a trading strategy based on Elliott Wave Theory - page 204
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Let's start with a hypothetical and very distant topic for most traders and speculators. Suppose there is a factory where some parts are milled, and there is quality control of these parts in this factory. This control is concluded in the fact that they measure some parameters of already milled parts. So, while the process is going on under specified conditions and technologies are being observed, quality control shows that everything is normal, within tolerances, but as soon as process deviations occur it is reflected in the results. The task is simple, identifying a breach in the process, based on some formal attributes. This is the first part of the problem, the second part of the problem, is the "timely" detection of the disturbance. In mathematical statistics there are some methods which allow to solve these problems, within certain limits.
More generally, a stochastic process discontinuity problem. It was studied by Kolmogorov and Shiryaev in the last century. Suppose there is a stochastic process, it has some characteristics (it can be mean, variance, etc. to your taste, including Hurst). Let something happen, and the stochastic process changes its characteristics, i.e. it decays, the definition of the fact and the moment of decay is the solution of the problem of decay. The problem was once proposed for searching targets in the background of interference and for target tracking. Adaptive optimal filter construction problem is adjacent to this problem. And so on.
As I understand from reading this thread, that's what you all have been doing all along. You find a "stationary" region in the process, or rather in its implementation in the videadata of prices, and describe it by a regression (linear or otherwise). Assume, implicitly, that such "stationarity" areas exist. As far as I understood it, it was suggested to determine the moment of change of "stationarity" areas by Hearst or by "breakdown" of statistical significance...
It's awful how unfriendly the forum engine is...
Not exactly what we do (there are several, if I may say so, "forex martial arts schools" in the thread :o), at least for me it's a bit more complicated.
Linear regression, or similar, in my opinion, does not describe a trend as such, i.e. the "strength of relationship" between samples is not assessed in any way, but only "fits the analytical function into the raw data by the NK method". Of course, there are criteria, such as the coefficient of determination, which can only be used to assess how well the function "fits", or in other words, how well the raw data are "explained" by the selected model. The channel (and in the discussed modifications of strategies it is the basis) is often compared to LR, which in my opinion is not very correct. So I decided to share my views and experiences with alternative approaches.
Yes, very close to the topic.
This, by the way, could be a starting point. Not start with a trend, but with a stationary series. As far as I understand, the stationarity criterion of a series is a well-defined thing. And the trend lies beyond stationarity. Therefore, a necessary (but not sufficient) condition for the presence of a trend can be that the conditions of a stationary price series are not fulfilled.
What is a stationary series? What criteria for stationarity are the most acceptable in this situation?
Probably, the general picture of the market dynamics can be presented as follows: areas of temporary "stationarity" and temporal "trendiness" connected by areas of transients. In this case the problem definition comes down to identification of borders of these sectors and the most adequate parameters defining these borders. That is, in general terms - decomposition and quality control. :-))
2 grasn
Sorry, Sergey, but it doesn't explain anything to me.
What is "statistics and criteria are analysed" ? What is "trend found", "trend disappears", "trend not detected" ? What does all this have to do with the numbers that are obtained by the formulas you have given ? What is the meaning of transitions over 0 ?
...Not really doing it (there are several, if I may say so, "forex martial arts schools" in the thread :o), at least for me it's a bit more complicated.
This is quite noticeable, especially taking into account the total inconsistency of the discussion with the original topic.
Linear regression, or similar, in my opinion, does not describe a trend as such, i.e. it does not assess the "strength of the relationship" between the samples in any way, but only "fits the analytical function into the raw data by the NK method". Of course, there are criteria, such as the coefficient of determination, which can only be used to assess how well the function "fits", or in other words, how well the raw data are "explained" by the selected model. The channel (and in the discussed modifications of strategies it is the basis) is often compared to LR, which in my opinion is not very correct. So I decided to share my views and experiences with alternative approaches.
I merely suggested looking at the problem more widely than it has been discussed so far, and merely informed that such a problem has already been solved and might be worth looking how. By no means am I imposing my point of view.
After all, what is a channel? If you subtract the corresponding LR values from the series values, you get the so-called "residuals". The analysis of "residuals" is a long and well-established thing. This is one. Two, someone has already mentioned but nobody paid attention to it that these "residues" must have a normal distribution if HR adequately describes the process. Further, there is an opinion that as soon as normality of distribution is violated, we can consider that the process is violated too. And so on...
Yes, very close to the subject.
This, by the way, may be a starting point. Not start with a trend, but with a stationary series. As far as I understand, the criterion of stationarity of a series is a well-defined thing. And the trend lies beyond stationarity. Therefore, a necessary (but not sufficient) condition for the presence of a trend can be that the conditions of a stationary price series are not fulfilled.
What is a stationary series? What criteria for stationarity are the most acceptable in this situation?
Probably, the general picture of the market dynamics can be presented as follows: areas of temporary "stationarity" and temporal "trendiness" connected by areas of transients. In this case the problem definition comes down to identification of borders of these sectors and the most adequate parameters defining these borders. That is, in general terms - decomposition and quality control. :-))
Stationarity is a very ambiguous thing, in fact. So is the concept of trend, as they are two sides of the same coin.
Keep in mind, "stationarity" is "trend", and it doesn't matter whether it is directed upwards or has a zero slope.
