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It is useless to look for context using purely mathematical methods, and neither are the parameters that lead to it. We must proceed from what physically determines the context in the market. For this purpose in trading there is a notion of "sentiment". This is the will or the need of a certain part of the participants to buy or to sell. Be it loss taking, or entry/exit using general TA methods, etc. Anything that causes them to enter and exit synchronously enough to set a trend (possibly a micro-trend) that can be exploited.
That is, any context involves a probabilistic prediction that a particular group of participants will actively enter or exit a position at certain points. More generally, we can talk not only about buying/selling, but also about predicting that participants will follow a certain strategy. Not necessarily the same, but similar enough.
In order to parameterise such a context, we need to find the technical tools that best represent this mass desire. imha
p.p.s. Недавно копал на тему корреляционной размерности. Сильно не понравился lim N->inf. Для eurusd получалось значение около 9.
Can you elaborate on that?
I tried calculating the correlation dimension by Potapov, via FFT. But so far we are interested in the number of degrees of freedom - m. I also assume that we will be interested in the regions with minimal m. That is, we can try to limit ourselves to rather "short" vectors z. For this reason application of FFT looks somehow doubtful to me. And it's always interesting to have a "frontal" implementation as a benchmark.
And can you give any links to more effective algorithms?
чисто математическими методами контекст искать бесполезно,
...
Для того, чтобы параметризовать такой контекст, нужно найти технические инструменты которые отображают наилучшим способом это массовое желание. имха
This is the way we think about it:
In order to look for such tools, you need to have examples of the implementation of given contexts at your disposal. That is, to be able to identify them in history. Mathematics comes to mind precisely as a means of finding realizations of contexts in the past.
How do you see a practical approach to finding such tools?
That's what I got out of it, there are more details to look for.
>> thank you, I'll look into it.
Всё зависит от инерционности рынка. Наверное, надо взять какое-то фиксированное значение баров, много меньшее времени, за которое обычно происходит отказ стратегии. Те.е. скажем для машек, если известно, что они прибыльны в течении 3-х месяцев, то оценивать мгновенное сосояние рынка можно по 2-м неделям, например.It is unlikely that there will be any guaranteed duration of one state or another. And as a way of selecting contexts on the history, it will be just an implicit task. You can count not by time but by number of deals. Say, if out of n consecutive n trades k breakouts and l rebounds were successful, the "coordinates" will be k/n and l/n.
However I can't think of more than 2 strategies: entering "to the move" and entering "against the move". Another thing is that there may be any number of ways to select moments for making decisions (i.e. signals). Therefore, perhaps the primary task is to find a reference algorithm for generating signals. By the way, it may be more difficult to standardize the outputs. Although for the zigzag it is just as easy.
Alternatively, one could continue to come up with a richer basis.
What operations are allowed on the elements of the basis?
How will we determine completeness and independence of the basis?
Well, let's start from the beginning, i.e. let's define a ring of operations over which the space will be built. Or are you going to build a non-linear space?
Alexey, it seems to me you are not only going to take the bull by the horns, but also twist his head off. Isn't it too cool? :-)
IMHO, a phase space need not necessarily be linear vector space, nor does it need to have not only two, but even one operation over its elements. I believe there is only one requirement that must be taken into account: the parameters of the system state, which may be the coordinates of the phase space, must be continuous in time. This requirement ensures continuity of the trajectory of the system in phase space. If there is no such continuity, any attempt to draw any conclusions about the system's behaviour even in the near future turns into a meaningless effort.
On the other hand, if we have a continuous trajectory, then there must be a certain notion of proximity of points. It follows that the phase space must be metric. It is possible that the explicit form of this metric does not even play a role and the Euclidean metric can be used. However, it is unlikely to do anything without it.
It is useless to search for context by purely mathematical methods, as well as for parameters leading it. It is necessary to proceed from what physically defines the context in the market.
In order to parametrize this context, it is necessary to find the technical tools which reflect in the best way this mass desire.
Seconded. I just wouldn't fixate on mass desire. The arguments are as follows.
As you know, crowd desire sets a positive feedback loop. The greater the desire, the clearer the crowd understands where to run, the more the crowd is drawn in that direction and the greater the desire becomes. The end of this trend occurs when there is no longer anyone to entrain, i.e. when desire is maxed out. Banks and big players take advantage of this and manipulate the crowd in this way. I would therefore consider it most promising to find instruments which reflect the mood of the banks and big players and which will be ahead of the crowd's desires. But this is not in opposition to "instruments that reflect this mass desire in the best possible way", but in addition, for balance, for completeness of the picture.
To look for such tools, one must have examples of the realization of given contexts at one's disposal. That is, to be able to highlight them in the story. Mathematics comes to mind precisely as a means to find realizations of contexts in the past.
How do you see a practical approach to finding such tools?
Highlighting contexts in history is not that difficult. Our mutual love of ZZ is quite suitable for this. Except that we need to add criteria to filter out activity. Like liquidity, for example.
