Volumes, volatility and Hearst index - page 12
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In your original reasoning, you introduce a variable h and call it the Hearst exponent. This is incorrect, it is not a Hearst exponent.
Point out where I am doing this? Here is my original post:
In a random walk, the average run is proportional to the square root of the number of steps. So the result of the calculation a la Hurst, reduced to h = Log(High-Low)/Log(N) or similar, after applying simple arithmetic, reveals the following:
1) High - Low = k * sqrt(N);
2) h = log (k * sqrt(N)) / log (N);
3) h = 1/2 + log(k) / log (N);
4) h -> 1/2 when k << N, which the table proves perfectly.
The Hurst coefficient for SB in the formula High - Low = k * sqrt(N) lies in sqrt. You do think that Hurst for a price series or its derivatives is reduced to the addition of Hurst for SB and some variable that depends only on the number of measurements?
h = Log(High-Low)/Log(N) - This is Jurix's formula, he is the one passing it off as Hurst in his original post. Don't confuse me with him. I just called it a la Hurst, reduced to a primitive from Jurix.
The answer will be 1/2, but it won't be the Hearst figure, the Hearst figure is calculated through the spread.I love this kind of thing. As soon as you ask me to calculate a test case, it's like it's no longer Hurst.
to Candid
показатель Хёрста рассчитывается через размах
No, there are many ways of calculating the index. Using the spread is the most crude of them
to Candid
No, there are many ways of calculating the index. Using the spread is the most crude of them
to Candid
No, there are many ways of calculating the index. Using the spread is the roughest.
It's also simple enough, though not enough to reduce it to h = Log(High-Low)/Log(N).
Or it is complicated enough to understand that any h = Log(High-Low)/Log(N) is declared as Hurst.
It's up to anyone. :)
Point out where I am doing this? Here's my original post:
h = Log(High-Low)/Log(N) - This is Jurix's formula, he's the one passing it off as Hearst in his original post. Don't confuse me with him. I just called it a la Hurst, reduced to a primitive from Jurix.Yes, I've already forgotten Yuri's original post :). Well, I take back your accusation of authorship of formula h = Log(High-Low)/Log(N). I can even apologize :). By the way, I began to fight with this formula at once there :).
The thing is that afterwards a lot of water has flowed, and Yury and I still had a private discussion. One way or another, the correct approach was used when calculating the table.
So both the table and the conclusions from it were made within the framework of the correct approach, and you are arguing exactly with the conclusions.
Well, isn't the formula High - Low = k * sqrt(N) yours?
Now that we have something to compare it with, we can see how the Hearst exponent behaves for SB with different values of the interval N.
Let me remind you of the formula used to calculate the Hearst ratio as defined by its author.
H = (Log(R2) - Log(R1))/ (Log(N2) - Log(N1))
The two-point calculation scheme is due to the need to get rid of the unknown factor that is present in the Hurst formula.
To simplify the calculations, to be more clear and to maximize the research range, the number of ticks in the interval N was also changed in powers of two. That is, N = 2^n was taken. The base of the logarithm in the formula for H does not play a role. Therefore it was assumed to be 2, so Log(N ) =n.
The calculation algorithm was as follows:
The results are in the table.
(Unfortunately, I failed to paste the whole table - the editor doesn't accept text of this size. I had to split it into 2 tables, saving the first two columns for convenience. The first one will be referred to as 2a, and the second one as 2b.)
I mean the definition, and there may be any ways of calculation, as long as they do not contradict the definition.
I can't say I'm a biographer of old Hirst, but he didn't seem to have such a definition - through the spread. He had a purely practical problem (to put it very, very crudely) - will the selected type of platinum in a particular place survive another 10 years under difficult climatic conditions, or you need to invest even more money into construction.
He introduced an assumption about a degree dependence of the process, and later on this very degree was named after him. The spread has nothing to do with it - it is just one of the ways of calculating the degree. The spread does not define the meaning of the coefficient and the phenomenon as such.
to Andrei01:
1. The properties of the market (as a whole) are very close to random. Consistently came to the following conclusion (I will even highlight :o):
2. You can't treat a quotation process as a whole. Moreover, the quoting process as a single process does not exist in nature - it is an illusion. It is senseless to take and examine any statistics of quotes, even the reduction to a stationary series will not give anything. It is senseless to take any lengths, and it is impossible to take the whole history.
PS: TV always works, it should not be confused with TV's conclusions about "something" as not working.Doesn't the first postulate contradict the second?
If there are no statistics or they are meaningless, then how can we apply TV that deals only with meaningful statistics and meaningful processes?
I can't say I'm a biographer of old Hirst, but he didn't seem to have such a definition - through the spread. He had a purely practical problem (to put it very, very crudely) - will the selected type of platinum in a particular place survive another 10 years under difficult climatic conditions, or you need to invest even more money into construction.
He introduced an assumption about a degree dependence of the process, and later on this very degree was named after him. The spread has nothing to do with it - it is just one of the ways of calculating the degree. The spread does not define the meaning of the coefficient and the phenomenon as such.
The question here is not what definition Hearst personally gave, but what is the officially accepted definition of the value called the Hearst exponent.
And if through the spread is not the definition, then what is the definition? The question is not rhetorical, I am really curious?