Machine learning in trading: theory, models, practice and algo-trading - page 3641

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Maxim Kuznetsov #:

at first glance: the 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

It is necessary to build Akf, often even specialists can't determine it by eye ).

We are already the second day doing some c..., it's time to stop.
 
Maxim Dmitrievsky #:

It should be like this for a stationary row

And it turns out like this


It is correct, the acf of a stationary process does not have to be zero. For example, autoregression or moving average model are stationary processes, but the acf there is non-zero.
Our test function has an acf, the periodic component of the series can be clearly seen.
 
Evgeniy Chernish #:
That's right, the acf of a stationary process does not have to be zero. For example, autoregression or moving average model are stationary processes, but the acf is non-zero there.
Our test function has acf, the periodic component of the series can be clearly seen.
We were taught that it must :) for example, the acf of stationary residuals of a trained model must be zero.
 
Aleksey Nikolayev 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, accordingly, depends on time.

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

You can get confused about anything. I'm not a DSP expert, but why can't I formally calculate the acf of some process? Maxim has just given a graph of acf, as you can see, everything counts. And if we take a shift in time, the acf will not change as it should be for stationary processes.
Just calculate the sample mean and acf at different periods and it will be the same and it will converge with increasing number of samples equally.


 
Maxim Dmitrievsky #:
We were taught that it is required :) for example, the acf of stationary residuals of a trained model must be zero.
But this requirement is stronger than just stationarity - it is a requirement that the residuals be white noise.
 
Maxim Dmitrievsky #:
We were taught that it must :) for example, the acf of stationary residuals of a trained model must be zero.
Do not confuse the residuals of a trained model, which may not be stationary, and the acf of stationary processes in general.

It is clear that a good model will catch all dependencies and there will be only white noise in the residuals, the acf of which is zero. But the acf of the sp in general, and not the sp of white noise, does not have to be zero.
 
Can it be cyclical? It's seasonal or cycles. The book says that a series with seasonality is not stationary.
 
Evgeniy Chernish #:
You can get confused about anything. I am not a DSP specialist, but why can't I formally calculate the acf of some process? Maxim has just given a graph of acf, as you can see, everything counts. And if we take a shift in time, the acf will not change as it should be for stationary processes.
Just calculate the sample mean and acf at different periods and it will be the same and it will converge with increasing number of samples equally.


To begin with, it is worth to define what we are talking about - a specific analytically defined deterministic function, which we start to consider as a random process, or a time series, which we obtain from this function by taking its values at discrete moments of time and studying it by means of matstat.

In the first case there is no stationarity unambiguously because of the time dependence.

In the second case, the answer about stationarity will depend on a) the time segment where discretisation is done, b) the frequency of discretisation.

Here I will conclude my participation in the discussion of such a fascinating and full of sense topic).

 
Maxim Dmitrievsky #:
Can it be cyclical? It's seasonal or cycles. The book says that a series with seasonality is non-stationary.
How can seasonality be non-stationary? Seasonality implies some constant period. We have summer summer and winter winter every year, we don't have some random change of period.

Seasonality and cyclicity are stationary processes. If the period changes randomly, then these are already non-periodic cycles and of course they are already non-stationary.
Imho.


 
Evgeniy Chernish #:
How can seasonality be non-stationary ? Seasonality implies that there is some constant period. Every year we have summer in summer, winter in winter, we do not have some random change of period.

Seasonality and cyclicity are stationary processes. If the period changes randomly, then these are non-periodic cycles and of course they are non-stationary.
Imho.

Yes, but it is considered as a non-linear trend :) and series with a trend are non-stationary.

Linear trend is also constant and there is no random change.
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