Author's dialogue. Alexander Smirnov. - page 30

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to Yurixx
Did you put the differentiability clause somewhere?

I posed the question in the beginning, although I gave it purely as an example. There was an idea to get such a criterion by taking the curvature of the curve as a basis...

That's why I say that the question of smoothness should be put more precisely... ...Maybe then we can talk about it.

I haven't found a precise definition of smoothness, not for BP as a whole, nor for local areas. Probably just not, if I'm wrong - just give me such definition. But I don't really need an "absolute truth", a simple, rough criterion is enough. Of all the candidates I received BP, all will suit me, but the best will be the one that is the smoothest, so on and so forth :o)

Parameters of what ??? Your signal model ?

I meant the method you suggested:

It is always possible to interpolate any BP by a polynomial of the appropriate degree with absolute accuracy. And a polynomial of any degree (not just a straight line) is quite a smooth function.

Will not be the best. Maximum "smoothness" can be achieved by selecting certain parameters of the polynomial. And the criterion for smoothness in this case can be any, including the one you suggest:

PS :

Brownian motion is not differentiable in the sense that its derivative is also a random series.

This may upset you, but Brownian motion is not differentiable in any sense. :о(

 
to Mathemat

Ну вот такой (только что придумал): берем ряд первых разностей (returns) и вычисляем с.к.о. returns. Отношение м.о. returns к с.к.о. может служить такой мерой. Чем оно выше, тем ряд глаже.

I remember, it's a really good criterion, it's described by Bulashov as a criterion of "predictability" of BP, if I'm not confused again. Seems to really work, thanks

 

One of the criteria for 'smoothness' can be the derivative, 1st, 2nd etc. As in splines. There "smoothness" is quite specific, due to the fact that it ensures the continuity of these derivatives, usually no older than the second derivative, and as a consequence provides "minimum potential energy".

"Smoothness" can be, and has already been said to be, a degree of approximation to some describing curve (e.g. first order).

"Smoothness" can be, in terms of fractal dimensionality, as the ratio of the run length of the actual curve to the describing curve.

There seem to be some other "smoothnesses", I do not remember now. And what do you need as a result?

 
It seems that by smoothness grasn means the same thing as Smirnov means by hesitancy. But what is needed he does not want to admit. :-)
 

By the way, I got this link http://www.library.dgtu.donetsk.ua/fem/vip80/80_02.pdf made this middle one from Smirnoff (SAMA). I felt it. The conclusion is that on small periods it does not behave very well (a lot of noise - kinks). But on the contrary, on large periods it is not bad at all. Somewhere even faster than JMA. In short - you have to try..... Maybe there's something to this......

 

to Yurixx

It seems that by smoothness grasn means the same thing that Smirnov means by hesitancy. But he does not want to admit that he needs it. :-)

Yuri, at the very beginning grasn by smoothness meant the criterion of minimum curvature, which he carefully wrote about. But remembering your scientific approach:

Colleagues, is there really any other definition of smoothness than mathematical?

I regret to note that I never waited for this very mathematical definition of smoothness. Maybe it's not you, but me

I don't know if I'm too old or too backward for my own good.

:о)))

PS: and if you really read the question carefully, (and in conjunction with the fact that there is no unambiguous definition of smoothness), it becomes clear that the author of the question himself does not understand what smoothness is, and asks about it.

In this regard: to Northern Wind

Thank you very much, it's quite clear, I'll poke around with the suggested parameters.

 
The practical criterion of smoothness "for us" does not correspond to the mathematically rigorous notion of smoothness.
The point is that we are looking for autotrading, which means that smooth is anything that does not give false positives.
For example, if the EA misses a non-smooth bump, then it is smooth for the EA and smooth "for us",
although mathematically, the first derivative passes through zero.
So, in autotrading, we should search for smoothness at some smallness not tending to zero,
and this smallness is functionally dependent on the Expert Advisor's algorithm.
 
grasn:

to Yurixx

It seems that by smoothness grasn means the same thing as Smirnov means by fluctuation. But he does not want to admit that he needs it. :-)

Yuri, at the very beginning grasn by smoothness meant the criterion of minimum curvature, which he carefully wrote about. But remembering your scientific approach:

Colleagues, is there really any other definition of smoothness than mathematical?

I regret to note that I never waited for this very mathematical definition of smoothness. Maybe not from you, but from me.

PS: and if you actually read the question carefully, (and in conjunction with the fact that there is no unambiguous definition of smoothness), it becomes clear that the author of the question himself does not understand what smoothness is, that is what he is asking about.


There is nothing in your post on page 28 about the criterion for minimum curvature. You may have written about it before, but I missed it. Sorry, as it is actually a very constructive criterion. If you interpret it as a constraint on the values of the modulus of the second derivative, you can already build something on that basis. However, I haven't encountered such an approach before and haven't tried it myself, but it seems to me quite promising.

I gave the known mathematical definition of smoothness on page 29. Perhaps you missed it. Maybe even as a revenge for me skipping about curvature. :-)

Precisely because the term "smoothness" is not clear enough in this situation, I asked you to clarify what it is all about and what is actually needed. Not in the spirit of fighting for pure mathematics, but out of a desire to understand the essence of the matter and, if it is within my power, to help. If you remember, we discussed the smoothing curve behavior and false extrema at the very beginning of our acquaintance, about 1.5 years ago. As we can see, it is still topical for both of us. :-))

 

to Mathemat

P.S.

1.By taking these steps, it counts quickly, and you don't have to fear further complication of the formula.
2. Even in this form it is of practical interest.

 

to Yurixx


...

Precisely because the term "smoothness" in this situation is not clear enough, I asked you to clarify what we are talking about and what is needed. Not in the spirit of fighting for pure mathematics, but out of a desire to understand the essence of the matter and, if it is within my power, to help. If you remember, we discussed the smoothing curve behavior and false extrema at the very beginning of our acquaintance, about 1.5 years ago. As we can see, it is still topical for both of us. :-))

That was a military trick - to ask without specifying, in case there are some new ideas. :о)))

to Korey

The practical criterion of smoothness "for us" does not correspond to the mathematically rigorous notion of smoothness. the point is that we are looking for autotrading, which means that smooth is anything that does not produce false positives. For example, if the EA misses a non-smooth bump, then it is smooth for the EA and smooth "for us", although, mathematically, the first derivative passes through zero. I.e. in autotrading, we should search for smoothness at some smallness not tending to zero, and this smallness depends functionally on the Expert Advisor's algorithm.

Not for my case, the curve and criterion are not used directly to generate signals.

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