Market phenomena - page 30

New comment
 
gpwr:

At first I am interested in a question: taking a signal which is known in advance to consist of a linear combination of a finite number of unknown basis functions, is it possible to find these basis functions and the coefficients of this linear decomposition?

Why a linear combination? It is a simplification of the same order as the known set of basis functions that you want to avoid. It is my belief that the market is non-linear. The hysteresis loop comes to my mind the most for some reason to describe it, only it sort of still has different energy levels - it can expand and contract.
 

I agree that the market is non-linear. Various books and articles describe at least three different methods of accounting for this non-linearity:

  1. Nonlinearly distort the price series at each time interval and describe it by a linear combination of basis functions
  2. Nonlinearly distort the basis functions (i.e. generate in advance a wide set of these functions and their distorted versions) and describe the price series by their linear combination.
  3. We describe the price series by a non-linear combination (e.g. a polynomial) of the basis functions.

I will think about this later, after I figure out the algorithm for finding the basis functions themselves from the signal consisting of their linear combination.

If someone wants to help in this direction, here's a simple example from the link.

  • Take a random sequence of +1 and -1. This is our initial digital information. Let's denote it by I[k] where I[0]=+/-1, I[1]=+/-1, etc.
  • We replace each +1 by f(t/4-k) and each -1 by -f(t/4-k) and get signal s(t) = SUM( I[k]*f(t/4-k), k=0...999 ), where basic function f(t/4) is sinc-function f(t/4) = sin(pi*t/4)/(pi*t/4) defined on interval t = -20...+20. The signal will look like this

  • Input this signal to the input of our algorithm for search of the basis function and get

I will repeat it again. This example has little to do with the market that has more than one basis function and where there are non-linear distortions. But if we understand the basis function search algorithm, the non-linearity can be taken into account by the same methods used in speech recognition.

 
Putting aside the possibility of analytical recording, which looks imho unrealistic, the approaches have already been voiced - GA and/or NS. We could start with a combination of SOM+RBF, first beating a number of quotes into fragments, e.g. according to Hearst index or other attributes. The author has got two alpha and omega processes, which intuitively want to attribute to such features as a trend and a correction. In this case the flat is described as a series of opposite corrections. But the further task is to break each process into "waves", i.e. basis functions. The question is - why do we need such a degree of detail in describing the market? After all, it is essentially enough for us to know where the trend is going, and the set of specific basis functions is, by and large, unimportant.
 
marketeer:
... We basically just need to know where the trend is going...

Knowing "where the trend is going" is not enough, we can know it very well at least every tick, but it will be of little use.

We need to know "where the trend is going" (generally the direction of the position) and "how long it will go there"

Or, alternatively, it is enough to know: "where the trend will go" for a "given amount of time".



Any other variants will lead to uncontrolled trading (trading by MA - uncontrolled trading, so we may either reverse every bar and lose horribly on the spread, or never wait for the exit signal at all)

 
joo:

Knowing "where the trend is going" is not enough, we can know it very well at least every tick, but it will be of little use.

We need to know "where the trend is going" (generally the direction of the position) and "how long it will go there"

Or, alternatively, it is enough to know: "where the trend will go" for a "given amount of time".



Any other variants will lead to uncontrolled trading (trading by MA - uncontrolled trading, so we may either reverse every bar and lose horribly on the spread, or never wait for the exit signal)

Agreed, but mine is a little different:

It is not enough to know "where the trend is going", we may know it very well even every tick, but it will be of little use.

One must know "where the trend is going" ( the general direction of the position) and "what the price change will be, if it goes there till the end" - entry conditions, if the change is greater than a given value.

Or, alternatively, it is sufficient to know: "where the trend will go" for a "given number of pips". - also an entry condition.

The exit is a violation of the entry conditions.

 
joo:

Knowing "where the trend is going" is not enough, we can know it very well at least every tick, but it will be of little use.

We need to know "where the trend is going" (the direction of the position in general) and "how long it will go there"

Or, alternatively, it is enough to know: "where the trend will go" for a "given amount of time".

Any other variants will lead to uncontrolled trading (trading by MA - uncontrolled trading, so we may either reverse every bar by MA reading and lose horribly on spread, or never wait for exit signal at all)

I disagree. Apparently there is a misinterpretation of the trend. A trend cannot reverse on every bar - it is not a trend. I will give my definition simply for terminological reference in this discussion, I do not pretend to be absolutely correct. A trend is a stable movement in one direction within a period (a significant part of a period) of a used trading strategy. I.e. the trend by definition includes a sufficient amount of time, limited from below, but unlimited from above. If a trend is entered at its beginning (and not in the middle or at its end), then there is at least half a trading period to break-even. Of course there can be unexpected turns, but this will always happen in any TS with any basic functions. We do not need to know the exit time in advance, if we are constantly monitoring the trend strength.

The price level is primary in trading. Once you have entered the market, there is an opening price and if we move in the profitable direction, it does not matter whether we wait for the exit signal or not. It would be a fairy tale if it were true and we could close at any moment with profit, and the more time passed.

Let's return to the basis functions. They have forgotten for some time about the noise on the market that is better not to include to the basic functions. So I argue that minus the noise, at any forecasting horizon the best basis function would be a straight line.

 
marketeer:

A trend is a sustained movement in one direction within a period (a significant part of the period) of the trading strategy used. That is, a trend, by definition, includes a sufficient amount of time, limited at the bottom, but unlimited at the top. If a trend is entered at its beginning (and not in the middle or at its end), then there is at least half a trading period to break-even. Of course there can be unexpected turns, but this will always happen in any TS with any basic functions. We do not need to know the exit time in advance, if we are constantly monitoring the trend strength.

The price level is primary in trading. Once you have entered the market, there is an opening price and if we move in the profitable direction, it does not matter whether we wait for the exit signal or not. It would be a fairy tale if it were true and we could close at any moment with profit, and the more time passed.

Let's return to the basic functions. They have forgotten for some time about the noise on the market that is better not to include to the basic functions. So I argue that minus the noise, at any forecasting horizon the best basis function would be a straight line.

Very vague and undefined. Besides, there is a hidden contradiction - if you enter on trend tops, you will get, attention, that the entry is always AGAINST the trend.



Moreover, one should not use the absolute price values at all and try to predict (like Yusuf) its quantitative change in the future - this is impossible.

 
joo:

....
Also, don't get hung up on absolute price values at all and try to predict (like Yusuf) a quantitative change in price in the future - it's impossible

I don't know about Yusuf, but it is very possible.
 
joo:

Very vague and undefined. In addition, there is a hidden contradiction - if you enter at the top of the trend, then it turns out that the entry is always AGAINST the trend.

In addition, one should not bind oneself to the absolute price values and try to predict (like Yusuf) its quantitative change in the future - it is impossible.

There's nothing wrong with what I said - definitely and without contradiction.

That's what a "trend top" is, it's not clear to me. The beginning and the end is clear. The entrance is always within the trend.

No one spoke about absolute values and binding to them. The price level, the opening price - yes, it exists, it cannot be avoided. I meant that previous post was about the necessity of knowing the time, so I think the price is primary, not the time. And it is clear that we will measure both relatively.

 
marketeer: But the further task is to beat each process into 'waves', i.e. basis functions.
Why are basis functions waves? They can be anything - flags, head&shoulders, etc.
1...232425262728293031323334353637...75
New comment
Reason: