Machine learning in trading: theory, models, practice and algo-trading - page 2535
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https://www.mql5.com/ru/articles/222
Returns (returns) are for theorists. The practitioners have their own methods.
sampling of price logarithm increments
Still try sampling d[i]=log(bid[i]/bid[i-1])=log(bid[i])-log(bid[i-1]).
You can also try approximation without logarithms d[i]=bid[i]/bid[i-1]-1
Surprisingly, these formulas do not work
bid[i]/bid[i-1]-1 log(bid[i]/bid[i-1])
And the result is very close, even if you squint your eyes you can't see the difference. The axes are offset by a few pixels. I checked it several times.
Returns (returns) are for theorists. The practitioners have their own methods.
Then I do not understand what we are talking about
As a theorist, I don't really understand either.
And the result is very close, even if you squint your eyes do not see the difference. The axes are offset by a few pixels. I checked it several times.
It should be so, because with small x approximately log(1+x)~x. In this case x=bid[i]/bid[i-1]-1
Surprisingly, these formulas do not work.
Perhaps the well-known thick-tailed effect of the returnee distribution is manifesting itself. Larger returnee values appear more often than they should in the case of a normal distribution.
The price of currencies does not change by times, why does it need a logarithm? But the increments do.
One reputable scientist wrote that the price must be logarithmic, and all theorists blindly continue to do so.
One reputable scientist wrote that the price must be logarithmic, and all theorists blindly continue to do so.
So he must have written about stocks.
I haven't read it, but the Bleck-Scholes formula is derived from it and it doesn't say it's only about stock options. Although of course it is not exactly true for anything, it is used as a starting point for all option theories.