Discussing the article: "Two-sample Kolmogorov-Smirnov test as an indicator of time series non-stationarity" - page 3

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Aleksey Vyazmikin #:

How is this possible? Did I understand correctly that the previous day and the one 100 days ago will have similar evaluation metrics, as if the previous day and the day before were not similar? I.e. the difference varies within a narrow range?

Well, it's just as interesting to look at a histogram of the frequency of distribution change.

The Smirnov distances themselves will certainly be different when calculated in pairs sequentially and in the way you suggest, but the distribution of these distances should not change.
It seems to me to compare a thousand parrots by height in pairs or one last parrot with all previous ones we will come to the same results =)
 
Aleksey Nikolayev #:
It must be N/2.

How do you come to this conclusion?

I may have misunderstood something in the method....

 
Aleksey Vyazmikin #:

How do you come to that conclusion?

It is a very shallow intuition based on theorver/matstat. It is common on this forum to study these sciences for money from your deposits, but there are free ways - you can try the method on SB and compare with real prices.

Matstat and practice says you shouldn't try to pull too much information out of a sample. Therefore, I am just horrified by much of how MO is used for prices.
 
Aleksey Nikolayev #:

I usually use its implementation from the trend package in R. There are references to sources in the description.

I wonder what kind of test can be applied to realise that the profit from the TS is not accidental

 
mytarmailS #:

I wonder what test can be applied to realise that the profit from TC is not made by chance

You can take some trend test and check equity. For example, in the same package there is sens.slope() to calculate the slope of the trend and the confidence interval for it. This test is also widely known in narrow circles.
 
Евгений Черныш #:
Smirnov's criterion (and similar ones) is an indicator, if I may say so, of the zero, basic level. It does not tell you whether you should buy or sell, it tells you how much data to take to analyse the first level indicators such as FDI, which already give signals for trading. At least that is how I see it.

No, fractal dimension is another indicator of market "certainty" and does not give buy or sell signals. That's why I suggested that it should be similar to Smirnov (adjusted for parameters).

 
Stanislav Korotky #:

No, fractal dimension is another indicator of market "certainty" and does not give buy or sell signals. That's why I suggested that it should be similar to Smirnov (with correction for parameters).

You were correctly told by the author that Smirnov is simpler because it is defined by a one-dimensional distribution of increments. Fractality is defined, at a minimum, by the two-dimensional joint distribution of two successive increments.

 
Stanislav Korotky #:

No, fractal dimension is another indicator of market "certainty" and does not give buy or sell signals. That's why I suggested that it should be similar with Smirnov (with correction on parameters).

I wasn't paying attention, sorry. I took a quick look from my phone and thought it was one of the variations of a standard technical indicator.

The FDI indicator tries to answer the same question as the Hirst indicator: "Is the given time series a random walk or not?".

Smirnov indicator answers the question: "Is this time series homogeneous (stationary) or not ?"

The Smirnov indicator can distinguish two random walks from each other if they have different statistical properties, but it does not determine whether real prices are random walks. To be more precise, the Smirnov indicator reacts to the presence of dependencies in the data, as can be seen from the Smirnov distance distribution for autoregression and logistic mapping, but it primarily (and this is its main task) captures heterogeneity in the data. I wrote about it in the paper and I will repeat, I don't know how to separate purely non-stationary influence from the presence of dependencies in the series. Therefore, the Smirnov indicator with the SB question can help only indirectly.

On the other hand, the FDI needs the definition of the sampling window. If we take a fixed sliding window (let it be 30) and plot the distribution of values of this indicator, this is what we get:

PDF FDI(30) EURUSD Daily


As you can see the distribution of the indicator is white Gaussian noise with a mean of approximately 1.5.
And what does it mean for this indicator? That calculated in a fixed moving window it accepts the efficient market hypothesis. Another question is how it calculates this fractal dimension, how correct this algorithm is. I can't say anything here, as I don't know how it is calculated correctly.
 
Aleksey Nikolayev #:

The author correctly wrote to you that Smirnov is a simpler thing, since it is defined by a one-dimensional distribution of increments. Fractality is defined, as a minimum, by a two-dimensional joint distribution of two successive increments.

In this FDI indicator there is no empirical distribution function used there at all. Neither univariate nor multivariate, it takes price increments in a sliding window, each increment is normalised by the sample size, then the sum of such absolute normalised values (length) is actually found, after which the formula for finding FDI is applied.

val[i]=1+(MathLog(length)+MathLog(2))/MathLog(2*inpFdiPeriod);
 
Евгений Черныш #:

This FDI indicator does not use empirical distribution function at all. Neither univariate nor multivariate, it takes price increments in a sliding window, each increment is normalised by the sample size, then the sum of such absolute normalised values (length) is actually found, and then the formula for finding FDI is applied.

I meant fractality as such, not a specific indicator of it. It is usually associated with persistence/antipersistence of a series, which are related to the dependence of neighbouring increments, which in turn is determined by their joint distribution.

If we talk about specific indicators of fractality, FDI is not very good, because it requires a lot of data for calculation and does not give values for the confidence interval of dimensionality.

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