Market etiquette or good manners in a minefield - page 8
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Writing. The spread is subtler here: monkeys play their part. And the system has to be Bernoullian in terms of transaction results. Otherwise the estimates will be inaccurate. But I have not reached a purely analytical solution.
I am so far only able to draw certain conclusions about Bernoulli systems. There aren't too few of them really. Non-Bernoulli systems are harder to model - apparently Markovian processes have to be involved. The apparatus for analysing such systems will be more difficult.
P.S. This is often the case - flipping a coin, but asymmetrical. I mean a sandwich.
I am so far only able to draw certain conclusions about Bernoulli systems. There aren't too few of them really. Non-Bernoulli systems are harder to model - apparently Markovian processes have to be involved. The apparatus for analysing such systems will be more difficult.
P.S. This is often the case - flipping a coin, but asymmetrical. I mean a sandwich.
Got it. I've been working too hard. You can also set the probability at 0.9. I'm stuck on 0.5. ))
1. I don't know, Sergei, the question is very non-trivial. In my article on sandwiches I pointed out the gold mine that I had struck upon - Bernoulli systems.
Let me reread your article again - I'll try to swallow your culinary masterpiece whole :-)).
By the way, here's another thing: in the formula for deposit growth
member
is responsible for the characteristic time of deposit doubling (time quantum is equal to tau - timeframe for which volatility was estimated). We can see that an important parameter determining this time is the square of the ratio of the selected instrument volatility to the spread. By this parameter we can estimate "attractiveness" of an instrument. The higher this parameter is, the better the instrument is. I estimated this parameter for 33 symbols presented by Alpari:
Here the first column shows the spread, the second column shows the hourly volatility, the third column shows normalized relative volatility and the fourth column shows its normalized square. The data in the columns is ranked in descending order of volatility.
Thus, EUR/USD is the most attractive pair in this sense - its level is considered as 100%. GBP/USD is the next one with the value of 59%. Looking at the last formula we can see that, all else being equal, the time required to double the deposit at this pair is almost twice longer than at EUR/USD. Remember, this same formula for estimating the doubling time includes the fourth parameter p characterizing the predictability of the instrument. Its consideration can greatly shift this estimate. It's very important to learn how to make the limit p-estimate proceeding from general considerations and time series properties without using the experimental "scientific gut feeling" method (life is not enough). Such a method would be a real breakthrough. There would be a theoretically grounded predictability limit for the selected symbol, knowing that, until a certain moment, it would be possible to improve the TS for its correspondence to the ideal!
I have done a parameter estimation for 33 instruments presented by Alpari...
Useful analysis. >> Respect! ;)
Unfortunately, I have not been able to implement any way of estimating predictability ( p parameter) for price-type time series. I was going to use "immersion" method as the main idea, as described in "Predicting financial time series" by Ezhov, Shumsky. However, either the authors are deceiving themselves, or my hands are crooked - the result is definitely sloppy... In short, I decided to give up indirect estimations and decided for myself that as soon as the neural network is the optimal catcher of various explicit and not explicit regularities, let it catch them, while we at the output of NS will only calculate the relative number of correct price movement directions guesses, i.e. we will estimate p parameter (see above post) by direct methods. Of course, it's not certain that NS will catch everything that is buried in the price, but for lack of the best - let's consider it the best!
For this purpose I sharpened a simple Perseptron with the number of entries d, which serve as the algorithm's parameter, and divided the time series into several trading horizons with minimal step of 10 points for EUR/USD and 5 points for EUR/GBP during this year. The opening prices of one-minute bars were taken for the analysis, and the sign of the vigorous movement was predicted. Then, the number of guessed directions was calculated and related to the total number of directions. The obtained value was divided by 2, this is the required parameter p.
It can be noted that BP EUR/GBP has much better predictability than EUR/USD. Perhaps, this is the reason why some traders have chosen this pair at the Championship as the most promising one. At p=0.04, sigma=18 points/hour, Spread=2 points for EUR/USD, and p=0.15, sigma=8 points/hour, Spread=3 points for EUR/GBP (see the table above), the ratio of typical times of deposit doubling for these pairs can be estimated by the formula (see above):
It turns out 17 times, in other words, all else being equal, the difference in predictability of these GPs allows you to deposit at the rates different almost 20 times more in favor of EUR/GBP! Using the formulas given above, you can estimate the optimal values for H - average size of the bribe and L - optimal leverage. So, for the EUR/USD pair H=50 pips, L=8. For the EUR/GBP pair H=20 pips, L=75.
