Put in a good word about the occasional wanderer... - page 3
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как это не связаны? Нормальное распределение стационарно и приращения СБ распределенные по НР - стационарны, а я изначально говорил именно о приращениях.
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Вы считаете что НР нестационарно? Или нельзя для каждого непрерывного распределения сказать - является оно стационарным или нет? :)
This is the definition of stationarity, where is there any mention of distribution? Stationarity is a property of a process, not a distribution. The process has some kind of distribution. A process with a normal distribution may or may not be stationary. It does not depend on the distribution. Of course, you cannot say anything about the stationarity of a process just by knowing its distribution.
Concerning SB itself (as cumulative sum of increments): There will be no "heavy tails" described by you in the previous post
.Because the SB itself is also normally distributed, but with a variance t times larger than for a single increment (at time t from the start of the reference). Yes, the variance of the SB distribution increases with time, and this distribution is actually the sum of independent random variables distributed normally (increments), which corresponds to the definition of stability in your link. Heavy tails over 3 sigmas for example, but for SB if you calculate the variance at a specific point in time (and you can do it analytically) - everything will be as for normal. It will be normal with specific parameters - finite variance and mo
Before writing, I simulated the situation in Matlab, i.e. I am responsible for my words. And you're just blathering on at random here. If you "sometimes" double the value of the increments, as Avatar wanted, then the variance of the "large" deviations increases, and kurtosis increases. The increments cease to be normally distributed even if they were so initially. But SB itself will not have any tails, SB has a normal distribution and is non-stationary, regardless of the nature of the increments.
Here is the definition of stationarity, where is there a word about the distribution?
I am saying that for each distribution you can find out if it is stationary or not, or if the same process will be stationary or not. And I wrote that SB increments are modeled by stationary distributions. If the distribution is e.g. normal, then the process is stationary. Can a process that is normally distributed be non-stationary?
Stationarity is a property of the process, not of the distribution. The process has some kind of distribution. A process with a normal distribution may or may not be stationary. It does not depend on the distribution. And of course, knowing only the distribution of a process it is impossible to say anything about its stationarity.
Where did you get that from? Give me an example of a non-stationary process whose distribution would be normal.
Before writing, I simulated the situation in Matlab, which means that I am responsible for my words. And you're just blathering on at random here. If you "sometimes" double the value of the increments, as Avatar wanted, then the variance of the "large" deviations increases, and kurtosis increases. The increments cease to be normally distributed even if they were so initially. But the SB itself won't have any tails, the SB has a normal distribution and is non-stationary at that, regardless of the nature of the increments.
I don't quite understand what you modelled and how you got the heavy tails. As I understood what the avatar asked for - there shouldn't be any tails. Probably misunderstood :( Please give me at least a histogram of the resulting distribution and how you modelled
SB is non-stationary, is I(1) - the first difference is stationary (incremental) as I wrote about. It is also stationary and is a normal distribution for a fixed point in time. At moment t0, the distribution is stationary and one, at moment t1 another. But SB itself as a process from time x=F(t) is not stationary and is not normally distributed. This is because its variance is infinite at t->infinity. The first difference (increments) is normally distributed. I gave a link to the source in a previous post.
Откуда ты это взял? Приведи пример нестационарного процесса, распределение которого будет нормальным.
I have given this example three times already - random walk is a non-stationary process with a normal distribution.
The distribution is the shape of the person, and the non-stationarity is the height: a fat person can be tall or short (this is the distribution), and he grows up to 25 years old and then down, and his width changes, getting fatter and fatter with age, i.e. he is non-stationary. But growth is not related to shape.
Stationarity is not a property of the distribution, but a property of the process.
I have given this example three times already - random walk is a non-stationary process with a normal distribution.
The distribution is the shape of the person, and the non-stationarity is the height: a fat person can be tall or short (this is the distribution), and he grows up to 25 years old and then down, and his width changes, getting fatter and fatter with age, i.e. he is non-stationary. But growth is not related to shape.
Stationarity is not a property of the distribution, but a property of the process.
The increments and distribution of SB at a certain fixed point in time from t reference point are stationary and normally distributed. For them it is possible to calculate mo and variance as opposed to SB as a function of time
Несовсем понял что ты смоделировал и как получил тяжелые хвосты. Как я понял что просил аватара - никаких хвостов быть не должно. Возможно неправильно понял :( Приведи, пожалуйста хотя бы гистограмму полученного распределения и как моделировал
was:
(i.e. |y(i)-y(i-1)|>= the strength of the hero on the i-th step, then his generated strength ( including minus - doubts) on the i+1 step should be doubled.
Highlighted in red must be i-1, otherwise there will always be equality. I.e. if the increment generated is large enough, it should be multiplied by two more. This increases the variance exactly in the area of large increments, which thickens the tails.
e(i) = s(i)-b(i);
if abs(e(i)) > abs(e(i-1))
e(i) = e(i) * 2
end
Price movements are completely unpredictable. we are dealing with psychology, not mathematics, and no formula will help.
you are wrong - SB as a function of time is not HP, non-stationary is.
You are arguing with the multiplication table, not me. And that's unfortunate.
Here's a 1000 random walk with a uniform distribution of increments. You can keep banging your head against the monitor that it's not a normal distribution. And I'm getting tired of it.
Price movements are completely unpredictable. We are dealing with psychology, not mathematics, and no formula will help.
You're contradicting yourself. If "completely unpredictable", then not only formulas will not help, but nothing will. And if there is still hope, somehow the psychology you propose may well be described by formulas.
You're arguing with the multiplication table, not me. And that's unfortunate.
Here's 1,000 random walks with a uniform distribution of increments. You can keep banging your head against the monitor that it's not a normal distribution. And I'm getting tired of it.
timbo this is the 3rd time I've written the same thing. Yes SB generated at some time interval e.g. 0-1000 (as on your picture) F(t1000)- distribution is both normal and stationary. mo=0, disp=1000*Disp_adjustment. And at any other fixed time interval, the distribution will be stationary and normal, and the variance will be proportional to its length. But the SB process itself, as a function of time F(t) is not nonnormal nonstationary. its mo will also be=0 but the variance is infinite. For stationary and HP, whatever t is taken, the variance will be the same and a fixed number - it does not change over time, which is the condition of stationarity.
timbo уже 3 раз пишу одно и тоже. Да СБ сгененрированное на каком-то отрезке времени например 0-1000 (как на твоей картинке) F(t1000)- распределение и нормально и стационарно. мо=0, дисп=1000*Дисп_приращения. И в любой другой фиксированный промежуток времени распределение будет стационарным и нормальным, а дисперсия будет пропорциональна его длине. Но сам процесс СБ, как функция от времени F(t) не является не нормальным не стационарным. его мо так же будет=0 но дисперсия бесконечна. Для стационарного и НР, какое t не взять - дисперсия будет одинаковой и фиксированным числом- она не меняется во времени, что и есть условие стационарности.
In general any segment of variable length will give a normal distribution. What kind of distribution do you think the SB has, is it non-stationary? Move away from these increments, look at the process from another angle. If you see a well-defined limited bell, it does not mean that the process forming it is stationary.