Machine learning in trading: theory, models, practice and algo-trading - page 3640

 
It's funny how the 2 llm's keep giving almost mutually exclusive answers. Apparently sometimes you need to flip like trades in plivator TCs :)
 
Maxim Dmitrievsky #:

Well there's kind of a difference of opinion here :)

Mistral:

Dipsic:


Dipsic has confused himself. If the period changes with time, of course this process cannot be called stationary, logically. But if the characteristics of a periodic process do not change, then it is stationary.


Mistral is a weirdo, "If a process is periodic, then its statistical characteristics change with each period." This is a masterpiece ).

 
Evgeniy Chernish #:

Dipsic has confused himself. If the period changes with time, of course this process cannot be called stationary, logically. But if the characteristics of the periodic process do not change, then it is stationary.


Mistral is a weirdo, "If a process is periodic, then its statistical characteristics change with each period." This is a masterpiece ).

Maybe there is a confusion between stationarity for time series and some other?

 
Evgeniy Chernish #:

The answer from Deep Seek is correct (the analytical solution is easily verified by numerical calculations, construct mo and disp as a sampling function for example) but it is not complete, because he only mentioned the definition of stationarity in a broad sense. The same function is stationary in the narrow sense, i.e. the distribution does not depend on time.

Here is a histogram of the first 5000 data and the next 5000 data. As we can see the distribution is independent of time.

Not true, of course. At each point in time, the distribution is degenerate, centred at different time-dependent points. Therefore, the expectation depends on time (obviously, it is equal to this function)

If we construct a numerical series on this function and study it without paying attention to its source, then for stationarity in the broad sense we need a) constancy of expectation, b) constancy of dispersion, c) independence of the autocorrelation function from time. Obviously, there will be problems with this if we take it on a time slice containing zero. If we take a time slice far from zero, we will get a series with a cyclic trend and noise component, which will become stationary after the trend is removed.

That is, if we take different time sections and different sampling frequency, the result of checking the obtained series for stationarity will be different.

 
Radio amateurs have coined the term "quasi-stationary" for non-stationary but periodic processes, because they have such processes all over the place. The point is that their favourite spectral theory is well transferred to such processes.
 

Yeah, the amateur radio optimisers have made a mess of things.

Rows with periodic components are not stationary.

It has been discussed 100 times but forgotten for uselessness.

https://education.yandex.ru/handbook/ml/article/analitika-vremennyh-ryadov

Аналитика временных рядов
  • education.yandex.ru
Временной ряд – зависимые между собой наблюдения. Например, температура воздуха сегодня достаточно сильно зависит от вчерашнего показателя температуры. Эту зависимость хотелось бы описать численно. Для этого часто используют разные виды коэффициентов корреляции, например, корреляции Пирсона, Спирмена и Кендалла. Каждый из этих коэффициентов...
 
Aleksey Nikolayev #:

Of course not. At each point in time, the distribution is degenerate, centred at different time-dependent points. Therefore, the expectation depends on time (obviously, it is equal to this function)

If we construct a numerical series on this function and study it without paying attention to its source, then for stationarity in the broad sense we need a) constancy of expectation, b) constancy of dispersion, c) independence of the autocorrelation function from time. Obviously, there will be problems with this if we take it on a time slice containing zero. If we take a time slice far from zero, we will get a series with a cyclic trend and noise component, which will become stationary after the trend is removed.

That is, if we take different time sections and different sampling frequency, the result of checking the obtained series for stationarity will be different.

And variance and expectation and acf do not change with time (check on different time segments), there is no trend in this function (where did you see it ?) and noise (the function is deterministic)?

I took different time sections and I see that the distribution has not changed.

We are talking about this function - SIN(t)/4 + COS(t^2)/4 + 0,5 I understand correctly ?

 
Evgeniy Chernish the autocorrelation function is not defined, so we will assume that we are talking about the autocovariance function, which will be zero everywhere. The variance is also zero everywhere.

The points about variance and acf have been fulfilled, the expectation remains. Obviously, the expectation value at each moment of time is equal to the value of the function at that moment - it follows from the fact that the expectation of a constant random variable is equal to this constant. Therefore, the expectation will be equal to the function itself and therefore time dependent.

I don't see how one can get so confused about the very basis of theorver.

 
Evgeniy Chernish #:

And variance and expectation and acf do not change with time (check on different time steps), there is no trend in this function (where did you see it ?) and noise (the function is deterministic)?

I have taken different time steps and I see that the distribution has not changed.

We are talking about this function - SIN(t)/4 + COS(t^2)/4 + 0,5 I understand correctly ?

It should be like this for a stationary series.

And it turns out to be like this


 
Maxim Dmitrievsky #:

Yeah, the amateur radio optimisers have made a mess of things.

Rows with periodic components are not stationary.

It has been discussed 100 times but forgotten for uselessness.

https://education.yandex.ru/handbook/ml/article/analitika-vremennyh-ryadov

at first glance: series (i) should be viewed in log scale. Then it is linear and const deviations. To look in detail - it is about summer+winter electricity, i.e. strict alternation. And separately they are two even lines