Bernoulli, Moab-Laplace theorem; Kolmogorov criterion; Bernoulli scheme; Bayes formula; Chebyshev inequalities; Poisson distribution law; Fisher, Pearson, Student, Smirnov etc. theorems, models, simple language, without formulas. - page 8
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Do as you like. I can't advise you as I don't know the characteristics of the ticking process.
It's not about simulating a real tick process. On the contrary, all I need so far are the classical normal distributions in the form of OHLC. Roughly speaking, the problem comes down to determining High and Low, if Open = Close-1, and Close = sqrt(N), where N is the number of ticks.
It's not about simulating a real tick process. On the contrary, all I need so far is a classical normal distribution in OHLC form. Roughly speaking, the problem is to determine High and Low, if Open = Close-1, and Close = sqrt(N), where N is the number of ticks.
As far as I remember, for a random series the |Close-Open| candlestick body length is equal to the average sum of upper and lower shadow lengths. Therefore having modeled Close as sqrt(N), then we model the upper shadow length as |sqrt(N/4)| and similarly the lower shadow. Of course, this is a variant of the symmetric sb (mo=0). For asymmetric one it is slightly different
As far as I remember, for a random series the |Close-Open| candle body length is equal to the average sum of upper and lower shadow lengths. Therefore having modeled Close as sqrt(N), then we model the upper shadow length as |sqrt(N/4)| and similarly the lower shadow. Of course, this is a variant of the symmetric sb (mo=0). For an asymmetric one it is slightly different
though no, it will be wrong. Because the length of candlestick body and shadow lengths are dependent. That's why it's better to generate lots of candlesticks, and then to get new series as an arbitrary candlestick from this set, than to look for analytical distribution of shadows
I thought, why not make it simpler: we take four generated values: the first will be the difference between Open and Low, the sum of the second and third will be the difference between Low and High, and the fourth will be the difference between High and Close:
With large amounts of data Close will converge to Open, and the High-Low spread will have double the variance of the value of the segments (four numbers with a given variance).
It's not about imitating a real tick process. On the contrary, all I need is the classical normal distribution in the form of OHLC. Roughly speaking, the task is to determine High and Low, if Open = Close-1, and Close = sqrt(N), where N is the number of ticks.
Once upon a time, a long time ago, I was generating random artificial quotes. I did the following - for each minute I found 3 independent random variables H, L and dlt - shift per bar. I find them following the Gaussian method (in points) with expected payoff zero and a specified variance. At the same time I took the obtained value modulo. Also I chose the direction of shift - sgn - by chance, 50/50. So Close = Open+sgn*dlt, to find Hg I took the greater of (Open, Close) and added H to it; to find Lw I took the lesser of (Open, Close) and subtracted L from it.
Of course obtained quotes are compared to real ones (though on the level of subjective perception). I was amazed then that the only quantity that defines the "similarity" of artificial quotes to real ones is the offset variance - dlt. For it to be similar to natural cotiers, the offset variance must be very small, i.e. most of the minute offsets must be zero. Otherwise an ultra-volatile market would result. The variance of Hg and Lw influenced the degree of ''shagginess'' of the quotire. In order to imitate a trend, I slightly changed probability of direction selection - 49/51 - we got a powerful trend if we view it on one day.
So, as a result, we got a very simple model of generation of different modes - I needed a highly volatile trend - I increased the variance of shift and changed the probability of direction. I needed a low-volatility flat - I made the shift variance very small and the direction 50/50.
I thought, why not make it simpler: we take four generated values: the first will be the difference between Open and Low, the sum of the second and third will be the difference between Low and High, and the fourth will be the difference between High and Close:
With large amounts of data Close will converge to Open, and the High-Low spread will have double the variance of the value of the segments (four numbers with a given variance).
...But it's a very slow and pointless method.
It's not that slow, you won't have time to light a cigarette.
Are bootsrap ideas inappropriate?
What is bootsrap?
Not so slow, you won't have time to light a cigarette.
I have a question on the subject
I am trying to understand the scope of the following distributions:
Generalized Pareto Distribution(GPD) and Extreme Value Distribution(GEV)
What is the relation of these distributions to each other, to a normal distribution and respectively to a uniform distribution? In other words, how in real life can events occur that they describe?
What is bootsrap?
There are in VIKI.
The idea is to swap a randomly available sample so as to obtain a convergence of frequencies to the probability of the parameters available on the sample.