Sorry, Sergei, but that doesn't explain anything to me.
What is "statistics and criteria are analysed" ? What is "trend found", "trend disappears", "trend not detected" ? What does all this have to do with the numbers that are obtained by the formulas you have given ? What is the meaning of transitions through 0 ?
Yuri, this is just one of the criteria for trend detection. I am not at all claiming that it is the best criterion, the most reliable, and I am persistently continuing my research in this area, including with autocorrelation. I did not invent it, and in this case I "play" by the rules of these comrades Woodyer, Woodward, Gielchrist. There is no arbitrariness, only strict adherence to the rules:
For this particular sample:
n=1000
statistic (number of transitions through zero)
R(1000)=0
this is just the parameter whose values will determine the presence or absence of a trend according to the criterion. For autocorrelation, the statistic will be something else, perhaps the autocorrelation itself. Number of zero crossings is a measure of data connectivity
PS: to feel "physicality" of zero crossing, you can hand draw a straight line of 45 degrees, or a sine wave, and estimate the form of the V function, counting the number of crossings.
Criterion for statistics
I choose confidence probability alpha=0.95
Critical values for n=1000 and alpha=0.95:
R1(0.95, 1000)=6
R2(0.95, 1000)=83
Criterion itself: condition R1<R<R2 is not satisfied
Conclusion
Sample contains trend. That's it. No arbitrariness, everything is by the rules.
How to use
Simple, fix the current bar and in steps of 1 (or different) take samples:
{100: 0} is R1(n, alpha)<R(n)<R2(n, alpha) satisfied? If yes "no trend", no "trend"
{101: 0} is R1(n, alpha)<R(n)<R2(n, alpha) satisfied? If yes "no trend", no "trend"
{102: 0} is R1(n, alpha)<R(n)<R2(n, alpha) satisfied? If yes "no trend", no "trend"
{103: 0} is R1(n, alpha)<R(n)<R2(n, alpha) satisfied? If yes "no trend", no "trend"
{104: 0} is R1(n, alpha)<R(n)<R2(n, alpha) satisfied? If yes "no trend", no "trend"
...
{Bars: 0} is R1(n, alpha)<R(n)<R2(n, alpha) satisfied? If yes "no trend", no "trend"
(1) The trend can be found immediately at {100: 0}, then we need to find its origin.
(2) The trend may not be present in the first sample, then there may be several options:
2.1 stop searching for a trend, wait for a new bar to arrive
2.2 continue searching, assuming there may be a trend, but of a "higher order".
... There may be more variants on its search
More complicated cases, earlier cited, when the R statistic is at one of the critical boundaries but does not reach one transition. Thinking ... what to do.
PS: Yuri, I tried, exhausted all my meagre vocabulary... :o)
Just suggested looking at the problem more broadly than it has been discussed so far, and just advised that a similar problem has already been solved, and might be worth looking at how exactly. In no way am I imposing my point of view.
Latitude can kill any endeavour, it is very dangerous. You suggested, for example, introducing quality control, like in factories. My profession is connected with IT and I can authoritatively say that quality control is the HARDEST module to implement in factories. But this is lyrical digression.
It is better to give references, where it was solved, and what of the problems you listed?
Северный Ветер
Всего лишь навсего предложил посмотреть на проблему шире, чем она обсуждалась до сих пор, и всего лишь сообщил, что подобная задача уже решалась, и может быть стоит посмотреть как именно. Ни в коем случае не навязываю свою точку зрения.
grasn 07.01.07 19:31
Latitude can kill any endeavour, it is very dangerous. You suggested, for example, that quality control should be introduced, like in factories. I am connected with IT by profession and I can authoritatively say, that quality control is the STRONGEST module to be implemented in factories. But this is lyrical digression.
It is better to give references, where it was solved, and what of the problems you listed?
You misunderstood me. All I was trying to say is that the problems being solved in this thread, somehow akin to the problems of quality control, which in turn, more "mathematically" formulated in the problem of divergence. It is not about the process of organizing quality control, although there are interesting points there too. It was about the problem of determining the violation of a stochastic process (strange as it may seem, but, for example, the size of parts in production is a stochastic process, and with 'memory'). If you put aside the conventions, you will see that in its essence, the schedule of price changes (the market processes behind it) is very similar to quality control (read: production process control).
The shortest and most succinct description of key terms is in the electronic handbook of mathematical statistics for the program Statistica, on their website, in Russian.
And by the way, while we're on the subject of lyrics, there's a digression. Successful trading is nowhere near as easy as organising quality control in a factory.
You got me wrong...
No, I got you right, it was a joke of sorts and the "statistics" site I've also poked around. But there is some truth in every joke...
The only thing I can add is that if one decides to go the "official mathematical" way, one will inevitably come to the time series analysis. And here he will be a disaster waiting for him, in the form of ARIMA and others. Wonderfully well-founded methods, but unfortunately (my personal opinion) not working in the market.
To be clear, time series analysis consists of three simple things, despite the complex mathematics. The first is the assumption that the price series is a time series (a series in which values arrive in strictly defined time intervals, which is not the case, we should rather talk about a stochastic sampling series). Second, it is stationary in a sense and has a trend. Third, the series has seasonal and cyclical components and noise.