Discussing the article: "Two-sample Kolmogorov-Smirnov test as an indicator of time series non-stationarity" - page 2
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It is interesting to compare iSmirnovDistance with fractal dimension (like this https://www.mql5.com/en/code/20586).
In general, the article is good.
For me, the window for observations is too small.
However, even if we take this small window, maybe it makes sense to compare it not with a neighbouring window, but with windows for the last year or five years? It will be such a chessboard from which we can see how many windows were similar, group them and perhaps classify them. And then evaluate for patterns and their probabilistic outcomes.
Eugene Chernysh, have you done something like this?
Евгений Черныш #:
I understand that pettit is based on ranks, I have found almost no information about it.
I usually use its implementation from the trend package in R. There are references to sources in the description.
To me, the window for observation is too small.
However, even if we take this small window, maybe it makes sense to compare it not with a neighbouring window, but with windows for the last year or five years? It will be such a chessboard from which we can see how many windows were similar, group them and perhaps classify them. And then evaluate for patterns and their probabilistic outcomes.
Imho, this would be typical p-hacking.
To me, the window for observation is too small.
However, even if we take this small window, maybe it makes sense to compare it not with a neighbouring window, but with windows for the last year or five years? It will be such a chessboard from which we can see how many windows were similar, group them and perhaps classify them. And then evaluate for patterns and their probabilistic outcomes.
Eugene Chernysh, have you done something like this?
Imho, it would turn out to be typical p-hacking.
How do you see it? I'm talking about a study on the similarity of days, and the similarity of predictor behaviour on those days.
I don't know the outcome so there is no purpose in fitting the study to the desired outcome.
If we can classify such groups, even within a day, we can use separate models for them on predictors with higher probability.
distribution of Smirnov distances will be the same as in the calculation of consecutive two days.
How is this possible? Do I understand correctly that the last day and the one 100 days ago will have similar estimated metrics, as if the last day and the day before last were not similar? I.e. the difference varies within a narrow range?
But to collect statistics of the average number of days between two rejections of the null hypothesis of homogeneity is something you can do. Get an idea of how much time on average we have until a new distribution is established in the market.
Well, it is also interesting to look at the histogram of frequencies of distribution change.
How do you see it?
As usual, multiple repetitions of the same test on the same data. If there are N days, then the number of repetitions of the test is N*(N-1)/2 (the number of pairs of days). It has to be N/2.
Not that I'm trying to forbid anyone to do this) Just, imho, this is the first step to self-deception.