a trading strategy based on Elliott Wave Theory - page 189
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Personally, I am guided by its good rule fit. If from {0:0.5} then price is likely to reverse etc (rules of use you described earlier).
Oh how, Neutron, I just don't get your point anymore. Previously you highlighted in bold letters that:
... The results suggest that cycles in the foreign exchange market exist but are stochastic, i.e. there are no cycles with a stationary or near-stationary period...
Grasn, I'm not lying. In the same post, below, it is written that it is because of the lack of stationarity of periodic processes and trends that they are of no practical value! It is rigorously proven mathematically that one cannot beat in the long run, with any TS, a time series constructed by integrating a stationary series with zero expected payoff (this, with some reservations, is analogous to price series of currency instruments and resembles the Brownian motion of a particle), although this series will contain both trends and periodic fluctuations, but they are not STATIONARY. The stock market has stationary trends and seasonal fluctuations and this is its advantage, but the financial market, nevertheless, for all its unpredictability, has its twists and turns and this is what attracts me to it.
In my strategy, I abandon the search for trends and cycles and focus on finding autoregressive models that adequately describe present price behaviour. This model, more or less reliably, predicts several future bars. But the spreads existing today are often comparable in their magnitude to the forecast amplitude, and the research purpose is thus reduced to searching for a criterion allowing to estimate the perspective choice of this or that instrument and the adequacy of the applied forecast model.
Grasn
Personally, I am guided by its good rule compliance. If from {0:0.5} then price is likely to reverse etc. (you described the rules of use earlier).
This more than requires justification. I'll go the other way round...
Let's take a random time series (such as the one described in this post above) and affect it with a Hurst operator. Of course it will not equal 1/2, but will hang around this value with the amplitude that depends on the sliding window size (the bigger the window, the less indicator noise is, but the bigger phase delay of signals it generates). As a consequence, we will make a familiar mistake, by the time the signal appears, our random time series will change and we'll be left with nothing at best. This follows from the postulate that it is impossible to earn consistently on a random value.
Moving on to the real market... Grasn, can you prove the non-randomness of price behavior on your selected timeframe, and consequently, the correct work of the Hurst indicator?
In my strategy, I abandon the search for trends and cycles and focus on finding autoregressive models that adequately describe present price behaviour. This model, more or less reliably, predicts several future bars. But currently existing spreads are often comparable in their magnitude to the forecast amplitude, so the purpose of my research is to find the criterion allowing to estimate the perspective choice of this or that instrument and the adequacy of the used forecast model.
I know that trends, periodics are not stationary. Of course it is sad, but it's not that bad at all. The matter is that I have "fumbled" for a way of detecting trend/channel termination using spectrum analysis (based on wavelets). In combination with other components of the system, it gives good results.
This more than requires justification. I'll go the other way round...
Let's take a random time series (such as the one described in this post above) and affect it with a Hurst operator. Of course it won't equal 1/2, but will hang around this value with the amplitude that depends on the sliding window size (the bigger the window, the less noise the indicator makes, but the bigger the phase delay of signals it generates). As a consequence, we will make a familiar mistake, by the time the signal appears, our random time series will change and we'll be left with nothing at best. This follows from the postulate that it is impossible to consistently earn on a random value.
Moving on to the real market... Grasn, can you prove the non-randomness of price behavior on your selected timeframe, and consequently, the correct work of the Hurst indicator?
Of course, requires justification, as does your approach to forecasting. It reminds me somewhat of linear prediction by Berg's method. Works extremely shitty (may the moderator forgive me).
I don't use any sliding window. I do not calculate the indicator the way you do. That the price changes is a fact that cannot be disputed. I gave examples of calculations and my views on its usage in my posts 90-91 :o)
I see that the dialog becomes more and more scientific. This is good, because it forces to address fundamental issues and get away from unsubstantiated claims. However, since not all here are experts in DSP, spectral analysis, mathematical statistics and other tricks of the trade, I propose to formulate the criteria, which could be used in the answer, simultaneously with raising questions.
