Distribution of price increments - page 7
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I think in the case of a non-Markovian process you have to trade against the trend, but for a Markovian process you have to trade along the trend.
That's weird. I thought it was the other way around. The trend is the memory effect of the process (the dependence between observations). While the Markov process is a non-memory process. Correspondingly, it is necessary to trade with a non-Markovian process along the trend, and against the trend - with a Markovian one.
Only in practice the nature of quotes is likely to change back and forth.
That's weird. I thought it was the other way round. A trend is the effect of process memory (the dependence between observations). And a Markovian process is a memoryless one. Correspondingly, we should trade with a non-Markovian process along the trend, and against the trend - with a Markovian one.
Counter-examples for those who like to "think":
If the AR(1) model is followed - both trend and counter-trend trade can work; the resulting process is Markovian. If we add fractional order integration, the process becomes non-Markovian, but both trend and counter-trend trade will work.
The AR(1) model does not have many parameters to know which of them determine whether trend trading works or not, unless the issue is whether the process is Markovian or not.
Dear traders!
At my leisure I have read many threads in this forum - many of them discuss the problem of determining the type of distribution of a random variable returns (the so called price increments). I realized for myself that this problem hasn't been solved and having some :) :) :), appropriate education and skills, I decided to take part in solving this problem.
So, the task definition:
To determine from tick data of a certain currency pair a probability distribution of successive price increments Bid and Ask (i.e. analyzed a data set consisting of the difference between the current and the previous Ask prices and the same set for the Bid price). The formulas for the probability density function, the distribution function and the quantile function of a given distribution must be presented in analytical form.
The task has certainly proved to be difficult. Let me say that this distribution is not one of those widely discussed - neither normal, nor logistic, nor Laplace, nor Cauchy, etc., etc.
Before I tell you this distribution (more precisely, it is a family of distributions, since different currency pairs have different values of the coefficient of scale, which, in general, does not coincide with the standard deviation), please answer me a couple of questions - what exactly does knowing this distribution provide? How does it help in Forex trading?
Sincerely,
Accidentally passing by and interested in Forex market
Alexander_K :) :)
1) It does not help.
2) Not helpful in any way.
Of course, this is the most important question.
I think in the case of a non-Markovian process we should trade against the trend, while in the case of a Markovian process we should trade with the trend.
Next week I will investigate the probability distribution of tick arrival time - let's see what it is for different pairs.
If it is nonexponential - then the processes are not Markovian and vice versa.
I will post the results on the forum.
Forgive me, Alexander_K, but this is, to put it mildly, nonsense.
Forum on trading, automated trading systems and trading strategy testing
The market is a controlled dynamic system.
Oleg avtomat, 2013.06.12 17:35
Strictly speaking, the noiseshould be"red".
This is the intrinsic noise of any "proper" dynamic system.
Turn the amplifier up to maximum volume with no music being fed to the input and we'll hear SHHHHHHHH)).
Strictly speaking, noise doesn't have to be, but can be anything, including "red" and "pink" and "white"... and "gray-brown-raspberry" -- anything.
The same is true for increments.
GARCH models with logarithm of increments as input consist of three parts: a trend model, a volatility model andan incremental distribution model. There is a huge literature about these distributions, their influence on the algorithms, differences of currency pairs by distribution types and others.... The question you raise is one with a 30 year old beard. The main mathematical tool in financial markets is GARCH, of which there are many. In the machine learning thread I gave a selection of literature - I'm clinging to it again.
By far the most widely used is the beveled t-distribution. But I repeat that a complete model consists of three components.
There are off-the-shelf software packages that are widely used in real trading. Results are available in public publications. Of R, fgarch and rugarch may be named, but they are not the only ones.
Dear San SanFomenko.
If you are Fomenko who laid the foundation and developed clusterindicators, congratulations!
However I would like to point out an important aspect of mathematical decomposition
In order to get any distribution of a price function, it must be continuous over time
This condition is axiomatic for all integral and differential functions
This condition of continuity of a function must be fulfilled for any function that we want to differentiate or integrate even further if we want to decompose it in order
Unfortunately the nature of forex is such that in my opinion it cannot guarantee the smoothness and continuity of the price because of the tick nature of its formation
So I think any price distributions you create will either be faulty or at least be a pseudo distribution
Regards Stefan StoyanovFinally some professional comments are coming in!!! I'm very happy about that.
However, it is not customary among engineers to retreat in the face of difficulties - is it? The first thing to do is to reduce the results to a known model. I repeat - not invented, but known.
1. The results I obtain now about the ticking times show that the probability distribution of the ticking times is not exponential.
2. What do you think, if I start to read quotes in time intervals, which satisfy the exponential law, will it help me? After all, logically, I will get a Markov process, with some pseudo-states of quotes, when there was no trade, but the current state of Bid and Ask is considered as coming tick.
Dear San Sanych Fomenko.
If you are Fomenko , who laid the foundation and developed clusterindicators , congratulations
However I would like to point out an important aspect of mathematical decomposition
In order to get any distribution of a price function, it must be continuous over time
This condition is axiomatic for all integral and differential functions
This condition of continuity of a function must be fulfilled for any function that we want to differentiate or integrate even further if we want to decompose it in order
Unfortunately the nature of forex is such that in my opinion it cannot guarantee the smoothness and continuity of the price because of the tick nature of its formation
So I think any price distributions you create will either be faulty or at least be a pseudo distribution
Regards Stefan StoyanovIn this case we are talking about an approximation of a probability distribution. My research shows that the first approximation, the probability distribution of price increments is a Student t2-distribution with the scale coefficient different for various currency pairs and not equal to the standard deviation. I think this is very important information. All that is left is to understand how to apply this knowledge.
All - ran 2 tick reading processes in parallel for EURJPY.
1. by real time of their arrival.
2. at intervals, subject to the exponential distribution law.
Let's see if there will be interesting results.
Congratulations to fans of probability theory!
Indeed, if one reads the ticks not by their real arrival time, but at intervals distributed according to the exponential law, then the pricing process becomes Markovian. Moreover, the distribution of increments taken modulo from it is not clear, it becomes geometrical with p=0.5.
It remains unclear how to apply this knowledge in practice, but it is obvious that we are on the right track.