First sacred cow: "If the trend started, it will continue" - page 64

 
avatara >>:

А вот типичная ситуация ( в продолжении темы ;) - обозначить-то обозначился, а вот продолжится ли?


МАХИ очаровывают ;)


This one will continue, and for quite a long time )))

 
Mathemat писал(а) >>

Purely in appearance, the picture resembles another process. Let's take a number line and throw points distributed by N(0,1) on it. The coordinates of these points depending on the moment of throwing will be plotted as a graph from "time". The trajectory will be somewhat similar, but the boundaries will not expand with time and the "trends" will not be so pronounced. But this second process is very often confused with the Wiener process.

Alexey, a similar picture can be obtained, but the process will not at all with independent increments (return) and with increasing dispersion of increments. And the theorem is known in the text - for the usual SB. That is why I was wondering what kind of illustration of trendiness is shown on this figure, because avatara, as it seemed to me, considers that the trends are tossing this graph between the boundaries of the "pipe". That is why I am getting more precise.

Mathemat wrote >>

P.S. 2 Avals: The particular graph is one implementation of a Wiener process. Well, here it is so regular. It is also possible.

anything is possible, but the probability that an ordinary SB (Wiener process) with constant dispersion is realized into such a periodic structure is negligible and certainly atypical and illustrates nothing. And the boundaries of the bounding "pipe" would be different.
 

What's a Wiener return, Slava? Its Hearst index is exactly 0.5. Or did I misunderstand you?

I doubt that avatara is taking this illustration so literally.

 
Mathemat писал(а) >>

What's a Wiener return, Slava? Its Hearst index is exactly 0.5. Or did I misunderstand you?

I doubt that avatara is taking this illustration so literally.

That's exactly what it's not, unlike the illustration.

I wonder who the author is and what he wanted to say with this illustration. Because he (the graph) is clearly misleading for those who are not quite familiar with statistics (the readers of this work?) :)

 

Well, yes, the drawing is, to put it mildly, overly optimistic.

 
Mathemat писал(а) >>

Well, yes, the drawing is, to put it mildly, overly optimistic.

>> grail beckoning)))

 
avatara >>:

Мда...

Колокола не вижу в упор. Трубу вижу. формула приведена.

Tilt your head to the left with your left ear against your left shoulder and you will see a bell.

Here are 100 real Wiener processes in a bell sqrt(2t log(log(t))


 

Let's not say 'bell'. It's too immediate to think of a Gauss.

Let's go with 'expanding trumpet'.

But now the illustration is convincing and life-like.

 
avatara >>:

Вы безапелляционны:

1. Если знаете - поясните и докажите.

2. Иначе - верите, НО В ДРУГОЕ. Тогда сами идите в то, "другое", место.

What is my lack of conviction that this forum is not the place to discuss matters of faith? There are plenty of thematic resources for that. And here I suggest we stay within the formal evidence.

I don't know if there are trends in fin.date. I don't know of any way to prove they exist. "I see" is not proof. If you can't prove presence, you have to admit absence.

A price chart is not a random stray, this has been proven repeatedly. However, the difference between it and a random one is so small that it can generally be disregarded. Although it depends on the model used, the instrument, the position of the stars, etc.

 
timbo >>:

Наклони голову налево, прижав левое ухо к левому же плечу, и увидишь колокол.

Вот тебе 100 реальных винеровских процессов в колоколе sqrt(2t log(log(t)))




Did you, dear timbo, see the Gaussian?

You're a true believer... ;)

And the authors of the illustration I dared to put up - A.V.Bulinsky, A.N.Shiryaev.

Would you like biographies? Do they have an ear to the shoulder as well?

----

Strange branch - one philosophy...

Sceptically sullen.

You are not interested in theory or practice?

What about Alexey?