From theory to practice - page 117
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Age matters ONLY in face-to-face interactions, otherwise age is irrelevant - ONLY the essence.
Everything you are trying to lay out here in a naive way has already been developed, used and there is a generalisation of practice. And it is all extremely well developed.
1. Your accounting for probability density - today it's a chip called Realized GARCH
2. Your consideration of the type of distribution - the t-distribution - there is evidence that among a number of skewed distributions, the t-distribution is the most suitable
3. Your interest in modelling long memory is a necessary part of the model. And there is evidence that it makes sense to bother with it if the Hurst index differs from 0.5 by at least 10%: less than 0.45 - sideways, more than 0.55 - trend model.
There are problems with the size of the window, but with them purely technical difficulties: your 12000 observations - purely technically difficult to maintain dynamically.
Take it, read.... Without regard to physics and age.
Thanks, SanSanych Fomenko, for that info on the Hurst index. It turned out to be an interesting thing, this index, and it is also firmly connected with Aleksander_K2 methods , for illustration I give a picture from the attached article "Kirillov D.S., Korob O.V., Mitin N.A., Orlov Yu.N., Pleshakov R.V. Distributions of Hurst index of nonstationary marked time series // Preprints of IPM named after M.V. Keldysh. 2013. № 11. 16 с. URL: http://library.keldysh.ru/preprint.asp?id=2013-11".
How not to recall here Alexander's usual histogram logos of Olympics-80. As it seems to me, much in the article turns out to be close to what Alexander highlights as stages, or main points of his work. Here are excerpts:
As for the flux of events, it has a clear diurnal periodicity. The weighted average minute intensity w(m),
defined by formula (18), is shown in Fig. 3. This profile is actually a flow parameter (m,1) during an aggregation unit (1 min).
For the example under consideration, the number of ticks per day varies from 38k to 93k, the average daily value being about 70k. From the previous
analysis then follows that a typical time interval, in which a tick series behaves quasi-stationary, is about 1.5 days.
So in less than a day we can build trading systems using non-stationary indicators, and in more than
two days the sample will contain heterogeneous data that will lead to a great percentage of erroneous statistical inferences.
...
As for the determination of the Hurst index as a coefficient in the regression relation (7), in general it is not very high
for a window of small length N and increases with its increase. For a window of 10 thousand ticks the average determination is 0,35, but for a window of 100 thousand ticks it
becomes equal to 0,85. The distribution of determination values is unimodal, but not normal, and has a form more similar to the gamma distribution.
For my part, I was greatly helped by looking at the Hearst index in the article as a measure of degree:
For each time series, its Hurst index can be calculated as the regression coefficient of the logarithm of the normalized cumulative variance to
the logarithm of the sample length.The determination of such a regression will show with what accuracy the process under study can be approximated by the Hurst process.
The traditional interpretation of the Hurst exponent H is that the cumulative range grows faster above the value H = 0.5 than for
a random walk, i.e. the series is more likely to maintain its changing trend over the sample of the length for which the index has been computed
indicator, and if H < 0.5 then the trend is more likely to reverse. Hearst's figure is therefore often used in financial market analysis
Therefore the Hurst exponent is often used in the analysis of financial markets to estimate the trend duration or to estimate the sample length for which the moving averages should be calculated [3-4].
In my research (e.g. https://www. mql5.com/ru/forum/221552/page73#comment_6203173) the law of the square root is often applied, and I have not yet been able to explain so widely its applicability, dilettante guesses https://www.mql5.com/ru/forum/221552/page77#comment_6208896 can be disregarded. Now, knowing the role of the exponent 0.5 in forex, I can give a justification for why the square root law is so often true. Let me remind you, it is the proportionality of the swing characteristic to the square root of the time interval.
Our retail forex does not affect the real interbank foreign exchange market in any way. Among the reasons leading to this conclusion, suffice it to point out one - there is no such thing as a "close trade" in real forex. Retail forex is purely speculative and there is no supply of currency on it. Therefore, it implements its own laws for its own needs. Indirectly hrenfx(getch) wrote about this, telling how one could quote to win (from clients). As we know, there are already tens or hundreds of thousands of EAs, one part of which win on the flat, the other on trends. In order to keep both of them from winning, the alternation of trend and flat is maintained automatically on the retail Forex, i.e. the Hurst index varies about 0.5. The square root law is thereby maintained.
Vladimiris back!!! I am insanely happy about this event! I greet you in the New Year and also recommend to read Shelepins (see attached file). In these articles old Shelepin absolutely clearly and understandably described the mataparatus of non-Markovian processes, while young Shelepin, not understanding what dad writes about, put stupid Fibonacci numbers instead of quantile function and that's the end of it.
As for the determination of the Hurst figure as a coefficient in the regression relation (7), in general it turns out to be not very high
for small window of length N and increases with its increase. For a window of 10 thousand ticks the average determination is 0,35, but for a window of 100 thousand ticks it
becomes equal to 0.85.
From your example it appears that Hearst was first measured on the sideways and then the window was widened and there was a trend in it.
So what?
The point is that any analysis (TA, statistics or anything else) is bullshit, it's like a coin: tails on one side, but when you flip it over, it's empty. And where to with such a coin?
For some years now I've been pushing a seemingly obvious idea on form: analysis is only interesting if we can make predictions from it, if the analysis has predictive power, if the patterns that are identified can be extrapolated into the future.
