From theory to practice - page 379
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Here I am going to paste this text from Shelepin's work until I've friggin' squeezed the Grail out of these equations. for that's what my TS is built on.
He can't hear. Gone to the future.
Sorry for the repetition.
He's like Dirac catching the grail at the tip of his pen).
As I indicated above, we consider a process satisfying equation (12) in a strictly defined sliding time window. And the characteristic magnitude of jumps (increments) lamda is calculated for this window and has the dimension pips (conditional).
Accordingly, the constant C has dimension pips/sec.
And the quotient C/lamda should tell me about the frequency of jumps (increments). Hm... However!
I.e., if I put (I repent, without even thinking about it) for EURUSD the constant C = 0.0001, and the average value of increments (jumps) in the time window conditionally lambda = 0.00002 (i.e. 2 pips), it turns out that the conventional jump frequency C/lambda = 0.0001/0.00002 = 5 times per second for EURUSD.
For EURJPY, I have the constant C = 0.01, and the average value of increments (jumps) in the time window conditionally lambda = 0.0025 (i.e. 2.5 pips), then the jump frequency C/lambda = 0.01/0.0025 = 4 times per second for EURJPY.
Is it so? But, this is certainly wrong. It completely contradicts my practical data, according to which the frequency of tick quotes for EURJPY is much higher than for EURUSD.
Silly old me, I'll tell you what.
Is it OK that the process is not a single process, for which the wavefunction is actually suitable?
But a superposition (and not necessarily linear) of several processes, for which the use of the wave function is not suitable.
The question is rhetorical.
Is it OK that the process is not a single process, for which the wavefunction is actually suitable?
But a superposition (and not necessarily linear) of several processes, for which the use of the wave function is not suitable.
The question is rhetorical.
Nobody cares :-) the nature of the process, its structure, periodicity, components, noises, nobody cares at all.
"pigs looking for truffles" ... pardon the crude comparison, but very similar.
Seeking distribution (or other properties) without considering/perceiving the nature of it and not even without an idea of how to apply it is a search for a precious truffle solely by smell and only for the sake of the search itself
Is it OK that the process is not a single process, for which the wavefunction is actually suitable?
It is a superposition (and not necessarily linear) of several processes for which the use of the wave function is not suitable.
The question is rhetorical.
We do not consider the wave function (equation (13)) since we have, on the contrary, the price is a nonrelativistic particle described by equation (12).
In this case, we have C - not speed of light, as for free relativistic particle, but stupidly average speed of the particle itself!!!
But here's the question - is the average velocity in a sliding time window or over a long time t --> to infinity?
I'll take the liberty to argue that in our case C is precisely the average velocity over a long time window (at t --> to infinity).
Hence, the standard deviation of the price from the mean in the sliding window = 4 hours takes the form:
sigma = Root((SUM(ABS(return))/T)*(SUM(ABS(return))/N)*14400)
where T is the running time of the system(--> to infinity).
Now we have to deal with the multiplier of this sigma, to determine the confidence interval.
Remembering Asaulenko's rampant monologues, something like: "what difference does it make - what distribution is there? I don't care at all and I help myself with my own hands, since I am a drowning man..." (well, something like that, very close in meaning), we can say that - yes, there is no normal distribution, so we should use Chebyshev or Petunin-Vysokovsky inequalities.
That, uncles, is how such problems are solved!
Yes, but theory without practice is dead, isn't it?
So, in view of the fact that we have just obtained a refined formula for calculating the standard deviation of the process, I am immediately putting the updated TS to work.
And Erlang's flows will have to wait.
I will let you know the results.
Regards,
A_K2