To follow up - page 27
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Hope hasn't gone away yet. I've been trying to finish the cockroach theme lately, which has so far stalled on Uninhabitable a couple of months ago. A lot of water has flowed, the idea has changed considerably in an attempt to get away from the unreasonable parametrization that so frightened you. More precisely, the original idea remains the same, trivial, but there is a "binding" in the form of multicurrency, which is technically not so easy to do, because of the need for data synchronization. But hopefully I will be able to cope with these problems.
And your idea is good, very good. I'll have to think about it to ask some tricky questions.
No, here it is the realtime inputs, set before any parameterisation. That's exactly what was the point of contention. Read it again :). In fact, I'm just now going back to where I left off a year and a half ago. I assure you, you were already aware of my approach then :) . By the way, and that's the question I seem to have asked :).
Well since two parameters, of course there will be a surface. And the profit is simply taken as an average by a given number of nearest points.
All right, let's have realtime inputs. But you didn't enter it from a torch, did you ? There was a decision-making source, wasn't there? So he implicitly set the algorithm for determining points of the phase space, by which his division into contexts is further evaluated. There is still a misunderstanding between us. I argue that trading decision points should be set in advance (which you have done with a sequence of trades). And the parametrization of the phase space is sought later and independently based on the requirement of clustering the points representing the trades. (Concerning application of NS in this approach you were absolutely right - it is self-evident, especially for more than 2 parameters). Exactly this program has been implemented. Congratulations, interesting result!
I didn't quite understand about the surface. So you really averaged it over some local area ? Did you have sufficient deal density for that ? What do you mean closest ?
Here is an illustration of "my" approach. We take a set of inputs, count for each input the values of some two parameters (taking into account the context). We obtain a two-dimensional phase space (PS). More precisely, a cross-section of the phase space by a plane, since adding new state parameters will increase its dimensionality but will not require recalculation of those already calculated. This is precisely the advantage of the fixed-entry approach. Now on this plane we construct a rough estimate of the dependence of the profile on the parameters, which is in some sense akin to the probability density function. We obtain a nice picture
The blue dots are entry points and they are located on the zero plane, i.e. where they dive under the surface the estimate of the profit becomes positive. Now let's look at this case from the top
We can clearly see the areas that promise positive profit (i.e., areas where the points are hidden by the surface). In this two-dimensional case, we can literally draw their boundary by hand. For larger dimensions of the phase space we can no longer do without mathematics.
The question remains - is it a fitting or not? Who knows :). IMHO, it all depends on the parameters. I don't like these particular ones, they're not invariant enough in my opinion. Besides I'm not sure about correctness of estimation of probable profit, it's quite primitive.
P.S. In case anyone doesn't get it - it's bait for suitable "newbies" :) .
This is not a fitting, but a statistic that requires additional research which may discard this parametrization, or increase the chances that it is correct.
In essence, it is a definition of the optimal zone width, only for 2 parameters at the same time. The wider the optimal zone (for the 2-dimensional case, the truer the area), the better. However it is better to directly build the dependence not on the profit but on the more complex indicator, which also takes into account the equity smoothness, for example the FF. In this case, however, we will have to add an additional condition of credibility - to take into account the parameters when the number of trades is at least 100.
Further, we can additionally study the optimal zone. A good indicator is the consistent improvement of the system in terms of profit/risk at tightening the filter parameters. If you take PF as a basis for estimation, it should increase, but the number of deals decreases at the same time. In fact, it turns out that part of deals are sequentially selected. I.e. if we have, for example, 1000 deals, we will have fewer and fewer of them when filtering is weak but the FF for them is increasing. It is an important statistical indicator that the filter works and really shows context. If there is more than one parameter, each must have this property. Although if they are logically a whole, they don't have to be. imha
Eventually specific filter parameters will be chosen as a compromise between high PF and total profit (actually number of trades). But the system performance can also be checked based on equity with less rigid filtering parameters. It will be a better indicator since there will be much more trades.
Мы совершенно чётко видим области, сулящие нам положительное МО прибыли (то есть области, где точки скрыты поверхностью). В данном двумерном случае мы можем нарисовать их границу буквально вручную. Для больших размерностей фазового пространства без математики обойтись уже не удастся.