Does Hirst have predictive powers? I don't know that, but I do know that models based on ARFIMA models that allow fractional differentiation of time series (Hurst) don't work. Such circumstantial evidence that Hurst has no predictive ability.
A coin must have two sides: tails (analysis) and heads (prediction). Only then is it of value.
From your example it appears that Hearst was first measured on the sideways and then the window was widened and there was a trend in it.
So what?
The point is that any analysis (TA, statistics or anything else) is bullshit, it's like a coin: tails on one side, but when you flip it over it's empty. and where to with that coin?
For some years now I've been pushing a seemingly obvious idea on form: analysis is only interesting if we can make predictions from it, if the analysis has predictive power, if the patterns that are identified can be extrapolated into the future.
Does Hirst have predictive powers? I don't know that, but I do know that models based on ARFIMA models that allow fractional differentiation of time series (Hurst) don't work. Such circumstantial evidence that Hurst has no predictive ability.
A coin must have two sides: tails (analysis) and heads (prediction). Only then is it of value.
I didn't separate my words accurately enough from the quoted part, sorry. The example is not mine, it is from an article.
But "where to with such a coin", I hope to find out from the results that Alexander gets.
I didn't separate my words accurately enough from the quoted part, sorry. The example is not mine, it's from the article.
And this is "where to go with that coin", I hope to find out from the results that Alexander gets.
It doesn't matter if you separated it or not - I was just stating my thoughts.
Why do you think that the results obtained here can be proof of anything?
That's the whole problem!
What's more, the proof of the future is not in the tester, it's not in the demo or the real - all these results say: this is how it was. And from this "was" it does not at all follow the future, and this future is based only on faith and hope: the future will be the same as the past. And on what basis?
If, for whatever reason, we do not use the (very extensive) available knowledge, then the first question in relation to our favourite idea is: does this idea have a predictive power? If it does, why?
Why do you think that the results obtained here can be proof of anything?
That's the whole problem!
I said "where to go with that coin", for some reason it was you who started worrying about proof. Of whatever.
If it is proof that you really want, I would agree with you - it really is a problem. That's why I'm not in the business of proof. I have enough verification on stories. Naturally, by my own adequate means. I am not looking for any other evidence. It is good if there is at least a sensible explanation for the observed patterns.
...That's the whole problem!
Moreover, the proofs of the future are not in the tester, are not in the demo or the real - all these results say: this is how it was. And from this "was" it does not at all follow the future, and this future is based only on faith and hope: the future will be the same as the past. And on what basis?
If, for whatever reason, we do not use the (very extensive) available knowledge, then the first question in relation to our favourite idea is: does this idea have a predictive power? If it does, why?
I absolutely agree with SanSanych here. This is a cornerstone problem. Even if the [econometric] model is chosen correctly and has passed all the tests and checks, there is no guarantee that the market will not break it in the future.
For example, a ban on cross-border funds transfers, bankruptcy of the DCs and so on and so forth. There are no guarantees against this. Or didn't people here experience the disappearance of dozens of VCs in 2015 along with their clients' money?
Why should we want one component of a complex system to be more reliable than the others?
I said "where to go with that kind of coin", for some reason it was you who started worrying about proof. Whatever it is.
If you really need exactly a proof, I would agree with you - it really is a problem. That's why I don't do proofs. I have enough of checking on stories. Naturally, by my own adequate means. I am not looking for any other evidence. It is good if there is at least a sensible explanation for the observed patterns.
While this is the point and there are no deals, I will begin to teach my esteemed Vladimir, for he has grasped the root of t and does not want to retreat.
I tell him to read Shelepin's articles, except for insertions about Fibonacci numbers (obviously, imposed to him by his unreasonable child) - he doesn't read.
See page 9 of part 1.
For pseudo-Markov processes:
The variance S^2=c*t*l, where:
l - mean value of jumps
t - observation time
s - jump frequencies in time t (number of ticks)
By jumps we mean tick increments of price.
We have:
S^2 = (N/t)*t*mean(|Ask(t)-Ask(t-1)|) = N*mean(|Ask(t)-Ask(t-1)|)
S = sqrt(N*mean(|Ask(t)-Ask(t-1)|)), where N is the number of ticks during observation time t.
Now, Vladimir, do you understand the difference with your root of t?
By the way, I just described one of my algorithms, which is still under development.
For example, a ban on cross-border funds transfers, bankruptcy of the DCs and so on and so forth. There are no guarantees against this. Or didn't people here experience the disappearance of dozens of VCs in 2015 along with their clients' money?
Why should one of the components of a complex system be more reliable than the others?
You don't have to pick island DCs. They should ONLY be based on broker banks and with European licenses. And this risk can be neglected.
Apart from that there are other risks.
But the risks of instability of the model itself are in our hands. We just need to always keep this in mind and focus our efforts on solving this problem.
The author of this thread is carrying around a distribution and trying to use the distribution parameter in trading.
And what distribution statistics is stable? And we are talking about t-distribution.
I just came across an article on kurtosis.
Here is the graph of kurtosis when the window is moving
Everything changes: the value and direction of the slope.
This is for the distribution.
Very similar graphs for other distribution statistics.
And if we take an ordinary linear regression, values of its coefficients will have approximately the same graph, moreover, in the confidence interval with the width multiple of the coefficient value.
Similar picture for ARMA, ARIMA, GARCH
These should be dealt with instead of suffering ....