a trading strategy based on Elliott Wave Theory - page 206
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2. Suppose there is a normally distributed random variable with zero expectation and positive correlogram.
If the series is long enough, we may mark out any lengthy stretches of directional price movement. Let us call such a trend a deterministic one. Deterministic trend can be detected by means of digital lowpass filters or their derivatives. For example, crossing of two moving averages with different periods is nothing else but approximation of a smoothed time series derivative. It is clear that this works as mathematics requires: a derivative greater than zero means that the function is increasing, less than zero means that the function is decreasing. But only few people know that it works only for series with a positive FAC, and ALL currency series in all TFs have a negative FAC! And, as a consequence, the method does not work in the market, or works, but accidentally...
Continuing the theme.
Main Problems of Time Series Analysis
The principal differences between a time series and a sequence of observations that form a random sample are as follows:
- first, unlike the elements of a random sample, the members of a time series are not independent;
- second, the members of a time series are not necessarily equally distributed.
This means that the properties and rules of statistical analysis of random sampling cannot be extended to time series. On the other hand, the interdependence of time series terms creates its own specific basis for the construction of predicted values of the analysed indicator based on observed values.
Classification of the main factors under the influence of which time series values are formed.
Generally, 4 types of such factors are distinguished.
1. Long-term factors which form a general (in the long term) tendency in changes of an analysed indicator. Usually this trend is described by a non-random function (whose argument is time), usually monotonous. This function is called a trend function or simply a trend.
2. Seasonal, which forms periodic fluctuations in the analyzed attribute at certain times of the year. Since this function is to be periodic (with periods multiple of "seasons"), its analytical expression involves harmonics (trigonometric functions) whose periodicity is usually determined by the essence of the task.
3. Cyclical (conjunctural) forming changes of the analysed attribute caused by long-term cycles of economic or demographic nature (Kondratieff waves, demographic "pits", etc.).
4. Random (irregular), unaccountable and unrecordable. Their impact on the formation of time series values just causes the stochastic nature of series elements, and hence the need to interpret the members as observations made on random variables. Let us denote the result of the impact of random factors by means of random variables ("residuals", "errors").
Of course, it is not necessary that all four types of factors are involved simultaneously in the process of forming the values of any time series. Conclusions as to whether the factors of a given type take part or not in the formation of the values of a particular time series can be based both on the analysis of the substantial part of the problem, and on a special statistical analysis of the investigated time series. However, in all cases, the participation of random factors is assumed. Thus, in general terms, the data formation model (with an additive structural scheme of the influence of factors) looks like a sum of all or some of the factors.
OK, let's continue:
Neutron, did I get it right that only the series which has zero expectation and positive correlogram can be considered deterministic?
2. Suppose there is a normally distributed random variable with zero expectation and positive correlogram.
If the series is long enough, we may mark out any lengthy stretches of directional price movement. Let us call such a trend a deterministic one. Deterministic trend can be detected by means of digital lowpass filters or their derivatives. For example, crossing of two moving averages with different periods is nothing else but approximation of a smoothed time series derivative. It is clear that this works as mathematics requires: a derivative greater than zero means that the function is increasing, less than zero means that the function is decreasing. But only few people know that it works only for series with a positive FAC, and ALL currency series in all TFs have a negative FAC! And, as a consequence, the method does not work in the market, or works, but accidentally...
Let's continue with the theme.
Main tasks of the analysis of time series
The principal differences between a time series and a sequence of observations that form a random sample are as follows:
- first, unlike the elements of a random sample, the members of a time series are not independent;
- second, the members of a time series are not necessarily equally distributed.
This means that the properties and rules of statistical analysis of random sampling cannot be extended to time series. On the other hand, the interdependence of time series members creates its own specific basis for the construction of predicted values of the analyzed indicator based on observed values.
Classification of the main factors under the influence of which the time series values are formed.
Generally, 4 types of such factors are distinguished.
1. Long-term factors which form a general (in the long term) tendency in changes of an analysed indicator. Usually this trend is described by a non-random function (whose argument is time), usually monotonous. This function is called a trend function or simply a trend.
2. Seasonal, which forms periodic fluctuations in the analyzed attribute at certain times of the year. Since this function is to be periodic (with periods multiple of "seasons"), its analytical expression involves harmonics (trigonometric functions) whose periodicity is usually determined by the essence of the task.
3. Cyclical (conjunctural) forming changes of the analysed attribute caused by long-term cycles of economic or demographic nature (Kondratieff waves, demographic "pits", etc.).