In particular, Neutron, could you please formulate what behavior of the price you call random and what you call non-random. And, if these are qualitative in nature, could you also formulate a quantitative criterion for the non-random behaviour of a numerical series.
Don't jump to conclusions about what can and cannot be applied. You don't know that! You already have a similar experience (13.11.06:52).
And if you're going to put beginners on the right path, then write on websites honestly that "only 1-5% of you will succeed in something, and it's likely to be bad and not always good".
About the 1-5% of course you are absolutely right! It is simply extremely difficult to believe in it without an explanation - it is just his psychology. Although explanations do not always help either - look at the website mql4.com every day from branch to branch asking the same questions that have been answered a million times in detail, but people still think they are smarter than their predecessors ;o))). Pure psychology.
Well, as for parabolas, the following can be said. Parabolas are just an attempt to move away from non-stationarity of periodic regularities appearing on Forex. Parabolic regression does not care about frequencies of a sample. It simply shows areas, in which the price, in its opinion, is at its extreme positions. Of course not everything is always what it should be from the point of view of a parabolic regression, but this is the stochastic nature of Forex market itself, which cannot be conquered, but only possible to adapt to it somehow by building a strategy.
More than six months ago, I came to the idea that oscillators, whose main task is to display some periodic patterns in the market, fail to cope with their main task due to non-stationarity of cyclic features of the market, as mentioned above. The only application I could find for oscillators is detection of the turning points of the market when it is possible to say with a very high degree of probability that the price will not be lower or higher than this or that level in 1-2 hours. At that time I implemented a simple Expert Advisor based on this principle and it is now participating in the MTS Championship https://championship.mql5.com/2012/en. In the Championship the risk of the Expert Advisor is very high to make it show something. But in practice with low risk the winnings can be compared to the bank interest. At the same time he can lose quite a lot. That's all I was able to apply more or less successfully to oscillators with fixed settings (fitted on historical data). Since we selected a very high "tipping level" during optimization in order to obtain the maximum percentage value of winning/lossing positions, we see a very small number of deals according to the Expert Advisor's results. That is how many "tipping points" there were during the Championship in terms of parameters fitted to the history. I am monitoring the work on a test demo account - everything coincides with the accuracy of +/-2 pips.
In particular, Neutron, could you please formulate which price behaviour you call random and which non-random. And, if these determinations are qualitative in nature, could you also formulate a quantitative criterion for non-random behavior of a numerical series.
There is nothing more contrary to reason and the constancy of nature than randomness. God himself cannot know what happens by chance. For if he knows it, it will definitely happen, and if it definitely happens, it is not accidental.
Cicero. On devinatio.
Correlation moments is a quantitative measure of the degree of statistical relation (mutual dependence or correlation) of random variables Xi and Xj. The concept of correlation coefficients is also used as a dimensionless normalized characteristic of the degree of correlation of random variables. The values of correlation coefficients r range from -1 to +1. If r = 0, random variables are considered to be independent of each other, and if |r| = 1, they are fully correlated (e.g., the variables X = b*Y with an arbitrary value of b); in all other cases the closer |r| is to 1, the greater the correlation between random variables that may be either forward or backward (r<0). By the way, if correlation coefficients of statistically independent random variables are always equal to zero, the inverse statement about statistical independence of random variables if their correlation coefficient is zero is true only for Gaussian distributions and is insufficient in the general case.
A special case of the correlation function is the autocorrelation function (AFC), which is widely used in signal analysis. It is a statistically averaged product of centered (residual) random function values at time moments ti and tj and characterizes the fluctuational component of the process.
Properties of autocorrelation and autocovariance functions.
1. The maximum of the functions is observed at t=0. This is evident, because at t= 0 the degree of correlation of samples with itself is calculated, which cannot be less than the correlation of different samples. The value of the maximum of the covariance function is equal to the average power of the signal.
2. The autocovariance and autocorrelation functions are even: r(t) = r(-t). To put it differently, the mixed moments of two random variables X(t1) and X(t2) are independent of the sequence in which these quantities are considered, and are respectively symmetric about their arguments.
