Building a trading system using digital low-pass filters - page 22
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I can't figure it out, but somehow managed to read his *.ppt file, his report. How did that happen? There's nothing so detailed there, but it's still a very interesting mystery...
Download it again. There's a doc file for 2003. For 2005 it's really a ppt, but it's not about this. :)
Somewhere on the net I saw a more detailed description of his approaches. It's not exactly thorough, but still. But I am not interested in details, but I am interested in, shall we say, general methodological approaches. And what they are based on, and whether it is the average or something else, is not that important. Besides, the value of knowing the intricacies of building LRMAs out of averages is very tentative, in terms of understanding processes.
And this, in fact, explain to the dim-witted what Gorchakov is talking about. I've read something, read something, but I haven't deduced the idea or its depth :)
It's all interesting if you read it carefully. Of course, the indicators are very brief, but it is an opinion of a practicing trader about price series and models, once a professional in the field of applied statistics (I think that is what he said about himself). For me it is one of the most interesting works after Shiryaev's report. Much of what is there can be confirmed. Including the short-term differences between market and martingale (this is to the question of stationarity mentioned here). The material is not new enough, so I don't know if there has been any further development of ideas. I do not know, for each sentence there can be a page of abbreviated text.
It's all interesting if you read it carefully. Of course, the indicators are very brief, but it is an opinion of a practicing trader about price series and models, once a professional in the field of applied statistics (I think that is what he said about himself). For me it is one of the most interesting works after Shiryaev's report. Much of what is there can be confirmed. Including the short-term differences between market and martingale (this is to the question of stationarity mentioned here). The material is not new enough, so I don't know if there has been any further development of ideas. I don't know, you could write a page of abbreviated text for each sentence.
And here is "our answer to Chamberlain": http://monetarism.ru/articles/06/05/02/0644217.shtml
It appears that Gorchakov found asymmetry where it does not exist. We can conclude that if he had positive results in applying his idea to real trading, they were largely accidental, because the underlying premise was fundamentally wrong.
It's all interesting if you read it carefully. Of course, the indicators are very brief, but it is an opinion of a practicing trader about price series and models, once a professional in the field of applied statistics (I think that is what he said about himself). For me it is one of the most interesting works after Shiryaev's report. Much of what is there can be confirmed. Including the short-term differences between market and martingale (this is to the question of stationarity mentioned here). The material is not new enough, so I don't know if there has been any further development of ideas. I don't know, you could write a page of expletive text for every sentence in there.
And here is "our answer to Chamberlain": http://monetarism.ru/articles/06/05/02/0644217.shtml
It appears that Gorchakov found asymmetry where it does not exist. We can conclude that if he had positive results in applying his idea to real trading, they were largely accidental, because the underlying premise was fundamentally wrong.
:) the author is a famous clown who has the most general ideas about the subject of discussion. i'm too lazy to check who is right, it is enough for me that apart from the discussed statistics other methods show the same results.
[No, sorry, I dug in the old notes, I checked the criteria some time ago, I've forgotten already.
Well here is a little more reading http://www.howtotrade2007.narod.ru/articles/stan.zip I wonder if the author Stanislav Bulashev is the same?
Using black noise in market modelling
ps. haven't tested it myself
Using black noise in market modelling
ps. did not check it myself
I've published a very good book: "Signal Processing with Fractals", but in English. It's better than the presentation :o)
One possible hypothesis is that the logarithms of price changes follow a normal distribution, but this distribution is non-stationary. That is, both the expectation and the standard deviation of the distribution can vary over time. As a consequence, when processing an empirical sample using standard statistical methods that assume the entire sample is drawn from a single general population, we obtain a non-Gaussian sample. This can be expressed in the form of heavy tails of an empirical distribution (the kurtosis calculated from a sample exceeds number 3, i.e. the kurtosis of a normal distribution).
Another hypothesis is that logarithms of price changes initially follow a distribution with kurtosis greater than 3. In this situation, even if the distribution itself is stationary, the empirical sample drawn from this distribution can be regarded as non-stationary in time. The point is that the estimate of the mathematical expectation of a random variable x is the arithmetic mean of the sample:
<X>= 1/N * sum(x(i), i =1...N )
The arithmetic mean of random variables is itself a random variable. The standard deviation of the arithmetic mean depends on the standard deviation of the random variable and the sample size:sigma(<X>) = sigma(X) / sqrt(N)
Thus the standard deviation of the mean is less than the standard deviation of the random variable itself by a factor of sqrt(N), i.e. the accuracy of the mathematical expectation estimation can be increased by increasing the sample size. But this is only true for a random variable with finite mathematical expectation and finite variance. The point is that finite mathematical expectation only exists for those distributions whose probability density in infinity falls as 1 / |x|^(2+delta) or lower, and finite variance only for those distributions whose probability density in infinity falls as 1 / |x|^(3+delta) or higher ( delta - any small positive number). If we model a price chart using as logarithms of the price change a random sample taken from a stationary distribution with infinite variance and/or infinite mathematical expectation, and offer this sample for analysis to an independent observer, he may get an illusion that he deals with a non-stationary process in time.
Finally, we cannot exclude the case when not only the distribution parameters but also the law of distribution of price logarithms itself is non-stationary in time, and the time series of prices may contain the sections described by the distribution with infinite variance and/or infinite mathematical expectation.
This does not mean that nothing can be done in the sense of reversible transformation of price series into something stationary: it is possible to use not only returns. It's a bit early to draw the line.
There seems to be some workaround to the problem of synthetic generation which is not related to the stationarity of the process. But this is still only a genetic one. We should think it over.