a trading strategy based on Elliott Wave Theory - page 190
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As far as I understand, the centring is done by subtracting the average (mate expectation) from the whole row. Right ? The values of a random function at moments 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, i.e. actually (ti - tj). What is actually the case ?
It can be shown that the time series of a currency instrument does not contain stationary trends, so the centering procedure can be simplified by not calculating the average, but subtracting the previous one from each term of the initial series: x[i]=Open[i]-Open[i-1], then we find the FAC using the formula
formula:FAC=SUM{x(i)*x(i+1)}/SUM{x(i)^2}). [1]
Then, Yurixx, it all depends on what we want to investigate: if we want to plot the dependence of FAC on timeframe, we need to generate time series M2 from the available M1 and apply the formula [1], and so on up to timeframe t. This is how the FAC from the timeframe shown in the picture above was derived. Lego show that in this case FAC(t)=SUM{x(i)*x(i+t)}/SUM{x(i)^2}). As you correctly pointed out, I misused k instead of t, post above, and misapplied the term "correlogram" to it. This term is correct to use in relation to a function constructed as follows:
Take a centered time series, for example x[i] for M1, and find pairwise correlation coefficients for members of this series lagging behind each other by k bars:
r[k]=SUM{x(i)*x(i+k)}/SUM{x(i)^2}). This series will be sign-variable and show the dependence of the value and sign of the current bar from the bar to the left of it on the time axis by k steps. In this case we are dealing not with a single correlation coefficient that characterizes a pseudo-random value, but with a vector. This vector reflects statistical dependencies of price formation mechanism more completely.
1. change the required time frame, for example 3 min,
2. create the series x[i]=Open[i]-Open[i-1],
3. calculate the number of elements in the obtained series equal to -n points, -n+1 points,... -1 points, 0 points, 1 point, ... n-1 points, n points. We should plot the obtained histogram that is a distribution function, e.g. EURUSD 3 min 2004 by amplitude.
I want to draw your attention to the fact that it is not significantly normal; the distribution is rather exponential. This effect is stronger the smaller timeframe we use and it explains the presence of "fat tails" in the distribution. We know from statistics that a non-Gaussian stationary distribution of a random variable must have some mechanism to maintain it... mind you, an artificial one! All this is evidence in favor of the priority attention of a trader to studying peculiarities of price behavior on small timeframes. In the Forex press and literature, we often come across opinions about uselessness of working on small timeframes, about market noise that prevents us from recognizing any trends... It's a paradoxical situation. Isn't it?
I am expressing here my personal opinion only, and I will be very glad to receive constructive criticism.
So I am very happy to see you on the forum.
Thank you.
I don't think you can theoretically "show that the time series of a currency instrument doesn't contain stationary trends". And practically you can only show it on some piece of history. Which is really of no value whatsoever. You can always find significant sections where it holds, as well as those where it doesn't.
For example, you did your research on the history of 2004. According to my DC
01.01.2004 Open=1.2567;
03.01.2005 Open=1.3500;
If we sum up the series obtained on the basis of this statement, we will simply obtain the difference between the first and the last Open prices. As we see, it is almost 1000 points. There are approximately 250 trading days in a year. That is, the average you neglected = 4 pips approximately. I don't think this series can be called centered.
And if you take the history from 2002-2004, the difference is about 4500 pips (i.e. an average of 1500 pips per year). Doesn't it look like a stationary trend? :-) Moreover, I personally believe that this trend is not over yet and we still have so much more to go.
About the timeframes, FAC and correlogram, thanks. It seems to me the correlogram can of course be seen as a vector, but it can also be seen as a function. I don't know about sign-variability, but r[k] should decrease with increasing k no worse than FAC. If it really has the property of sign-variability and its cyclicity is more or less stable, then it can be used.
I fully agree with you. That's why I do all my research on M1 and only if I get something interesting do I compare it with other t/f's.
By the way, here's a recent example of what you're talking about: "MQL4: Nightmare on MT4".
In theory the histogram of distribution you cite should not be symmetric. At any rate, the areas under the right and left halves should differ by these very 1000 points.
