That in the "black box"?


But the central limit theorem shows the distribution of the sum of a large number of identically distributed and independent random variables. Why the action can be considered additive noise - is unclear. For example, if the interference effect on the price of an additive, their impact on the return will not be so. And what there is reason to assume independent interference in the economy, where everything is interconnected? And it does not understand how we can talk about the distribution of the same, if we do not even know what the noise effect.

Thus, none of the assumptions of the central limit theorem is not valid, and the conclusion of the theorem is presented as an immutable law of probability. For those of you not familiar with the central limit theorem - come. Let's see how the same author offers to check the independence of random variables. <In simple cases where it is necessary to establish the degree of correlation between the two series is calculated bivariate correlation coefficient, which can vary from -1 to 1. The closer the relationship, the closer the ratio to one, and, conversely, the absence of communication factor tends to 0>.

Indeed, the correlation coefficient of independent random variables is equal to zero. The converse is not true. Random variables with zero correlation coefficient may be dependent not only statistically, but also functional (for example, one of them may be another square). This is explained in any good faith (not short) course of mathematics (see, eg, [3]). But why should they be read when there is <Short Course ...> 2.

All this is not to speak of, whether such a phenomenon isolated. Unfortunately, the situation is just the opposite. In modeling the stock market probabilistic methods are used more often than all other methods combined. And the times when it is done correctly, are a rare exception.

Findings

The foregoing does not mean that I am fundamentally against the use of probability theory, neural networks, etc. Nothing good that the old woman money-lender hacked to death. But it does not follow that the ax - a bad tool. Just use it need to destination.

Statistical methods are essential for the identification phase models, that is, when the view of all the dependencies are already known, and it remains to determine the numerical values of some coefficients. Apply the same in other cases they simply because nothing else comes to mind, not worth it. And one should be recalled. Development of software packages aimed at the study of financial markets - is biznes3. Just like any other business, but not better. In particular, it can not exist without advertising. The difference between what is truly ready to make a package, and how it is described in the advertisement, may be significant, and therefore do not need to buy quality goods in a bright package. The product itself, it is sometimes quite complex, and to understand it as a real, significant efforts. But these efforts are justified. If you can not, for whatever reason, to assess the quality of the program, it is best not to use it at all, even if its authors are highly praised.

Footnotes:
1 encodes, for example, falling and rising prices.
2 Compared with <History of the CPSU (B)> suggests itself: <Short Course market Mathematics> about the same applies to mathematics as <History of the CPSU (B)> refers to the story.
3 Newspaper <Kommersant-Daily> on October 15, 1997 assessed the Nobel Prize awarded to Robert Merton and M. Scholes as clever publicity stunt winners. Some truth in this.