First sacred cow: "If the trend started, it will continue" - page 63
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I've heard of the Wiener process, but the fact that the price is random is not believable to the mind... ;)
Thank goodness you haven't yet advised me to realise the Slutsky-Yule theorem in economics, so that I don't start applying BFP!
The picture similar to yours, but with the symmetry line of the bell directed at an angle to the abscissa axis, will illustrate by a random walk with a drift (trend). And your picture naively inaccurately draws the return to 0 and the boundaries of the bell. It turns out as if the dispersion does not grow directly proportional to the square of time, but much faster. In short, the bell is correct for mo=0, but the price chart is a volatility amplifying flat with evident reversion.
случайным блужданием со сносом (трендом), будет иллюстрировать картинка подобная вашей, но с линией симметрии колокола, направленной под углом к оси абсцисс
hence ;)
Про винеровский процесс я слышал, а вот то, что цена случайна - ум не верит... ;)
Вы мне, слава Богу!, еще теорему Слуцкого-Юла не посоветовали осознать в экономике, чтобы я БФП не начал применять!
Does it believe in trends?
Questions of faith are probably best discussed elsewhere.
А в тренды верит?
Вопросы веры, наверное, лучше обсуждать в другом месте.
You're being unapologetic:
1. If you know, explain and prove it.
2. Otherwise, you believe, BUT IN OTHER place. Then go to that "other" place yourself.
случайным блужданием со сносом (трендом), будет иллюстрировать картинка подобная вашей, но с линией симметрии колокола, направленной под углом к оси абсцисс. И на вашей картинке наивно-неверно нарисован возврат к 0 и границам колокола. Получается как будто дисперсия растет не прямо пропорционально квадрату из времени, а гораздо быстрее. Короче, колокол верный для мо=0, но график цен - какой-то усиливающийся по волатильности флет с явной возвратностью
which "naively wrong" picture are we talking about? Fig 5.2.?????
:о)))
what "naively wrong" picture are we talking about?
:о)))
what kind of graph do you have inside the bell? :)
что за график у вас внутри колокола? :)
Yeah...
I can't see the bell. I see a pipe.
What do you mean, "categorical"?
Especially with such conclusions and assessments...
;)
Yeah...
I can't see the bell. I see a pipe.
What do you mean, "categorical"?
Especially with such conclusions and assessments...
;)
Let the pipe be your way))) I see the formula. I'm asking, what is the graph W(t) inside the "pipe" - it's not just drawn, is it? :) Is this an example of a Wiener process trajectory/random walk?
Apparently, yes, a highly simplified example to illustrate the theorem.
Of course, it should not be taken literally, it is too "regular" here. It simply shows the likely bounds in which its conventionally "extreme" values hang around. The uncertainty of time t0, the "beginning of times", adds to the problems in constructing a real boundary pipe: on the one hand the process remembers history, and on the other, it does not.
What's the book, avatara?
How can probabilistic boundaries be shown as a concrete graph? It's clearly a separate trajectory with incomprehensible corrections, "notches" and bounces from areas between the two "pipes". And what trend was supposed to be seen there? On a random rambling with zero mo increments :)
Purely externally, the picture resembles another process. Let's take a numerical line and throw points distributed on it by N(0,1). 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 and will also be conventionally bounded (easy to plot in Excel), 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.
P.S. 2 Avals: The specific graph is one implementation of a Wiener process. Well here it is so regular. It is also possible.