3. At t tending to infinity FAC values for signals finite in energy tend to zero, which directly follows from the physical meaning of FAC. This allows to limit FAC length to a certain maximal value tmax - radius of correlation, beyond which counts can be considered to be independent.
4. If we add a non-random function f(t) to the random function X(t), the correlation function does not change.
Calculation of FAC
Let there be a residual time series consisting of terms x(i), where i runs from 0 to n.
Then the degree of relationship between the members of the series spaced at distance t is defined by the formula:FAC=SUM{x(i)*x(i+k)}/SUM{x(i)^2}), where i spans values from 0 to n-k.
This results in a single value between -1 and 1. The criterion for randomness is the degree to which the result is close to zero. The answer to the question "how close is it?" can be obtained by processing a RARE time series of the same length, and collecting sufficient statistics. From my own experience I can say that the value of greater absolute value of 0.1 is of practical interest.
Of particular interest is the analysis of the FAC of the currency instrument on the time frame 1 min, 2 min, etc. to, for example, 100 min. I am attaching the correlogram. It shows a red line with blue dots for EURUSD 2004, blue line with red dots for EURCHF, turquoise line with blue dots for EURGBP, black crosses show the FAC of a time series generated by integration of a stationary RARE value whose distribution function and standard deviation are identical for EURUSD. Time frame in minutes is plotted along the abscissa.
You can draw your own conclusions.
Thanks for the very interesting results! I haven't come across such a study yet!
Judging by the image I understand that we can conclude that some kind of prediction is possible only for a short period of time, for example up to 100 minutes? And different currency pairs have different forecasting potential? In other words, judging by this picture EURUSD is very inefficient for making forecasts? This is a very interesting conclusion, because I think that most traders play exactly EURUSD. On the other hand it is very interesting to conclude from this picture that EURCHF and EURGBP pairs are more promising for making forecasts for them. Usually almost nobody plays these pairs. Traders simply believe that they are "low volatility". Really, average volatility measured as a ratio of the High-Low to the average price during a daily period is approximately the following:
EURUSD 0,8%
EURCHF 0,3%
EURGBP 0,5%
. How do you think these values may influence "predictability" of a currency? Looking at this picture we can assume that higher volatility may lead to higher unpredictability of the currency, at least for a given time interval up to 100 minutes?
Or maybe I misunderstood something, then please correct me.
PS: Speaking of which, could you present similar pictures for the other currencies available on Forex? It would be very interesting to get similar results for currencies according to the above principle. I am "dabbling" with calculation of correlations for the last month too in order to use them for forecasting. I am testing the following idea. We take a sample of some length and compare it to samples of the same length in history. Calculate the correlation coefficient. Select a sample in history with the maximum correlation coefficient. And then we draw that part of history that follows the most coinciding sample into the future, having of course recalculated it relative to the current price. Of course, for a forecast I am building an averaged forecast sample of several lengths to "increase the probability of hit" ;o). The principle itself is probably reminiscent of neural nets in a great distance. Something is compared with something and something is inferred on this basis. Only this principle is extremely simplified - only the correlation coefficient is compared and there is nothing more! It turns out to be interesting. So far I am collecting statistics by trading according to this principle on penny real. Maybe something will turn out as a result?
In short: on the determinism of random processes. I liked it a lot at the time.
I think all the parts are here, including the first part (Foundation) - http://www.izb.su/azimo/..%5Caut76a12.html
Thank you for the details. Now I understand better what we are talking about. :-)
I still have a few more clarifying questions. With your permission.
As far as I understand, centring is done by subtracting the mean (mathematical expectation) from the whole series. So ? The values of a random function at times ti and tj are two numbers. How is the statistical averaging of their product done ? I thought that FAC is a function of one argument and that argument is the interval between xi and xj, which is actually (ti - tj). How is it really like ?
There are too many letters here. :-)) The distance t is not used anywhere in the formula. If t and k are the same, then it makes sense to me. And it corresponds to my understanding of FAC. If not, then explain what it is.
How did you generate this random value ? How to calculate the EURUSD skew on a certain section of history I have an idea, but I can't even guess where to get the distribution function of the eura from. Please share the information where you got it from.
