a trading strategy based on Elliott Wave Theory - page 194
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Yurixx it's not hard to answer, but making predictions is almost the same
like predicting the weather. "Predictor" is a whipping boy :-)))
I currently trade on GBP/USD, the volatility here is higher than on EUR/USD.
Accordingly, there are more opportunities. :)))
Suppose I have two indicators, each of which shows the probability of some event (for example, that the price will go up by at least N points). The indicators are naturally correlated and their correlation coefficient can be calculated. How can we calculate the cumulative probability of an event from these two numbers?
I cannot give a strict proof of my assertion.
In this case we are dealing with the analogue of some binary detector. Let the detector indicate with probability p the presence of a substance in the sample. It is clear that having carried out a sufficient number of measurements N, we will in p*N cases get a confirmation of the presence of the given substance if it really is contained in the sample, and (1-p)*N confirmations of its presence - if it is not there. Thus, with probability close to one (as 1-(1-p)^N), provided we have a sufficient number of experiments N and (1-p)*N*R*N>N, we can establish the truth. For this purpose it is enough to see to what value the sum of detector readings converges, to p*N or to (1-p)*N. It is clear that there is no difference between performing N experiments in succession with one detector or using N detectors simultaneously in one experiment.
This example is not difficult to generalise to the case of an arbitrary probability p[i]>0.5 for each detector in each measurement. By analogical reasoning:
Carrying out a sufficient number of measurements N, we will in SUM(p[i]) (summation is carried out i=1...N) cases get confirmation of presence of the given substance if it really is contained in the sample, and SUM(1-p[i]) of its presence - if it is not there. It turns out that if sum of all beeping indicators tends to SUM(p[i]) or more, the event will happen. If the sum of all signalling indicators tends to SUM(1-p[i]) or less, the event will not occur. I cannot say about the probability of the outcome in this general case - I do not have enough knowledge, but in the special case, the event will happen with probability:
P=1-P(1-p[i]), where the product is conducted over all i=0...N, and p[i]>0.5,
if all N indicators are signalled simultaneously.
Accordingly, there are more opportunities. :)))
It`s strange, I have always considered the volatility of both currencies about the same. And the calculation of the average relative spread of daily bars (High-Low)/Close by days of the week confirms it:
EURUSD_1440_Day_of_Week_1 0.007266
EURUSD_1440_Day_of_Week_2 0.007871
EURUSD_1440_Day_of_Week_3 0.007981
EURUSD_1440_Day_of_Week_4 0,008332
EURUSD_1440_Day_of_Week_5 0.008522
GBPUSD_1440_Day_of_Week_1 0.007224
GBPUSD_1440_Day_of_Week_2 0,007431
GBPUSD_1440_Day_of_Week_3 0.007535
GBPUSD_1440_Day_of_Week_4 0.007863
GBPUSD_1440_Day_of_Week_5 0.008052
To calculate each value, 100 daily bars were taken for the corresponding day of week.
If we take the average absolute value in pips, using the formula (Average Relative Range)*Close[0], then of course this value will be different, because Close[0] is of course different for every currency. But where can "more opportunities" be hidden here - is it completely unclear? Because the stop loss and take profit on GBPUSD will simply be scaled to the ratio between currencies about 1.5 times? So the profitability of the strategy itself will remain the same!
Thanks for the volatility. I would like to ask your help with another question.
Suppose I have two indicators, each of which shows probability of some event (for example, that price will go up by at least N points). The indicators are naturally correlated and their correlation coefficient can be calculated. How can I calculate the total probability of an event from these two numbers?
Thank you in advance.
From New Market Wizards (Eckhardt):
"...Are there other practical implications of robust methods which would differ from the results of studies assuming a normal probability distribution?
- An important application concerns the situation where you have multiple indicators for a particular market. The question arises: how to combine several indicators in the most efficient way? Based on certain precise statistical measurements, it is possible to assign weights to different indicators. However, the choice of weights assigned to each indicator is often subjective.
You will find in the robust statistics literature that in most cases the best strategy is not to weight, but to assign a value of 1 or 0 to each indicator. In other words, to accept or reject an indicator. If an indicator is good enough to be used in principle, it is also good enough to be assigned a weight equal to the others. And if it does not meet this standard, it is not worth bothering with.
The same principle applies to the selection of trades. How do you best allocate your assets to different trades? Again, I will argue that the allocation should be even. Either the trade idea is good enough to be executed - in which case it should be executed in full - or it is not worthy of attention at all."
Feeling dissatisfied with my ignorance of theoretic laws, I quickly wrote a code, which by Montecarlo plays out events, and attached N indicators, each of which with probability p[i] predicts the next event. Then I filtered out those cases where ALL indicators coincided and calculated the percentage of correct event prediction.
