a trading strategy based on Elliott Wave Theory - page 233
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I have digressed a bit from the current process. Sergey, I already wrote that I haven't been searching for a trend as such for a long time; I am quite pleased with the strength of the connection between samples calculated using the autocorrelation function. Not long ago you wrote that in general there are varieties of trends in such series as well, but it's impossible to find them.
But it would be interesting for me to see my criterion on such a series. I would appreciate if you could provide a way to calculate the Wiener process, preferably a screenshot of a formula from Matcad, or the file itself. Check it out.
Oh, the file I posted is not enough? It's 10^6 ticks.
But I would be interested to see my criterion on such a series. I would appreciate it if you could provide a way to calculate the Wiener process, preferably a screenshot of the matcad formula or the file itself. Check it out.
Oh, the file I posted isn't enough? It's 10^6 ticks.
I don't use ticks as a matter of principle. And I don't see any sense in it. Moreover, I don't use OHLC and arithmetic combinations of them as input data.
And I confess I haven't tested components of my system on a "pure" Wiener process yet. Sergey, please, don't do harm, unless it's not a trade secret. :о)
n is the number of row members, sigma is the standard deviation.
Sergey, thank you. I will try my criterion.
Sergey, my criterion seems to work. It may be subjective, but at least the expectations were generally confirmed. So, the Wiener process generation was performed under the same conditions, and the current datum was chosen as the outermost datum in the sample. The strength of connection graph should be read backwards, i.e. from the rightmost value to the beginning (history).
Price series
EURUSD: This is a quite typical case for a huge number of price series calculations. It is characterized by large values of strength of connection between samples (in conventional units, from 350 to some thousands, I have not encountered values less than this yet) for the first ones and a prolonged, smooth fall to zero.
Wiener process.
In general, performed about 200 generations of the process according to your algorithm. I assumed that the criterion should show weak ties from the very beginning and a very fast decay of the correlation function to zero for the Wiener process. I detected three variants:
1 variant.
This variant was obtained in most tests. Very small values as compared to the price series, and very fast decay to zero.
Variant 2
It was not frequent and characterized by complete absence of connection between samples (I simply did not see such places in the price series).
Variant 3
It is a very interesting variant. It occurs quite rarely. What could it mean? I have not encountered this at all on the price series. It's so smooth, beautiful:
If it's not the third variant, I can quite easily distinguish (classify), the Wiener process from the price series. I have encountered very small values for first counts, but not that small. At least, it is absolutely clear, that it is advisable not to trade on such theoretical local places. Overall, these are the results.
Here x-axis is H, y-axis is H-volatility. These are kagi charts, I have not calculated them.
Blue colour represents GainCapital data on EURUSD, about 2 million ticks.
In red is the same series of random numbers posted earlier by Neutron, 1 million ticks.
The yield shown in Neutron's charts is easily obtained using the formula
f(H)=(Hvol - 2)*H
From this graph it is clear that at H>20 arbitrage quickly disappears.
And Sergey shows that for EURUSD kagi does not allow arbitration at all.
Similar results are more likely to be obtained for EURCHF and less likely to be obtained for EURGBP.
However, (1.92-2)*20=1.6, i.e. less than 2 points. This is barely enough to cover the spread.
...If not the third option, I can quite easily distinguish (classify), a Wiener process from a price series. I have encountered very small values for first counts, but not that small. At least, it is absolutely clear, that it is advisable not to trade on such theoretical local places. Overall, these are the results.
Sergey, the fact that your criterion for the Wiener process is not zero (or whatever it should be. If zero, how close to zero should the indicator be?) suggests a possible error in the code.
Please comment on the observation.
I, in my last post, posted the results of the criterion stability assessment for a number of minutiae for different years. The correct thing to do, first, was to give a justification for the applicability of the Kagi-renko construction method I used for a series of minutiae. For this purpose, we will construct a Wiener process with a distribution function (PDF) of the amplitudes of the first differences identical to the EURUSD 2004 1m series.
The FRs are shown on the left. The blue dots are EURUSD, the red are RNGs, and their correlograms are on the right. An inquisitive mind must have noticed the difference in strength of correlation between samples for the series EURUSD ticks and 1m...
Now we may look at the behaviour of f(H)=nt-2H, for a Wiener process identical to the minutes. We expect "zero" in the whole range of breakdowns!
As can be seen, "zero" for the kagi-building "1minute" did not work... Although, everything is fine for ticks (see two posts above). I haven't figured it out, but for sure the results of "minute" yield estimates from the previous post can't be used!
The file of Wiener process identical to EURUSD 2004 minutes can be found here:
https://c.mql5.com/mql4/forum/2007/01/RNDUSD1m.zip
H-volatility, for "large" intervals usually tends to be 2,
irrespective of H-value, as it should be in theory. On "short" intervals,
as well as H-Hurst can show anything. Since the data is quite
"random" the result (calculation of H-volatility) is also "random".
The task, in principle, is stated by Pastukhov - to find "markets" with anomalous
H-volatility. Long term.
I wonder how you distinguish between "long" intervals and long-term intervals?
If for "long" intervals the H-volatility tends to 2, and for "short" intervals
can show anything, then how can we determine long-run volatility which can be used practically?
that can be practically exploited ?
I think the highlight lies elsewhere. The H-volatility, just like the H-Hurst,
is a measure of the persistence-antipersistence of the market. Pastukhov for his experiments
took the SP500 and NASDAQ indices. These indices have been in an upward trend for centuries since
since their introduction. As you can probably guess it has to do with economics. Even if
the American economy stood still, that upward trend would still be there. If only because...
because prices go up because of inflation and devaluation and all that nonsense. And these indices
are a reflection of prices. The situation will probably remain the same in the future.
In forex the situation is completely different. No currency can be in a constant state of
up or down against the others. That could only lead to the collapse of the national
economy. Therefore Forex by its very nature does not allow for perpetual trends. And it follows,
that no long-term anomaly can exist in Forex. So Pastukhov's problem
must be solved somewhere else.
I wonder how you see the difference between "long" intervals and long-term intervals ?
If for "long" intervals the H-volatility tends to 2, and for "short" intervals it can show anything?
intervals may show anything, then how do you determine the long term,
that can be practically used?
Just as this concept is defined in statistics in general. For normally
normally distributed values, there are measures of confidence in the results. For example, depending on the degrees
of freedom. In general, many numbers are more confidence, assuming stationarity.
Actually, that's what I was talking about when I pointed out the lack of
of methods for determining confidence bounds. And transferring the properties from a Wiener process
with a Gaussian distribution to real-world ticks isn't quite right because
they're different processes. Unfortunately.
and H-Hurst's is a measure of the persistence-antipersistence of the market.
Let's just say that unlike H-Hurst, H-volatility is more understandable and easier
to study. With N-Hurst it is much worse. I'll get my act together one day and show it.
have been in an upward trend for centuries since they were introduced. As you can probably
as you probably understand it has to do with economics. Even if the American economy
economy was standing still, there would still be an upward trend. If only because..,
because prices go up because of inflation and devaluation and all that nonsense. And these indices
are a reflection of prices. The situation will probably remain the same in the future.
In forex the situation is completely different. No currency can be in a state of
or downward in relation to other currencies. That could only lead to a
the collapse of a national economy. It is for this reason that forex by its very nature does not allow for
of secular trends. And it follows that no long-term anomaly in forex
can not exist. That is, Pastukhov's problem must be solved somewhere else.
I've already said it at least twice in this thread.