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 studied 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.
Neutron, your conclusions about predictability of instruments and effective period based on autocorrelation function have little relation to real trading. Even if currencies behaved like your chart for SB, that wouldn't say anything either. It just tells you that prices do not depend linearly on the prices of k bars backwards over a long period of time.
First of all, no one is forcing you to trade continuously and close after k bars :). You are in fact only guided by price dynamics. Like this: 1. if prices rise or fall, then this dynamic will continue during k bars, and 2. on the contrary - if prices rise or fall, then they will reverse in k bars.
This is too primitive and will not give a statistically meaningful result. A fixed window of k does not reflect changes in price movements. A head-to-head statistic on the whole price series mixes everything up and gives an "average hospital temperature". Trading requires discretization of specific situations. The input is not limited to price differences over fixed periods, some price levels can be determinative, etc.
Therefore, IMHO, the conclusion may be roughly as follows:
Without more information on EURUSD it is impossible to say statistically reliably from the price dynamics (rise or fall) whether the current dynamics will remain or change to the opposite in k bars. But that does not mean that EURUSD is more or less suitable for trading, and it does not say anything about its trading horizon.
Of course you are absolutely right about the 1-5%! It's just that without any explanation it is extremely difficult for a person to believe in it - that's just his psychology. Although explanations do not always help either - look at the mql4.com site where they ask the same questions over and over again, which have been answered in details a million times, but people still think they are smarter than their predecessors ;o))). Pure psychology.
I don't know what the same issues you're talking about are. I was writing about spectral analysis. In the post to which you responded, I was only suggesting to use the power spectrum as an additional criterion. In my opinion, this is no worse than, for example, this criterion (and also has more justification):
...The RMS of the whole sample should not exceed the RMS of the first 2/3 of the sample (as the beginning of the sample we consider the oldest count in relation to the current time belonging to this sample)...
Vladislav's approach, I liked it very much. But studying it, I gradually abandoned the chosen criteria and the method of selecting stable channels. I have left only Hurst index, and that is not how I calculate it. I am deeply convinced that it is not Hearst that "noises", but the method used.
Regarding oscillators and parabolas. You have much better results than I do. I can't even identify the tipping point using oscillators. I don't know why you think I use them. And I can determine the tipping point, just in zone A (page 91 grasn 02.12.06 16:06) based on (among other things) spectral analysis. Perhaps I'll post the results soon. So far, the only important problem is that I cannot put the analysis "on automatic". I can see it with my eyes, but I haven't come up with an algorithm for automatic analysis yet. I have not changed my views concerning parabolas, I still do not consider them to be of much importance for price prediction.
Neutron, thanks for the research results. Very interesting. But let me disagree with you that price forecasting is possible for a small number of counts ahead. As I see it, it is not possible at all for any currency pair. I mean the movement of the price itself. I tried almost all possible (available) methods of price series forecasting (that is implemented in professional software) and I realized that nothing really works. Especially on one-minute charts.
Earlier I used autocorrelation just for predicting price movement. It was based on the well-known rule: the slower the autocorrelation series converges, the more reliable the sample for the forecast. In itself, a very good criterion, which I kept.
The only correct one, in my opinion, is "catching" local trends/channels and only them.
I also didn't suggest in any way that you use oscillators! Where did you get that from? I simply expressed my view on them in one post. Some people like to multiply several posts in a row for 1 paragraph, while I prefer just to state everything in one post, which in general corresponded to one topic - non-stationarity of cyclic processes in the market. But in principle it doesn't matter at all.
I'm not imposing parabolas on anyone at all! I'm just sharing what I use in real trading - that's all. After all, everyone has their own bicycle anyway! ;o) Their great variety is particularly well represented in the Championship. I, for example, was unpleasantly struck by the unfortunate performance of https://championship.mql5.com/2012/en. He is probably a very experienced specialist in Fourier analysis and other things related to market wave processes. Of course I do not know what exactly was the problem of this expert, but so far I do not have much desire to deal with the spectral analysis after such a result. I think the author is quite a weak Expert Advisor compared to my toy with 170 lines of code on one oscillator. And then at the very beginning of the Championship he was very much worried about his first unsuccessful transaction that, he believed, was solely the fault of the Championship organizers. But now we can see that there is something wrong with the Expert Advisor itself. Maybe he will show something more successful at the next championship? Let's wait.
