Author's dialogue. Alexander Smirnov. - page 29

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grasn:

Colleagues, there is a simple little question for scientific people: is there a parameter that measures the smoothness of a time series as a whole? And I don't care if there is correlation between them or not, it is important to distinguish that one series as a whole is smoother than the other.

Finding out this very question is where all this nerd fiddling should have started. The smoothest is the linear series or straight line, because there is nothing to smooth there. The less adaptive the mach, the smoother it is.
 
This very question should have been the starting point for all this botanical fiddling. The smoothest is a linear series or straight line, as there is nothing to smooth there. The less adaptive the mach, the smoother it is.

Nerd fuss was started by the author, a dialogue with which in my humble opinion has long been lost (colleagues, forgive my irony, but I think the author is a bit hurt and is unlikely to appear, although ... something tells me - you do not really need it).

So, this criterion is needed, not for AF (I've had enough of it, let my colleagues not miss out on the fun), but for the optimal choice of a few parameters which have nothing to do with the forum topic. Such a task has arisen. And the number of local extrema is not such a criterion.

 
grasn:
This very question should have been the starting point for all this botanical fiddling. The smoothest is a linear series or straight line, as there is nothing to smooth there. The less adaptive the mach, the smoother it is.

The botanical fuss was started by the author, a dialogue with whom in my humble opinion is long lost


Let's do without nursery school, i.e. without all sorts of "he started it first"?

The culprit is not the one who started it, but the one who fell for it.
 
grasn:

Colleagues, there is a simple little question for scientific people: is there a parameter that measures the smoothness of a time series as a whole? And I don't care if there is correlation between them or not, it is important to distinguish that one series as a whole is smoother than the other.


The Vertical Horizontal Filter (VHF) indicator. The ratio of the movement over a period of several bars to the sum of the movements on each bar over that period.
 
Integer:
grasn:

Colleagues, there is a simple little question for scientific people: is there a parameter that measures the smoothness of a time series as a whole? And I don't care if there is correlation between them or not, it is important to distinguish that one series as a whole is smoother than the other.


Vertical Horizontal Filter (VHF) indicator. The ratio of the movement over a period of several bars to the sum of the movements on each bar over that period.

Thank you, I will look into it.

 
Integer:

Vertical Horizontal Filter (VHF) indicator. The ratio of the movement on a period of several bars to the sum of the movements on each bar for that period.
sum=0.0; suma=0.0; 
for(i=0; i<p; i++)
{
    dfx = fx[i] - fx[i+1];
    sum += dfx;
    suma += MathAbs(dfx);
}
if (suma!=0) k=sum/suma; 
else k=0;

Sort of like a relative RSI, only for the function.

Smoothness is good, but the number of profitable trades is even better!

 
grasn:

Colleagues, there is a simple little question for scientific people: is there a parameter that measures the smoothness of a time series as a whole? And I don't care if there is correlation between them or not, it is important to distinguish that one series as a whole is smoother than the other.

Well, here's one (just invented): we take a series of first differences (returns) and calculate s.c.o. returns. The ratio of m.o. returns to s.o. returns can serve as such a measure. The higher it is, the smoother the row is.

It is clear that it may happen that neither r.m.s. nor variance of the general population exists (e.g. Cauchy distribution). But we always take a finite number of samples...

2 Korey: here's another one especially for you.

Quadratic Regression MA = 3 * SMA + QWMA * ( 10 - 15/( N + 2 ) ) - LWMA * ( 12 - 15/( N + 2 ) )

Here N is the period of the averages,

QWMA( i; N ) = 1/( N*(N+1)(2*N+1) ) * sum( Close[i] * (N-i)^2; i = 0...N-1 ) (the square-weighted scale).

 
Reshetov:
grasn:

Colleagues, there is a simple little question for scientific people: is there a parameter that measures the smoothness of a time series as a whole? And I don't care if there is correlation between them or not, it is important to distinguish that one series as a whole is smoother than the other.

You should have started all this botanical nonsense with figuring out this very question. The smoothest is a linear series or straight line, as there is nothing to smooth there. The less adaptive the mach mach, the smoother it is.


Either I am too old, or I am too backward. I do not understand.

Colleagues, is there really any other definition of smoothness than mathematical ? Enlighten me if there is, don't mind me. Because if there isn't, then all these contrivances are very arbitrary creations relying on vague criteria.

A function is called smooth if it has a continuous bounded derivative - in my opinion so. It follows that the question of smoothness of BP should be posed very cautiously. At least more accurately. After all it is always possible to interpolate any VR by a polynomial of appropriate degree with absolute accuracy. And a polynomial of any degree (not just a straight line) is quite a smooth function.

Sergey, if you know the signal, you can always determine (for example, with the help of sco) how smooth GR is relative to the signal, if by smoothness we mean the measure of deviation of GR values from the signal values. But in exactly the same way you can determine how smooth that VR is relative to any other given function. Therefore, if the intuitive notions of smoothness were sufficiently constructive, the smoothest approximations of all BPs, including the price series, would have long ago been constructed. And we wouldn't be chewing this mashup cud.

So your question should be supplied with an addendum: relative to what ?

 
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.

Of course, it may happen that neither m.o. nor variance of the general population exists (e.g. Cauchy distribution). But we always take a finite number of samples...

Thanks, very curious, when I get to the lab I'll have a look :o)



to Yurixx
After all, one can always interpolate any BP with a polynomial of an appropriate degree with absolute precision.

You can always interpolate, even Brownian motion, except that it theoretically does not diff anywhere, if I am not mistaken again :o)

if by smoothness we mean the measure of deviation of BP values from signal values.
It is always possible to adjust the parameters so that you can get good smoothness results on a bad BP
 
grasn:
to Yurixx
It is always possible to interpolate any BP with a polynomial of appropriate degree with absolute precision.

You can always interpolate, even Brownian motion, except that it is theoretically not differentiable anywhere, if I haven't got it wrong again :o)


Did you put the differentiability condition somewhere? That's why I'm saying that the smoothness question needs to be put more precisely.

Brownian motion is not differentiable in the sense that its derivative is also a random series. But its interpolation can be differentiable or even infinitely differentiable. It is not known, however, to what extent it will satisfy your needs. So once again I repeat: you need a certain formulation of the question of smoothness. What do you mean by this, for what purposes, what are the evaluation criteria and/or required properties.

It is always possible to select parameter values in such a way that good smoothness results can be obtained on a bad VR

Parameters of what ? Your signal model ? Or some of your other parameters, e.g. the VR analysis algorithm you use ?

What are "good smoothness results" ??? Explain to me what they are good for and I will tell you what criteria you use. Maybe then we'll be able to talk substantively.

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