No, it's not. In the comments to that article, I wrote that it's not enough to determine where price moves + or -. You need to be able to extrapolate that movement over some time horizon into the future. NS does not know how to do that.
The market is undoubtedly a complex, dynamic system, with its own laws, which as a rule have little in common with the laws of physics. But one thing is more or less certain - it is important for us, as direct participants of this weakly predictable process, first of all to know in what direction the price will go, second - how many points it will pass in this direction, and, perhaps, only in the third - how long it will move in this direction. Really, look again, Sergey, at the expression for the profit rate:
It follows that the accuracy of the expected direction of movement determines the rate of return as the fourth degree, the amplitude of this movement affects the rate of return as the second degree and the time during which this movement exists enters linearly. I.e. a 2-fold decrease in the accuracy of the forecast p will decrease our profitability by as much as 16 times! Forced to work with the amplitude of the expected movement half as much as you wanted - get a fourfold decrease in profit. Note that we are not talking about the necessity of predicting the amplitude as such, we only need the average value of this parameter, and you understand that it is not a problem to determine, it is an inertial indicator (a stationary parameter). Time will absorb everything (or almost everything) and we also do not need to predict this value at each step, it is enough to know the average value.
From all said, I do not quite share your pessimism concerning inability of NS to extrapolate this movement on any time interval, it is not a defining, key moment in such statement. It is much more important to throw all powers of intellect (and not only your own) into improving the accuracy of predicting the sign of the expected movement.
I was able to build an "estimator" of explicit and implicit patterns in BP based on NS. Now, by setting this beast on kotir, it is possible to estimate approximately parameter p - characterizing predictability of instrument and changing from 0 - random process, to 1/2 - completely deterministic system (unambiguously predictable).
Here are examples of estimates. In fig. on the left, there is a dependence of predictability of BP EURUSD on the trading horizon H (a characteristic scale of price change). The estimation of predictability from above (maximum possible) is shown in red, what my "optimal" neural network was able to detect is shown in blue. The estimation process is resource-intensive enough, so I will give full information for all tools shown in the table in a few posts above, only in a few days.
As for the given data. We can see that eurchf is more attractive for the forecasting than eurusd as it contains much more regularities in the instrument's price behavior. Attention should be drawn to the growth of predictability of this pair with decreasing lag, which makes the pair more attractive for potential pipsers. In general, it may be stated that eurusd is characterized by the parameter p=0.04 and if we use the above estimate for the optimal H (in the sense of MM), we will get
Hopt=Spread/p=2/0.04=50, it is an optimal size of the take in points.
Optimal leverage:
L=(S/Spread)*p^2=10^4/2*0/04^2=8
Typical time of deposit doubling when trading with this optimal MM:
t=tau/sigma^2*Spread^2/p^4, where sigma is the volatility of the pair on TF=tau. Let's take a pre-crisis variant: sigma=70 points/day, tau=day, Spread=2 points. Then,
t=1/70^2*2^2/0.04^4=320 days - approx. time of deposit doubling (of course, if I haven't screwed up somewhere).
It is much worse for eurchf pair. Although, the pair predictability is high, but the spread is equal to 3. At such parameters there is no area where with available p(H) (see Fig.) the optimal H is not larger than the current one! In other words, the pair is not promising.
I made an assessment of the predictability of p (ordinate axis) financial instruments available in the quotes archive of Alpari. The calculation was performed for different trading horizons expressed in points (abscissa axis):
The black line on each diagram shows the border of profitability, which conditionally divides the profitable from the unprofitable area. If you want the TS, which exploits patterns that are hidden in quotes, to show profitability in a statistically reliable manner, the blue bar must exceed the profitability level. The boundary was drawn according to the first formula in Fig. (second is its marginal variant for p<1/2).
For each symbol we can estimate a characteristic time of the deposit doubling - tau2, while maintaining the optimal MM (parameters H and L) that depends on the instrument volatility - sigma, on the characteristic time interval - tau, its predictability - p, and commission of DC - Sp (the last formula in the picture). Which I will do a little later.
Thus, it will be possible to quickly assess the prospects of working with this or that instrument without wasting time on writing TS, building MTS on its basis and waiting for the results of trading on a demo account.