To follow up - page 19
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Для меня вопрос в том, что приходится вводить дополнительный параметр (k в данном случае). Точно так же, как и при сглаживании по времени. Нужны какие-то соображения, хотя бы ограничивающие диапазон изменения этого параметра.
Yes, I think the considerations are the same as for time. Except that the sampling for filtering is smaller (less noise initially) - i.e. k will be closer to 1. Otherwise... well, what considerations can be made apart from noise removal? For example, selecting lower frequency movements. Or phase shift together with filtering. What else. Well, various indicators where MA are used. There, too - periods may be shorter than it is usual over time. It depends on the analysis tasks, in short.
(пожимая плечами) Я и не спорю.
Кажется, я в самом начале поста обозначил тему "Про сглаживание". Ни о чем др. я в посте не писал.
Вы хотите обсудить проблему размерности? Давайте. Пока у меня нет возражений на то, что вы сказали. И дополнить чем как-то в голову пока не приходит.
Развивайте мысль.
Let me try to develop my thought.
What we are trying to do here is to define market conditions unambiguously, right?
Well, from a mathematical point of view, we can work on any convenient basis, not just primary data.
As long as it really is a FULL and INDEPENDENT basis.
I propose to work with strategies directly.
Suppose, just as an assumption, that we analyse the phase of the market (determine the phase coordinate) by how well some particular strategy performs.
I.e., we determine the "trendiness" of the market by the profitability of the strategy of crossover, we determine the "failsafe" of the system by the profitability of Graders and other martingales, etc., we determine the parameter of "American bait" by how often an expanding triangle appears in the market, etc.
The key point is: you have to pick a "strategy baseline."
Then any ideal strategy can be decomposed, analysed and synthesised from elementary ones.
That is, we can of course work directly with volatility, liquidity, etc., but in terms of mathematics we can also work with strategies directly.
Да, это был бы интересный индикатор. Николай, ты можешь написать такой ? По мне так эта статья Шумского недостаточно конкретна в этом вопросе. Да и в остальных, похоже.
Theoretically, I probably could :) . Realistically - if I were ready to do it, I'd already be writing :)
But otherwise
...Well, what considerations can you have apart from noise removal? For example, to isolate lower frequency movements. Or phase shift together with filtering. What else. Well, various indicators where MA are used. There, too - periods may be shorter than it is usual over time. It depends on the analysis tasks, in short.
It is clear. How to make a decision about one or another value? Visually estimate the smoothing quality? Go through the values of the same k in the tester? If it is the first then it is an incomplete formalization of the task. The second - it depends on what will be the total number of parameters.
Т.е., "трендовость" рынка мы определяем по прибыльности стратегии пересечения машек, "безоткатность" системы мы опеределяем по прибыльности гридеров и прочих мартингейлов. и т.д., параметр типа "американский развод" мы определяем по тому, насколько часто на рынке возникает расширяющийся треугольник и т.д.
Ключевая мысль: надо подобрать "базис стратегий."
Тогда любую идеальную стратегию можно разложить, проанализировать и синтезировать из элементарных.
Т.е. мы можем конечно напрямую работать с волантильностью ликвидностью и т.д., но с точки зрения математики можно также работать со стратегиями напрямую.
And what lengths of price series segments would be needed to determine the "coordinate" values in this basis? Wouldn't the average hospital temperature be the same?
Theoretically, I probably could :) . Realistically, if I were ready to do it, I would have already written it :)
OK, tell me theoretically - I'll write.
Лишь бы это действительно был ПОЛНЫЙ и НЕЗАВИСИМЫЙ базис.
What operations are allowed on elements of the basis?
How do we define 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?
Ладно, раскажи мне теоретически - я напишу.
We can try the correlation dimension
Here C is correlation integral (normalized to N*N number of pairs of points whose distance between them is less than epsilon)
here theta is Heaviside function
Instead of "real" vector x we substitute vector z
where a is the analyzed time series. An estimate of the number of degrees of freedom will be the value of m, at which the dimensionality stops growing. If of course it stops growing :). If it doesn't, you may consider the series to be random. It is recommended to take first zero of ACF as k.
This I extracted from this, you can look for more details there.
Какие операции допустимы над элементами базиса?
Как мы будем определять полноту и независимость базиса?
Ну давайте начнем с самого начала, т.е. определим кольцо операций, над которым будет построено пространство. Или Вы собрались строить нелинейное пространство?
This is a serious question. I don't have a ready answer to it, unfortunately.
But here are some thoughts:
In order to define operations on the elements, we need to somehow determine the "distance" operation between the trade and the elementary strategies, i.e. we need to be able to determine whether a particular trade is "trending", "breakout", etc. It seems to me that a possible way to do this is to evaluate the membership function for each underlying strategy. We open a trade at F>0. If we have F1, F2, F3 at a given point, it is possible to determine "similarity" for a particular operation.
Further, about independence - it simply means that there are periods in history when strategy 1 and 2 work independently of each other, i.e. there is no correlation.
About operations:
if we open by identity function F1>0 and F2>0,
it is possible to define operations of union and intersection
F1>0 || F2>0, F1>0 && F2>0
И какой длины отрезки ценового ряда понадобятся для определения значений "координат" в этом базисе? Не получится средняя температура по больнице?
It all depends on the inertia of the market. We should probably take a fixed value of bars that is much shorter than the time it takes for a strategy to fail. I.e. for example, if you know they are profitable for 3 months, then you could estimate the instantaneous market condition by 2 weeks, for example.Here C is the correlation integral (normalised to N*N number of pairs of points whose distance between them is less than epsilon)
This formula is good to remember. Computationally, O(N^2) (more precisely, N*(N-1)/2 distance calculations) for the volumes of data in question is creepy. There are algorithms with asymptotic efficiency O(N*logN) and O(N); the first one isn't complicated (in mathcad it would be hard to implement it, imho), while I haven't figured out the second one.
p.s. There was a very good pdf on Pavlov's course on the site you gave a link to. // this is a note for those who haven't read it
p.p.s. Recently I've been doing some digging on correlation dimensionality. Didn't like lim N->inf very much. For eurusd it got a value of about 9.