Distribution of price increments - page 5

[Alexander_K]

Alexander Sevastyanov:

I believe that taking bare increments and working with them is not very efficient. Gradients should be tied to some context (filter, events, conditions). I.e. it would be more correct to differentiate (divide) the time series into components and process them separately from each other. Such features can be:

• Days of the week,
• Periods when the news disturb the currency pair, 2-3 hours lull before the news, usual market conditions.
• Trading sessions.
• There could be many more different classifications.

One and the same increment can and will have a different effect in different conditions. Perhaps the type of distribution of increments will also change from your initial t2 to another one, and most likely the distribution parameters will change depending on the characteristics.

I think it is the net increments that should be taken. It's them that allow you to see the picture presented in the attached file of distributions (see above post on the topic). don't forget that there is a sample of data for about a month (more than a million quotes)

[Alexander_K]

Here's what else I think. The GARCH models are certainly good, but they are only hypotheses. There is no rigorous mathematical justification.

A rigorous justification will appear only when someone says: "The distribution of a moving sample weighted average or any other estimate of expectation and variance of the process for which the distribution of increments is a t2-distribution is also a t2-distribution (or some other)". Naturally, with a reference to literature.

That would be a real breakthrough in understanding the process.

I keep waiting for such a person - there must be one :))))))

[Alexander_K]

Yes, please excuse me for the previously attached "truncated" Excel file (when saving in Excel 97-2003 format, most of the data was lost)

Now I am attaching the "real" file EURUSD_Ask.

Anyway, it does not change the essence of the matter - everything that was described above is true and interesting enough, but, alas, it does not give the understanding of the general probability distribution of the price, and therefore no understanding of the course of the process which is a must if one wants to succeed in any business.

Well, this is my strictly personal, old man's ^))) opinion - I will be glad to be wrong.

Respectfully,

Alexander_K

[Alexander_K]

I still haven't waited for someone to give me an analogue of Lyapunov's TPT for the price allocation of exchange rates:)))

I consider the topic closed.

Conclusions:

The process of exchange rates formation as a result of trading is a non-Markovian process (so called "memory process"), where the current and the previous price are related by a Student's t-distribution with 2 degrees of freedom.

Yes... It is extremely difficult to cope with such a beast. I take my hat off to traders who work in profit - it's just an art.

And what should simple physicists-mathematicians like me do? I'll try to handle it with the usual averaging of everything and everything - dispersions, kurtosis, asymmetries, etc., etc. on significant sample sizes as Soviet engineers used to do when trying to drive processes within some frames.

Finally, I lay out the tick histories I've been working with. Each one contains over a million consecutively collected quotes with no glitches or omissions from the NDD demo account.

[Alexander_K]

CADJPY

[Alexander_K]

AUDJPY

[Alexander_K]

EURGBP

[Alexander_K]

EURJPY

[Alexander_K]

EURUSD

[Alexander_K]

Good luck!

Regards,

Alexander_K