4. Random (irregular), unaccountable and unrecordable. Their impact on the formation of time series values just causes the stochastic nature of series elements, and hence the need to interpret the members as observations made on random variables. Let us denote the result of the impact of random factors by means of random variables ("residuals", "errors").
Of course, it is not necessary that all four types of factors are involved simultaneously in the process of forming the values of any time series. Conclusions as to whether the factors of a given type take part or not in the formation of the values of a particular time series can be based both on the analysis of the substantial part of the problem, and on a special statistical analysis of the investigated time series. However, in all cases, the participation of random factors is assumed. Thus, in general terms, the data formation model (with an additive structural scheme of the influence of factors) looks like a sum of all or some of the factors.
Neutron , you're fucking full of shit!!! :))))))))))))
Believe me, it's a lot simpler than you think...
my friend, what makes you think that the distribution is normal? Every corner is screaming about heavy tails...
(in fact, it is lognormal.)
and everything is described by something like a logistic equation, with all that it implies.
and another confirmation of this - experiments grasn (I do not remember exactly, but with fractal dimension, or with Hirst...)
P.S. by the way, there is a beautiful book by Haken "Information and self-organization. macroscopic approach to complex systems".
PS Северный Ветер, а что такое Н-волатильность ?
Here http://forum.fxclub.org/showthread.php?t=32942&page=9, about halfway down the page, there are brief excerpts from the original source.
Thanks for the link. And the topic is interesting.
I don't understand why people are so weird there. The thread about the coins is drowned in flood. Why?
It seems that the topic is of little interest to anyone, and they just want to scratch their tongues.
About H-volatility is too terse to understand everything, but enough to get an idea.
I wonder if access to the thesis itself is open ? Can it be accessed via the internet?
Neutron, did I get it right that only the series which has zero expectation and positive correlogram can be considered deterministic?
No, a deterministic trend is a trend generated by integration of a normally distributed random variable with zero expectation and a positive correlogram.
...mate, what makes you think that the distribution is normal? You know, they yell about heavy tails on every corner...
(in fact, it's lognormal.)
Just to be clear. The distribution need not be normal. Realistically, it is well approximated by a two-parameter exponential distribution. It gives those very thick tails.
Neutron What a load of crap!!! :))))))))))))
Believe me, it's much simpler than you think...
Not true! You are harbouring illusions about forex. It doesn't get any simpler than that.
It's been tested.
Grasn
Neutron, did I understand correctly that only a series with zero expectation and a positive correlogram can be considered deterministic?
No, a trend generated by integration of a normally distributed random variable with zero expectation and a positive correlogram would be deterministic.
I don't really get it. It turns out that the concept of a deterministic series does not exist? Let's go consistently. From your words I understood the following. We have some series, the characteristics of which, let's say, we don't know.
The first thing we do is to check compliance of the previously listed parameters (expectation and positive correlogram) and if the conditions are met, we pass on to integration.
Or do we integrate a series at once and look at its characteristics?
Or do we integrate the series by some random variable that possesses these parameters? But how?
...
About H-volatility too succinct to understand everything, but enough to get an idea.
I wonder if the thesis itself is open access? Is it possible to get it on the internet ?
starting point http://forex.kbpauk.ru/showflat.php?Cat=0&Board=mts&Number=139469&page=0&fpart=all
the thesis itself is available on the spider, in the book section, but registration is required there. i have the same.
I don't really get it. It turns out that the concept of deterministic series doesn't exist? Let's go consistently. From what you've said I've understood the following. We have some series, the characteristics of which, let's say, we don't know.
The first thing we do is to check compliance of the previously listed parameters (expectation and positive correlogram) and if the conditions are met, we pass on to integration.
Or do we integrate a series at once and look at its characteristics?
Or do we integrate the series by some random variable possessing these parameters? But how?
Sergey, those time series which we operate (price series) are already integrated series of the first order (as a rule). By taking successive differences we will get a stationary series of residuals the properties of which we will study. This is the right move. When opening a position, we actually operate not with the absolute value of the symbol rate, but with its expected increment for the time of holding the position, i.e. we work with a series of differences. As I said before, the entire variety of trading strategies comes down to a single action - predicting the price movement direction after opening a position...
It's too early to derive a criterion for detecting a deterministic trend. We need to build a complete and, if possible, internally consistent picture of price formation, and only then will it become clear how to build an optimal predictive model. My hope.
The dissertation itself is available on the spider, in the books section, but you need to register there.
Thanks, registration is, although I go there only "need". IMHO It's very dark.
I already did.