Остаётся вопрос - подгонка это или нет? Фиг его знает :). ИМХО, всё зависит от параметров. Вот эти конкретные мне не нравятся, они по моему мнению недостаточно инвариантные. К тому же я не уверен в корректности оценки вероятного профита, она весьма примитивна.
It's not a fitting. Although, who knows what the definition of fitting is.
The idea of mapping results is a good idea and it is a tool for analysis. Unfortunately (or maybe vice versa) it is not widely used. The next step, identifying sustainable areas of profit and loss, and tracking these areas over time. If such areas are found, and they are stable in space (changes of parameters) and in time - we bravely go to the centre of the area - and alright! ;) It is clear that in practice there are some subtleties - but the general idea is the same.
Ну хорошо, пусть реалтаймовые входы. Но ты же не от фонаря входил ? Ведь был же какой-то источник принятия решений ? Вот он и задал неявно алгоритм определения точек фазового пространства, по которым далее оценивается разделение его на контексты.
Why implicitly, quite explicitly. Actually, this is the main task of the algorithm. I am counting parameter values in the same way, in real time, but they have nothing to do with selecting entry and exit points. Then, after defining the context filter, we will be able to prohibit or permit the trade by these parameters. But it will be impossible to move entry and exit points.
Yes, but you argued that they should be perfect entries. I kept trying to explain to you that this is the weakest point of yourvision. For the reason that by doing your work and then trying to find your inputs and outputs in realtime you will get to where I'm starting from. I never claimed to have it the other way around :).
And the parametrization of the phase space is sought afterwards and independently based on the requirement of clustering the representing transaction points.
Didn't you confuse something? It seems that so far we have parameterized the price series and these parameters formed the phase space.
I did not fully understand about the surface. That is, you actually averaged it over some local area? Did you have sufficient deal density for that? What do you mean closest?
Hmm, how else to say. Each blue point is a trade, it has coordinates in this phase plane, (Xi, Yi). For each point of the phase plane (X,Y) we may calculate the distance to each blue point e.g. by Euclid: (X-Xi)^2+(Y-Yi)^2. Each blue point has a profit, positive or negative. We are interested in 10 blue points closest to X and Y. Average their profit and get the surface coordinate Z for every point (X,Y). That is, we don't set the averaging radius, but the number of neighbours considered, the averaging radius can be anything.
I, by the way, have already made a variant of weighted Gaussian summation, I still need to understand, from what considerations sigma should be normalized :). However, in densely populated areas the results are quite similar.
P.S. Once again: my trades not only have non-ideal profits, nothing prohibits some of them to be unprofitable.
... Но лучше сразу строить зависимость не от профита, а от более комплексного показателя, который учитывает еще и гладкость эквити - например ПФ. Тогда правда нужно вводить еще и дополнительное условие достоверности - учитывать параметры при которых число сделок не менее 100 например.
In principle I have been doing, as an option, averaging not the profit, but the sign of the profit (+1 or -1). This may be considered as some kind of local PF. But in general the profit value with rigid inputs and outputs is also a function of the context, so the current variant seems preferable to me. But the number of points used for averaging for the above pictures is exactly 100 :).
To control equity quality, I now look at the ratio of maximal profit to maximal drawdown and linear regression parameters by equity (slope and RMS).
PF can probably beuseful to investigate the optimum zone.
Eventually specific filter parameters will be selected as a compromise between high FF and total profit (actually number of trades). But in this case, the system performance can also be checked based on equity with less rigid filtering parameters. It will be a better indicator since there will be much more trades.
This is a curious trick. I believe the decrease in trade statistics when filtering is tightened to be a serious problem.
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.Selection of stable areas of profit and loss and tracking of these areas in time. If such areas are found and they are stable both in space (changes of parameters) and in time, we can easily find the centre of the area - and alright! ;)
Approximately so I see it, only I clarify that by moving in space we must mean the change of parameters of the algorithm setting transaction, not the state parameters. That is, it is rather a strategy adjustment to the context. It is also a slippery slope, you can go, but carefully controlling the correctness of actions, imho.