But it is more complicated with tool search. I think there is only one way: hypothesis => realization => analysis of results. It is better that the hypothesis is a brilliant guess. But this is a matter of luck. The analysis of the result is an easier task. For its solution, we need the phase space. Each context is represented in it by a point. If the various contexts are "clustered" in the phase space, thus defining the corresponding domains, then that's just what's needed. All that remains is to define the boundaries of these areas and you can go to your broker to get your Nobel Prize.
However, I have no imagination for more than two strategies: "on-the-move" and "against-the-move" entry. Another thing is that there can be any number of ways to select moments for making decisions (i.e. signals). Therefore, perhaps the primary task is to find a reference algorithm for generating signals. By the way, it may be more difficult to standardize the outputs. Although for the zigzag it is just as easy.
Alternatively, one could keep coming up with a richer baseline.
There are only two of them. We only need to consider the third option - to do nothing.
But these are not state parameters. State parameters have nothing to do with strategies. They are state parameters !!! So, imho, when choosing them, you have to forget what a trade and everything associated with it is at all.
Выделять на истории контексты не так уж и сложно. Любимый нами обоими ЗЗ подходит для этого вполне. Ну разве что к нему надо добавить критерии, фильтрующие активность. Типа ликвидности, например.
The zig-zag has one disadvantage - the presence of parameters. It deprives the allocation of contexts of unambiguity. At the same time, talking in terms of sentiment (whether crowds or market makers) means it is possible to unambiguously divide into contexts.
There are
only two of them
.We only need to consider the third option - to do nothing.
But it's not the state parameters
.State parameters have nothing to do with strategies. They are state
parameters !!! So, imho, when choosing them, you have to forget what a deal and everything associated with it is at all.I got away from the third option by introducing the concept of "signal".
So you're going to build up a historical base of contexts based on one of the state parameters? But in this case you sacrifice it, it will have to be excluded from the analysis. And the choice will be more or less oriented not to the final task (maximum benefit with minimum risk), but to the optimization of this context defining parameter.
For me, selection by the final criterion looks preferable.
Nah, misunderstood.
The ultimate criterion is, as you quite rightly pointed out, profit. But there's also the aggravating factor of personal preference. For example, I prefer to earn 100 pips or more, though not too often. And you - often, but by twenty. And the notorious pips player, very often, but by two. These are things that very much determine the context. And there may be other circumstances.
So, the ZZ parameter (and as we know it has one parameter) just sets a filter that does not deprive, but on the contrary, unambiguously defines the context.
But if you don't use this parameter to identify the context, but instead use the context to fit the parameter, you turn the task upside down. Of course, that's the only way to get a chasing grail in this case.
Я ушёл от третьего варианта введя понятие "сигнала".
All the more so. The tops of the gears with the right parameter are the necessary signals. And I can sacrifice this ZZ parameter with a light heart. Of course, no one knows and we will keep it a secret in this case, that we cannot trade by EZ (together with its parameter); therefore, it is just a means of graphic markup of history. Note, not even the analysis, but the mark-up. So, it cannot be and is not a state parameter. In fact, what is a state parameter that does not change over time?
:) . Just a classic example when close formulations have diametrically opposite stuffing. It seems that in this case the watershed lies in the following question: Can the resulting contexts of some algorithm be different? In other words, is the context identical to the algorithm that extracts it? It seems that in your interpretation, yes, it is. In mine it is not. But we can try to classify them by identifying a limited number of context types. In this paradigm, it is easy to find counterarguments to your arguments.
Конечный критерий - это, как ты совершенно правильно заметил, профит. Но при этом есть еще отягощающие обстоятельства - личные предпочтения. Например, я предпочитаю зарабатывать хоть и не слишком часто, но по 100 пунктов и не менее. А ты - часто, но по двадцать. А небезызвестный пипсовщик, очень часто, но по два. Это ведь вещи, которые очень сильно определяют контекст. А могут быть и другие обстоятельства.
In your interpretation, this choice is a matter of taste. In mine, it should be dictated by the type of context.
So, the parameter SZ (which, as we know, has one parameter) just sets a filter that does not deprive, but, on the contrary, unambiguously defines the context.
Now, this is a key point of divergence. My zigzag parameter is not a state parameter. The state parameter is what defines the type of context (or rather it should be defined by the set of state parameter values). And zigzag partitioning results in both breakdown and breakdown contexts.
But if you don't use this parameter to allocate the context, but instead use the context to fit the parameter, then you're turning the problem upside down. Of course, this is the only way to get the chasing grail in this case.
Here's a completely incomprehensible conclusion about parameter fitting ZZ, where does the need for fitting in my logic come from? After identifying the type of context, I simply choose the appropriate strategy.
Moreover. The tops of the ZZ with the right parameter selected are the necessary signals. And I can sacrifice this ZZ parameter with a light heart. Of course, no one knows about it and we will keep it a secret that we cannot trade by TZ (together with its parameter), that is why it is just a means of graphic markup of history. Note, not even an analysis, but a mark-up.
The tops in GZ cannot be signals. A signal in my definition is a moment in time to make a decision. That is why the fixation moment of a top in GZ may be a signal, but the top itself cannot be, for it is always determined with a lag.
I completely agreewith this:)