Discussion of article "Exploring Seasonal Patterns of Financial Time Series with Boxplot" - page 29

 
Maxim Dmitrievsky:

there are pairs of clocks for which the correlation is 0

what does that mean? I can't speak for maths and great scientists now, I'm just saying what I see

For example, I don't understand at all what Saber is looking for on non-intersecting intervals, because there will always be 0 there and only on occasion not 0

So he's looking for correlation in the mean/median increment bias, in my opinion, which is already there in that boxplots article

In any case, when calculating the correlation between two combinations of random variables, you should avoid the situation where some values fall into both combinations. In the variant with deviations from the mean, this error can also occur. The simplest and most obvious example is the correlation of subsequent SB values, since x[n+1] = x[n] + e[n].

You can try to divide the sample of increments into non-overlapping subsamples and see their correlation. For example, one subsample is the price increments for the first hour of the day, and the other is the price increments for the tenth hour of the same day. I'm not sure about the usefulness of this, but it's better than self-deception.

 
Aleksey Nikolayev:

In any case, when calculating the correlation between two combinations of random variables, one should avoid the situation when some values fall into both combinations. In the variant with deviations from the mean, such an error may also occur. The simplest and most obvious example is the correlation of the subsequent SB values, since x[n+1] = x[n] + e[n].

You can try splitting the sample of increments into non-overlapping subsamples. For example, one subsample is the price increments for the first hour of the day, and the other is the price increments for the tenth hour of the same day. I am not sure about the usefulness of this, but it is better than self-deception.

There will be a benefit, but it is already described in this article in other words

I am not satisfied with another situation, that if you substitute e[n] to the right of the last SB value as a distribution and make it tick, you can make money on SB. I'll offer the rest of the exploration later in the article (if it ever comes out). The main problem is to distinguish where this e will be from N or from some other distribution. In this context I am doing everything right now (presumably).

 
Maxim Dmitrievsky:

The other thing that keeps me going is that if you substitute e[n] to the right of the last SB value as a distribution and make it tick, you can make money on SB. I'll offer the rest of the exploration later in the paper (if it ever comes out). The main problem is to distinguish where this e will be from N or from some other distribution. In this context I am doing everything right now (presumably).

The problem is not that you can't make money on the SB, but that you can win and lose with the same probability (without taking into account the spread). And it doesn't matter what TS is used in this case.

 
Aleksey Nikolayev:

The problem is not that you can't make money on SB, but that you can win and lose with the same probability (without taking into account the spread). And it doesn't matter what TS is used in this case.

If there is a spread between SB points of another SB, is it impossible to make money? It depends on the number of ticks. All of Saber's TSs work on this, but I don't want bruteforce, I like analysis. Igor's brain is about to completely break down.
 
Maxim Dmitrievsky:

There will be benefits, but they have already been described in this article in other words

You investigated the dependence on one moment of time (the moment of increment itself), and here - on two (plus the moment of increment with which the correlation is considered). It is not sure that this complication of the model will be useful.

 
Aleksey Nikolayev:

You investigated the dependence on one moment of time (the moment of increment itself), while here you investigate the dependence on two (plus the moment of increment with which the correlation is considered). It is not certain that this complication of the model will be useful.

So if you calculate the correlation between the two sets of these points, it will show the displacement of the mean/median of the second set of points relative to the median of the first. That's what I've done. The higher the correlation the higher the second median is above the first and vice versa. It's like just comparing the medians of the distributions. It won't show anything else because the samples are independent.
 
Maxim Dmitrievsky:
If there is a distribution of another SB between the SB points of the distribution of another SB, can't you make money? Depends on the number of ticks. All Saber TSs work on this, only I don't want bruteforce, I like analysis. Igor's brain is about to completely break down.

If this matryoshka rises to infinity, you will get a continuous-time SB (Donsker's theorem).

However, at the level of ticks the price already looks more like the realisation of a Poisson process (if we neglect the discreteness of real trading time).

 
Aleksey Nikolayev:

If this matryoshka rises to infinity, we get a continuous-time SB (Donsker's theorem).

However, at the level of ticks the price already looks more like the realisation of a Poisson process (if we neglect the discreteness of real trading time).

Well, yes, in the sense of not SB inside, but Gaussian noise, for example. Don't kill the last hope :)
 
Maxim Dmitrievsky:
So if you calculate the correlation between the two sets of these points, it will show the offset of the mean/median of the second set of points relative to the median of the first. That's what I've done. The higher the correlation, the higher the second median is above the first and vice versa. It's like just comparing the medians of the distributions. It won't show anything else because the samples are independent.

Not so. If you add any numbers to the samples (or multiply), the medians change accordingly, but the correlation coefficient doesn't change.

 
Maxim Dmitrievsky:
Well yeah, I mean not SB inside, but Gaussian noise, for example. Don't kill the last hope :)

Obviously the price is not really SB. Just need to realise in what sense it will be non-SB in the near future)))