Примерно так и я вижу, только уточню, что под перемещением в пространстве нужно подразумевать изменение параметров задающего сделки алгоритма, а не параметров состояния. То есть это скорее подстройка стратегии под контекст. Тоже скользкая дорожка, идти можно, но тщательно контролируя корректность действий, имхо.
I suspect I don't understand half the terminology that is written. As such, I can't say yes or no. I can only say that what I was talking about has nothing to do with adjusting strategy to the context (whatever that context may be).
Подозреваю, что не понимаю и половины той терминологии, в которой написано. По этому, не могу сказать ни да, ни нет. Могу только сказать, что то о чем вел речь я не имеет отношения к подстройке стратегии под контекст (чем бы этот контекст не был).
Then it's me who's been carried away. Apparently you meant that over time, surface deformation can lead to a shift in the optimum zone.
Why implicitly, quite explicitly. Actually, this is the main task of the algorithm. I am counting parameter values in the same way, in real time, but they have nothing to do with selecting entry and exit points. Then, after defining the context filter, we will be able to prohibit or permit the trade by these parameters. But it will be impossible to move entry and exit points.
Well, this is what I am talking about. At the stage of building contexts, the parameters should not have anything to do with entry/exit points. However, when the clustering is done, these values can already play the role of an input-output filter. And moving them was out of the question in the first place. Especially in your case, when these points are taken as a basis for clustering.
Yes, but you argued that they should be perfect inputs. I kept trying to explain to you that this is the weakest point of yourvision. For the reason that by doing your work and then trying to find your inputs and outputs in real-time you will end up where I started. I never claimed it was the other way around :).
You see, if we are talking about profit maximisation (which is what we were talking about as the initial criterion for constructing a TS), then it is the ideal inputs that should be used to select the optimal (ideal) parameterisation of the FP. Ideally (:-) then we may not need an external trade filter at all, the FP parameters will be enough. But if we are talking about a ready I/O strategy, then it is just another matter - optimization of the existing strategy by the FP clustering method. If the strategy is worthwhile, the result will also be good. And the methodology is the same.
So you could say the opposite: by doing my job I achieve a result bypassing the very subjective step of creating an I/O strategy on the flat.
However, I hope you understand that these options are not opposed to each other. Either one is suitable, as long as it produces results.
Are you sure you're not confused? Until now we parameterized the price series and these parameters formed the phase space.
We are parameterizing the process. In other words: we create a model of the process, which will obviously have some parameters. This model should allow us to read the necessary numbers to describe the process, such as MO. Or the expected profit. And if we use the points depicting the transactions to construct the surface of the profit and the subsequent clustering of the FP, then this does not contradict anything I said before, nor does it contradict anything I said afterwards. And you're certainly right - these are the parameters that form the FP.
And what are yours ?
Um, how else to put it. Each blue point is a transaction, it has coordinates in this phase plane, (Xi, Yi). For each point of the phase plane (X,Y) we may calculate the distance to each blue point e.g. by Euclid: (X-Xi)^2+(Y-Yi)^2. Each blue point has a profit, positive or negative. We are interested in 10 blue points closest to X and Y. Average their profit and get the surface coordinate Z for every point (X,Y). That is, we don't set the averaging radius, but the number of neighbours considered, the averaging radius can be anything.
I, by the way, have already made a variant of weighted Gaussian summation, I still need to understand, from what considerations sigma should be normalized :). However, in densely populated areas the results are quite similar.
P.S. Once again: my trades not only have non-ideal profit, nothing forbids some of them to be unprofitable.
...
Hmm, I thought I had a rough idea of what you're talking about, but with this post you've completely destroyed that misconception :). But I'd like to get to the bottom of it. How about we start in order, in small steps? Using one parameter as an example.
So, here's the price series, here you go along it and at each bar you calculate the parameter. Or at every tick?
Then you build a phase space from these values. You said that the phase trajectories must be continuous. So you take ALL the values? From every bar (from every tick) ?
If not, how do you determine at which points in time to take values for further analysis ? And in what sense then did you talk about continuity?