Failures do happen, but in my opinion, you shouldn't judge a whole method by a single game. You wrote that you don't know what the EA's problem was, and I, in turn, don't even know what principles the EA is based on (I couldn't find a description). Whether the Fourier analysis is used there, where it is used, etc. These are, of course, details, but they determine the final result.
Completely agree! I haven't formed any opinion on the spectral method yet. I just need some real data, other than theoretical assumptions, to begin to form one. So far I have no such information. It is very possible, that in 2-3 months you will present a statement about work of your method on demo (Thanks in advance!)
I am constantly checking and collecting some information about other methods myself. It's still impossible to cover everything. I have to apply my own, perhaps very subjective, limitations on research in one direction or another. It is quite possible, that someday I will be engaged in specular analysis as well. I think everyone goes the same way. By trial and error. No one has any other options anyway!
Of course I will. True, there's still research ahead and the transition from MathCad to MT. Can't estimate how long it will take yet. Probably going to leave everything in MathCAD. To be honest, a little bit broke my word to myself to temporarily stop trading after my superficial forecast (91 pp grasn 04.12.06 18:17). I analysed it in details, believed in reliability of the channel I found and made some profit. But this, first try. :о)
I am constantly checking and gathering some information about other methods myself. It's still impossible to cover everything. I have to apply my own, perhaps very subjective, limitations on research in one direction or another. It is quite possible, that someday I will be engaged in specular analysis as well. I think everyone goes the same way. By trial and error. No one has any other options anyway!
Totally agree! That's the reason why I'm using MathCAD now. Saves a lot of time, given that I can't devote all my time to research.
Sorry for the flub, but I couldn't resist. According to the evidence of the TV show "Let them talk" (ORT) the above mathematician Perelman lives in absolute poverty and works as something like a loader in a vegetable shop. Not only did he not have the money to go for the prize, he simply was not allowed to do so. In his place, some random bureaucrats or thugs came to the ceremony hoping to steal the money. When they (of course) refused, they declared Perelman insane and said he didn't want to get a million quid. Woah, woah, woah, woah, woah.
Forgive me, dear grasn, but I independently investigated your proposed method and found no significant "twitches" of Hurst parameter, I used a standard "classical" formula, mentioned in many textbooks. The values never exceed 0.5. Hearst calculated as you say, sequentially for each channel. Either you are not telling the truth or the "twitches" are caused by glitches in MQL4.
Neutron You have said that you are dealing with neural networks. How do you think they are applicable for making forex forecasts? And what is the outlook for their application in forecasting? After my attempts (not without success) to reproduce Vladislav's system I finally started to work with neural networks.
Neutron You have said that you are dealing with neural networks. How do you think they are applicable for making forex forecasts? And what is the outlook for their application in forecasting? After my attempts (not without success in general) to reproduce Vladislav's system I am now very much interested in neural networks.
Dear Alien, there are no glitches. I used MAthCAD for calculations and did not use MT, unless you count my first version of indicator posted on page 30 of this thread (implemented in MT). But even there, I didn't find any glitches in MT operation. The basic algorithm of its work is stated there too.
You have written an amazing indicator, following which you can save all your money (just kidding, just in case). I can not say anything about your figure, for the simple reason that I met a lot of formulas for its calculation, but, for example, Neutron calculates it quite differently.
I'm going to cut in a little bit to your question addressed to Neutron. I am very fond of neural networks and I want to say everything that I think about them in a nutshell. It is a big mistake to predict the price of NS itself. Nothing good comes out of it. This is my own opinion, and not at all a reason to invite you to a discussion on the subject. I've spent a fair amount of time on it and don't want to increase it. :о)