Market phenomena - page 44
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It is only unclear why there is more normality as the timeframe increases. Smoothing? It seems like abnormal ticks should produce abnormal minutes, which in turn produce an abnormal day, etc.
There is a Central Limit Theorem and the Law of Large Numbers or the former or the latter leads to a set of large numbers of random variables (even those without a normal distribution) tending towards a normal distribution. The details of the formulation need to be looked at.
Here we see this effect of aggregation of ticks in bars and their normalisation as the number of ticks in a bar increases (TF increases).
The difference is huge. For open - open catches all the gaps and misses. Well yes, the minutes would be abnormal with those tolerances.
But gaps happen between Close and Open. Don't they?
Distribution of EURCHF series ticks is shown for Open[i]-Open[i+1] - red and Open[i]-Close[i] - blue:
As you see, there is no significant difference.
There is a Central Limit Theorem and the Law of Large Numbers either the former or the latter leads to a set of large numbers of random variables (even those without a normal distribution) tending towards a normal distribution. The details of the formulation need to be looked at.
Here we see this effect of aggregation of ticks in bars and their normalisation as the number of ticks in a bar increases (TF increases).
there is only one main condition in DTT - independence of SV. The fact that there is a stable difference between the distribution and the NR suggests that there are dependencies in the price increments. But not necessarily in direction, maybe in magnitude (memory in volatility).
there is only one main condition in DTT - independence of NE. The fact that there is a persistent difference between the distribution and the NR suggests that there are dependencies in the price increments. But not necessarily in direction, maybe in magnitude (memory in volatility).
It does.
I just want to stress that this only applies to ticks (my opinion), which is the reason why their distribution is not normal. Minutes and above the TF, it is all a consequence of ticks abnormality and has nothing to do (weak dependence) with the connections between bars. In other words, the whole kitchen is in the ticks, the rest is just a consequence.
It is true.
I just want to emphasise that this only applies to ticks (my opinion), which is the reason why their distribution is not normal. Minutes and above the TF, it is all a consequence of ticks abnormality and has nothing to do (weak dependence) with the connections between bars. In other words, the whole kitchen is buried in ticks, the rest is just a consequence.
And this consequence applies up to hourly bars? Did I understand you correctly?
I am building on what you said earlier:
"At ticks we can already speak about normal distribution of increments. Further this condition is fulfilled more precisely".
As you can see, there is no meaningful difference.
there is only one main condition in the DTT - independence of the NE. The fact that there is a stable difference between the distribution and the NR suggests that there are dependencies in the price increments. But not necessarily in direction, maybe in magnitude (memory in volatility).
The fact that there is a persistent difference between the distribution and the HP indicates that there are dependencies in the price increments. But not necessarily in direction, maybe in magnitude (memory in volatility).
And this corollary applies to hourly bars? Do I understand you correctly?
I am building on what you said earlier:
Here is the distribution for the sentinels. The blue one shows the normal distribution. A good convergence with the Gaussian distribution can be ascertained.
Here is the distribution for the sentinels. The blue one shows the normal distribution. A good convergence with the Gaussian distribution can be ascertained.