What do you think... The probability of correct prediction of ALL indicators ONCE is the arithmatic mean of probabilities of each indicator:
P=SUM(p[i])/N, summation is i=1...N.
Really? I'm shocked!
As a consequence the probability P of the correct event prediction is smaller when several indicators are used together than when one of the most reliable indicators is used! That is, using several indicators together does not lead to a significant increase in prediction reliability.
I don't know, I think I've already stated my main thoughts on spreads here. It's all the same "convergent" regressions of the first and second orders, which I think everyone here already knows....
Not at all, your approach is very interesting. I assumed you would be based on statistics and "by eye" approach. The only thing I can think of is making a "smart window". I.e. our task is to control the current trend, and hence a possible reversal zone, using, for example ATR (it will need a little rewriting), therefore the algorithm may be the following (presenting the gist of the idea):
1. searching for the current trend (or rather, some interesting price movement)
2. we find a bar, symbolizing the beginning of a trend (movement)
We fix (calculate, fix) a window for this movement relative to the found bar
4. we move together with the price and look when the ATR comes to the border
5. it has approached - possible reversal
6. end of trend - look for a new one, repeat everything
Haven't tried it yet, other work is planned, but I will do it soon. I.e. it's like some way of eliminating the delay that comes with using a "hard" window. Or am I missing something, something very important in ATR?:o)
Yurixx, I remembered what row centring is! If I'm not mistaken, it goes like this. You have a series:
X[0], X[1], X[2], X[3], X[4].
The centred series is obtained as follows (it's easier with a formula than with words):
X[0], no value
X[1]=(X[0]+ X[1]+ X[2])/3
X[2]=(X[1]+ X[2]+ X[3])/3
X[3]=(X[2]+ X[3]+ X[4]/3
X[4] has no value
Avals
Hooray, it means I'm not the only one. I mean, I've read a lot of articles praising volatility, but I don't really understand what it gives me. :о)
For example, http://forex.kbpauk.ru/showflat.php/Cat/0/Number/40044/page/0/fpart/1/vc/1
Avals, thanks, interesting stuff.
Neutron
Consequently the probability P of a correct event prediction when using more than one indicator is less than when using the most reliable indicator alone!!! That is, using several indicators together doesn't lead to a noticeable increase in prediction reliability.
Quite right. This is exactly the reason why, when analysing Vladislav's strategy, I left the Hurst indicator only as the main (reliable) indicator and abandoned the "competing" approach of selecting reliable channels.
P=SUM(p[i])/N, summing is i=1...N.
Really? I'm shocked!
As a consequence the probability P of the correct event prediction when using several indicators simultaneously is less than when using the most reliable indicator alone!!! That is,using several indicators together does not lead to a significant increase in prediction reliability.
Well...
I liked the conclusion of previous post better. :-))
Probably because I myself was guided by the formula
if all N indicators are triggered simultaneously.
Maybe really using multiple indicators doesn't increase prediction reliability ? I don't know. However, my physical way of thinking does not want to agree with this conclusion. Something inside me tells me that there is something wrong here.
If indicators were independent I would be inclined to rely on the formula P=1-P(1-p[i]). However, since all indicators are based on price series, it is likely that they are all dependent to some extent. This is why I could not accept this formula unconditionally. And that's why I also wanted to get some refinement of it with the help of the correlation coefficient.
The conclusion that the probability is defined as an arithmetic mean is not satisfactory to me for the same reasons. An elementary analysis of the physical meaning of the situation says the following.
Suppose the probability is indeed calculated as the arithmetic mean of the two (for certainty) probabilities p1 and p2. If these two indicators are completely correlated (i.e. coeff = 1), then p1=p2=p0 and (p1+p2)/2=p0 seem to be correct. But if coeff =0, a contradiction arises. Since p1 and p2 are independent, we can measure simultaneously. And then, in the limit of large numbers, the ratio of positive outcomes to the total number of outcomes should tend not even to the 2nd, but to the 3rd limit: p1, p2 and (p1+p2)/2. There is something wrong here.
Unfortunately, I don't know the Monte Carlo method. But maybe it's the algorithm that reproduces it?
Just like a random number generator actually only generates a pseudo-random sequence ?
Maybe the matter is that these N indicators are not independent, i.e. correlate with each other?
Or maybe my considerations are wrong?
As for the existence of a correlation between the indicators and the main conclusions on the grounds that they are all derived from the same primary series, I disagree for two main reasons:
1 it is certain that not all indicators will depend on each other (e.g. ATR and any of the MAs). This is easy to check.
2 there is a fundamentally different use of these indicators themselves, and consequently conclusions (e.g. MACD and the same MA)