What makes an unsteady graph unsteady or why oil is oil? - page 34
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использует зависимость волатильности от предыдущих значений при прогнозе.
So? Is it like "time series memory"? There is not even such a term in this theory, and dependence is introduced in general by the definition of ARCH processes themselves, i.e. it is initially assumed that there is a non-trivial dependence and a point.
The fact that volatility and variance are not a constant, but change over time and depend on previous values is simple and obvious. But you claim that the variance is invariable. Although you can consider it that way if you can find something useful from it :)
I am not a psychic and say that such and such a variable of such and such a series is a constant. There are all sorts of methods for that. For a quotational walk the variance is non-stationary, I don't argue with that, for differences you can formally admit stationarity.
You'd be surprised, but this in no way contradicts the ARCH model
Don't like the word memory, let it be like Shiryaev's "consequence".
yes a good word, just clarify what you mean, you personally and not Shiryaev
so what? is it like "time series memory"? There is not even such a term in this theory, and dependence is introduced in general by the definition of ARCH processes themselves, i.e. it is initially assumed that there is a non-trivial dependence and full stop.
I am not a psychic and say that such and such a variable of such and such a series is a constant. There are all sorts of methods for that. For a quotational walk the variance is non-stationary, I don't argue with that, for differences you can formally admit stationarity.
You'd be surprised, but this doesn't contradict the ARCH model in any way
Well, if you're allowed to accept stationarity for differences, that's generally your business. Who forbids it? :)
yes a good word, just clarify what you mean, you personally, not Shiryaev
There's a problem with every point. As for point 3, I don't think it will work at all. Here's a very simple experiment:
1. Take a plot of what length from "now". And look for analogues by anything, for example - correlation. If the correlation is greater than some criterion, then this interval is used for calculations.
2. from the found "analogue now" we look what was at that moment "in the future" and construct a very simple "transfer function" (marked with inverted commas) symmetric with respect to "now":
We get such a matrix of "transfer functions" for some criterion and section (as an example):
3. Apply all our functions to the current situation and get a bunch of theoretical realizations:
We have the following picture as an example:
Only, it seems to me, "nearest neighbours" will not work in any way, on such rows.
ну если вам можно признать для разностей стационарность, то это в общем ваше дело. Кто же запретит? :)
Are you sure you're not confusing the process of changing the variance of a quote, like this (there's a lot you can do with it too):
with the returnees of the original series?
я уже пояснял и не раз. Это значит что волатильность зависит от значений в предыдущие моменты времени.
A-A-A-A!!! I think I've got it!
You think that if the variance is stationary, then the implementation of the process cannot depend on previous values and the process will only ever output type one constants???? :о)))))))
Look, but it's not like that at all, scientifically it's perfectly acceptable that they are stationary. Moreover, read the mathematical definition of these processes - three conditions :o)
stationarity - the preservation by sub-samples of the general population of distributions. For price series volatility this is not the case, there are periods when volatility has a different distribution over a sufficiently long period of time than at other times. For example, during the last crisis volatility was significantly higher, both its average values and extremes. If we construct the distribution of volatility for this period, will it coincide with the distributions constructed for other periods?
стационарность - сохранение подвыборками генеральной совокупности распределений. Для волатильности ценовых рядов это не так, бывают периоды когда волатильность достаточно продолжительное время имеет иное распределение чем в другие моменты. Например, в период последнего кризиса вола была значительно выше, как средние ее значения, так и экстремальные. Если построить распределение волы за этот период, то оно будет совпадать с распределениями, построенными за другие периоды?
I'm not arguing with that, it's all correctly written. But there is a difference between "price dispersion" and "price incremental dispersion". The latter can, with some reservations, be regarded as a stationary process (I mean increments). But it is useless to use models to predict price increments, because the shape of distributions is very different, and if distributions of the initial (predicted) series and the model series do not coincide, a stable forecast is impossible in principle. But for RMS prices it is a slightly different situation
In general, I suggest a consensus :o)
I'm not arguing with that, it's all correctly written. But there is a difference between "price dispersion" and "price incremental dispersion". The latter can, with some reservations, be regarded as a stationary process (I mean increments). But it is useless to use models to predict price increments, because the shape of distributions is very different, and if distributions of the initial (predicted) series and the model series do not coincide, a stable forecast is impossible in principle. But for RMS prices it is a slightly different situation
In general, I propose a consensus :o)
ok :)