One more question. It concerns your use of the word "timeframe". Generally, in MT4 this word means "time division price" on the chart, i.e. what period of time corresponds to one bar. However, from the context of your post I understand that you mean the time interval t, for which the correlation coefficient is calculated. And the totality of these values for all t is FAC. If it is not so, correct me.
One last thing. You did the calculations on the 2004 history. What data did you use: M1, M5, etc. ?
My meticulousness has a definite explanation. Not so long ago, tired of the scientific poke method, I thought that there must be some objective methods to evaluate whether a particular TA tool has some (e.g. predictive) value or not. In general I came to a conclusion that such estimation can be a function of correlation of the instrument with the price. And the criterion is the condition that this function is greater (modulo) than FAC. Do you think it is possible in principle?
The indicators may be of interest, for which the correlation function has a maximum in the future. And the corresponding interval is the optimal forecast interval. It's not clear which one is more valuable: maximum of FC or maximum of difference (FC - FAC).
In short, I have outlined a program of research, but I have not yet begun to carry it out. Firstly, I have not yet finished what I started before. And secondly, I have not eliminated gaps in education yet. So I am very glad to see you on this forum. I hope I didn't bug you with questions. :-)
PS. Judging by the quotation Cicero was an ardent atheist. In any case he had no idea of dialectics.
And his idea of what is God, too, probably, did not shine with depth. If, of course, he said it sincerely. :-))
EURUSD 0,8%
EURCHF 0,3%
EURGBP 0,5%
. How do you think these values may influence "predictability" of a currency? Judging by this picture we can assume that higher volatility may lead to higher unpredictability of the currency, at least for the specified time interval up to 100 minutes?
Or maybe I misunderstood something, then please correct me.
PS: Speaking of which, could you provide similar pictures for the other currencies available on Forex? It would be very interesting to get similar results for currencies according to the above principle. I am "dabbling" with calculation of correlations for the last month too in order to use them for forecasting. I am testing the following idea. We take a sample of some length and compare it to samples of the same length in history. Calculate the correlation coefficient. Select a sample in history with the maximum correlation coefficient. And then we draw that part of history that follows the most coinciding sample into the future, having of course recalculated it relative to the current price. Of course, for a forecast I am building an averaged forecast sample of several lengths to "increase the probability of hit" ;o). The principle itself is probably reminiscent of neural nets in a great distance. Something is compared with something and something is inferred on this basis. Only this principle is extremely simplified - only the correlation coefficient is compared and there is nothing more! It turns out to be interesting. So far I am collecting statistics by trading according to this principle on penny real. Maybe something will turn out as a result?
Solandr, you got it right! That's exactly the conclusions I can draw when analyzing the results. Indeed, the reliability of forecasting of one or another tool decreases exponentially rapidly as the forecasting horizon increases. I purposely did not display the data with a timeframe of more than 100 minutes not because I'm hiding something of interest but due to the fact that there is statistical zero in this part of the correlogram. I would like to note that these conclusions go against the common methods of TC, based on the assertion about the feasibility of using large investment horizons. One can surmise where the roots of such claims stem from. The matter is that a person realizing the importance of having the return exceeding the spread of the DC in each transaction intuitively tends to work at times when the instrument volatility is much larger than the existing spread and thus he/she completely ignores the statistical nature of returns. Yes, in each individual transaction it gains or loses to the market much more than the spread, but adding together all the gains and losses and relating the obtained value to the number of trades, we see with horror that the average return is much less than the miserable spread! Because the average yield is determined not by the instrument volatility, but by its product of the FAC. This point is not considered... by anyone.
Solandr, the average volatility you obtain, measured by the ratio of the High-Low to the average price on a daily period, does not affect the "predictability" of a currency. On the contrary, it is a consequence of predictability under negative FAC.
Almost all of the pairs I examined in the FAC fit into the range shown in the figure. It is interesting that the Eurodollar is the most unpredictable pair! If you want to build correlograms for other instruments, you can use the expressions I gave.