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Thanks for the link, Vladimir. It's quite interesting.
While I'm still in touch, I'll allow myself one more post.
Many people, reading this thread, are wondering - why does this uncle need all this? Why the need for exponential, logarithmic time scales? Just take the ticks as they are and work with them as with BP, where the time between ticks is the so-called "Forex time".
You guys! You are completely clueless! You're just desperately stupid and that's all.
Let me remind you that we see the price movement as a kind of a Wiener process with drift. Like a Brownian motion. In fact it is lapace motion, but it doesn't change the essence of the matter and this model is quite suitable at first approximation.
So, for such model, astronomical time is the most important parameter. And the law of "root of T" for dispersion is derived by Einstein for this time, and not for some "Forex time".
Perrin in his experiments used time discreteness =30 sec. to observe the process.
In Mendeleev University of Chemical Technology (former MHTI) where my daughter studies, experiments are carried out at time discreteness =10 sec.
In short - we MUST consider time in calculations, otherwise we will not see good luck.
If there is no time, there will be no price change. The question is in right choice of time for analysis of the task. With what, in my opinion, many have a complete vacuum.
If there is no time, there will be no change in price. The question is the correct timing for analysing the problem. Which in my opinion many people have a complete vacuum with.
Exactly. And we are getting to the bottom of it.
I completed the processing of tick data for the pair AUDCHF over a day.
Tick data was received using the DDE protocol from MT4 in VisSim. The time stamp is TimeSec, which is rounded to integer values. Unfortunately, I don't know whether it's just taking an integer part of a decimal value or rounding to the nearest integer. If anyone knows how this operation is performed when passing data via DDE and can tell me, I'll be very grateful.
The distribution of time intervals between ticks looks like this:
Descriptive statistics:
A total of 34978 ticks, as you can see, came in a day (86400 sec.).
But, here's the problem - Wiener model is good for describing chaotic particle collisions at T between collisions -->0.
In Forex, there is no such thing at all. At night time, time intervals increase, at day time intervals decrease. In the time window = 4 hours, the process of coming of quotations is not Poisson's.
And vice versa - when considering ticks "as it is", there is a problem of ratio of a considered sample volume to the astronomical time. I.e. 5000 ticks can come in either 4 hours or 10 hours. And this process is also non-Poissonian. In this case, the law of "root of T" loses its force.
This is the contradiction between the Wiener's model and the real price movement, we need to minimize as much as possible.
And this can be done by introducing different time scales of quotes reading, the mean value of which correlates with some discrete astronomical time.
The tick sample volume (wave packet) in this case is replaced with some averaged model packet with the most similar statistics.
That's it, we're out of words. I need charts, figures but I have no time for that - I have to celebrate.
See you soon!
I would also try this: use seconds quotes, and calculate variance separately for each hour of the day (because the intensity of trading at each hour is different).
why is using ticks bad? it limits us. what maximal deviation can be in 10 ticks, if a tick is basically one point?
the maximum deviation in 10 ticks can be 10 pips. if all 10 ticks go in one direction.
and if we use seconds? in 10 seconds price can jump "any distance"!
using ticks, we also neglect time, i.e. price speed. and in such systems it is noticed that the higher the speed of price at which the signal came, the higher the probability of its triggering.
Exactly. And we are getting to the bottom of it.
I have completed the processing of tick data for AUDCHF over a day.
Tick data was received using the DDE protocol from MT4 in VisSim. The time stamp is TimeSec, which is rounded to integer values. Unfortunately, I don't know whether it's just taking an integer part of a decimal value or rounding to the nearest integer. If anyone knows how this operation is performed when passing data via DDE and can tell me, I'll be very grateful.
The distribution of time intervals between ticks looks like this:
Descriptive statistics:
In total, as you can see, there are 34978 ticks in a day (86400 sec).
Analysis of ticks on minimal time intervals will not give a picture of what is going on. How can this not be understood?
Over the week, the distribution of tick increments Bid for AUDCHF is as follows:
So, this is the problem I want to solve.
It is necessary to work at any time of day in such a time scale (uniform, exponential, or logarithmic), that the properties of this distribution of real increments are preserved as much as possible.
Once again I say - you cannot work simply with a sample of ticks (for example - 5000)! The connection with the astronomical time is lost. We do not know for what period of time this batch of 5000 ticks will be collected! We cannot, in this case, apply the theory of Wiener processes from the word "at all"!
And a second important conclusion.
If you look at it - the maximum time interval between ticks I had was 88 sec.
Conclusion: building and working with seconds timeframes S1, which many people dream of as a grail, is a complete nonsense.
We don't know in what period of time this batch of 5,000 ticks will be collected!
develop a tick density function, I did once, the principle:
analyse not the tick arrival time but the difference in time between ticks (delta)
having the arithmetic mean of these increments you can get the tick density per unit time, a second is not enough, but a minute is a very concrete value
having experimentally suiting you, you may operate with how many ticks you need for your statistics, i.e. define the conditions of ticks accumulation approximately as follows
1. if the density of ticks is < 20 per minute, you need at least x minutes
2. if tick density >40 per minute, then you need y minutes
3. if tick density >20 && < 40 per minute, then z minutes
similarly
HH: you can work out a recurrence formula with this ticks density, i.e. calculate current ticks density on current tick, and subtract/add to previous ticks density - get dynamically changing value
So there you go.
Why I think research into the time intervals between tics is extremely important.
Once again:
We see that this is not an Erlang flow (I have made comparisons with flows of various orders, it is nowhere near an Erlang).
It is a simple flow with some distortion that does not correspond to classical Erlang or Pascal distributions.
Is it legitimate in this case to apply quotation reading at time intervals:
1. uniform (in 2.5 seconds)
2. exponential (mean=2.5 sec.)
3. logarithmic (mean=2.5 sec.)?
The answer to this question will be statistical correspondence of obtained distributions of increments for these cases, to real distribution of tick increments Bid and Ask.
If you look at it - the maximum time span between ticks I had was 88 sec.
Conclusion: building and working with S1 second timeframes, which many people dream of as the Grail, is a complete nonsense.