Market phenomena - page 40
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(3) I sorted the increments into two streams, I didn't fill the holes in each stream with anything. Considered that the stream is interrupted
Give the condition.
What is the condition for separating? Maybe positive/negative increments?
Give the condition.
What should we separate them by? Maybe positive/negative increments?
(1)
Having obtained a series of increments over the whole history, we estimate the RMS, this is the criterion to start with.
(2)
Stream A: no tail
Stream B: only tail
(3) So far a very simple condition, i.e. a primitive one:
If the increment modulus is less than RMS, into stream A
If the increment modulus is greater than RMS, stream B
PS: I think the cleanest series would be between RMS 2 and 3
I see.
Just a minute...
I see.
Just a minute...
This is what you get when you divide by the amplitude of the increments equal to 0.2 standard deviation:
Here we show in red the sum by increments not exceeding 0.2 standard deviation, and in blue the sum by increments not less than 0.2
For sigma=0.5 we have:
Next:
And finally for sigma=2:
Actually, it's interesting.
Are you, Sergei, saying that Alpha is almost always increasing and Omega is decreasing?
Yes, here is the original EURUSD 1m price series:
(1)
missed my message:
(2)
No, alpha predominantly grows if you pick up the criterion and scale. By the way, try more than 3, somewhere between 3.14 and 3.5
(3)
betta does what it wants, but there is a similarity in its form to the final quote. I.e. what I claim to actually do:
The betta process, i.e. thick tails, pretty much determines the shape. structure, appearance, spreads, evasions etc. (however you want to classify it) of the quotation process.
Mind you, this is a primitive condition. You have to look for a more powerful classification.
And note that betta occurs "little" but, as I wrote above, practically completely determines the shape of the quote.
That's the kind of FAT tails :o) And that's just the beginning, if you poke around further.
Conclusions:
1. The cumulative sum of small increments is roughly equal to the sum of large increments. In other words, no matter where the market drifts slowly in small steps, it will always return to the initial position by several large and sharp movements.
There is random wandering set up by small investors and strong corrective moves organised by large investors?
2. ?
I need to think about what I've seen. Interesting in general.