flow and throw time out of analysis. Think about whether you can find any stable statistical patterns in it?
Before claiming that this indicator is more effective than another, you should understand that the word "efficiency" is a philosophical concept and it can be viewed from different angles. For example you have two shovels in the corner at home. The first one is more efficient than the second one (if you are digging), but if you are shoveling, the second shovel is better (more efficient).
I say that the most effective arbitrage indicator is equity. And no Cagi, Renko, N are even close. Note that I didn't add the word market here, because the notion of arbitrage refers to the trading system, not the market.
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.
I agree on the first point.
Sergey, you are my namesake. You yourself have agreed that in your pictures it is not FR, but the probability density function (see 1, 10 and 11 pages of this thread). And in the university it should have been taught correctly too. That's what I say as the 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. Even specially prepared a gift as you will contact.
1. The market will.
2. The market will be confident.
3. The 3rd Champ. will be very representative.
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"Shouldn't the conservatory be tweaked?" (e.g. the venue).
Sergey, you are my namesake. You yourself have agreed that on your pictures it is not FR, but a probability density function (see 1, 10 and 11 pages of this thread). And it should have been taught correctly at uni too. That's what I say as the 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. Even specially prepared a gift as you will contact.
Prival, dear. It's hard to argue with a head of department, even a former one. But I will allow myself to intervene slightly.
As written in Bulashev's "Statistics for Traders", there are two types of representation of the NE distribution law: integral and differential. The integral law is actually called NE probability distribution function, and you are absolutely right. A differential law is called a probability density function (loosely speaking, a probability density function). 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.
1. arbitrage or market inefficiency is characterised by the emergence of meaningful correlations between the price increments that have taken place and the expected movements.
2 I argue, without evidence, that the natural, optimal way to break BPs is to break them down on a price scale, because for us as speculators, only the absolute value of the price increment is of interest, and the time over which this increment occurred is not a concern. Thus, there is an optimal breakdown (in the sense of maximum possible profitability) of a price series, the Kagy structure. It also allows to naturally define the arbitrage level for a trend (H+ strategy) as well as for a flat (H- strategy).
I think it's the most effective indicator of market arbitrage. But how to be sure that I am not mistaken. Is it possible to strictly prove this statement?
In points 1 and 2 I have left out what I understand and agree with.
It follows from 1 that a natural way to identify these dependencies could be ACF. Open questions, however, remain about the parameters of the ACF, their nature (constant values or adaptive), the cagy-partitioning parameter, the measure of "significance" ...
I, too, believe that the cagey partitioning is optimal, but it is hardly possible to prove it. Another thing is if we shift the emphasis. Kagi is the basis of the approach, and above it one must build such a superstructure so that TC is optimal.
How "It does give a natural definition of arbitrability", I don't understand ? If it does - give that definition.
I can't say anything about your indicator. I don't feel it physically or mathematically. And I understand it poorly, alas :-(.
Besides, it's a graphical indicator and I'm attracted to the numerical characteristic.
Yurixx
The market has no such property. It is a property of the trading system (the trader). The market (quotes flow) doesn't care about your or my income. Maybe this makes it clearer that you cannot apply this concept to the market.
My opinion, sorry, is not an authority, but the concept of efficiency is philosophical. Please try to explain it to me, as I did on spades (see example above). Please don't refer to someone else, but as you understand it and do not step on the same rake again, don't attribute the same properties to stream of quotes (market) of a trading system that actually has a physically understandable to me efficiency (whether it (TS) brings me income, or washes money out of my pocket).
Don't get me wrong, I want to help you. You correctly said "that we can only talk about something by agreeing on concepts and in the same language". Plus I would like to add that you may study (investigate) only those properties of an object (phenomenon) that it has. I just once a long time ago I was taught to conduct research and waved my dingle goodbye. There is one simple rule when you start a research, the first is to define the physically understandable properties of the phenomenon (object, process ...), the purpose of research and how to achieve it. Second, you try to describe these properties mathematically and numerically. And the third bring the methodology (the algorithm, formulae) so that the other researcher by repeating all your calculations have the same results.
It is impossible to study properties that do not exist! Let's say the inefficiency (efficiency, arbitrage) of the market now = 9, a minute ago it was 32, and yesterday it was -15. Gentlemen, let's have the formula. There is no formula - let philosophers deal with this concept. There's nothing to calculate, nothing to study and research IHMO an empty sound that in no way brings me and you closer to the construction of a good TS.
Neutron
Skype, it's a program for quick communication. Like ICQ, but steeper and exceeds it (ICQ) on the capabilities as a filter Butterworth Mashka :-). Here is a link to get the business version.http://www.skypeclub.ru/skype_windows.htm