Obtaining a stationary BP from a price BP - page 23
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White noise is also not time correlated - this is its main condition - but its variance is finite. For example, the first difference in SB is noise.The cumulative sum of these differences is random walk, all right.Now take two or more highly correlated series (SB - cum. sum), do a regression analysis and get the residuals (white noise - cum. sum).
Residuals are not cumulative - they are regression error (variance). And they are not necessarily white noise, nor are they necessarily stationary. But even if they are, it does not say that there are no dependencies left in the series. They can be as many as you want, and even deterministic. What matters in this aspect is the period of these dependencies - how long they last in time. The shorter their lifetime, the less they will stand out in the series making it non-stationary. In the limiting case, when they act during one reference period - their presence has no effect on the shape and parameters of the distribution. I.e., the correlation between sampling frequency and time of validity of the dependences is important here.
Non-stationarity means that there are dependencies in the series that are sufficiently long in time (for a given sampling rate). But dependence is not necessarily a dependence on previous values of the series. Dependence on the starting point in time (as in the definition of stationarity and non-stationarity). For example, if trades turn out to be dependent, it doesn't mean that the market remembers their values or consistency but they just fell in time into a certain phase of the governing process development (up-trend, for example). I.e. dependence manifests itself by the fact that sometimes the series is distributed quite differently and this can last for quite a long time. And many people perceive it as in the case of dependent trades - that two losing trades will most probably be followed by a profitable one, though it is usually a random arrival at a certain phase of the managing process and not necessarily such a synchronization with it will occur again in future.
As a matter of fact, any TS looks for the moments when the distribution is stationary at the maximum and has a positive mo
The market always reserves the right to deceive you harshly, to put it mildly.
Residuals are not cumm. the sum is the regression error (difference). And they are not necessarily white noise, nor are they necessarily stationary. But even if they are, it does not say that there are no dependencies left in the series. They can be as many as you want, and even deterministic. What matters in this aspect is the period of these dependencies - how long they last in time. The shorter their lifetime, the less they will stand out in the series making it non-stationary. In the limiting case, when they act during one reference period - their presence has no effect on the shape and parameters of the distribution. I.e., the correlation between sampling frequency and time of validity of the dependences is important here.
Non-stationarity means that there are dependencies in the series that are sufficiently long in time (for a given sampling rate). But dependence is not necessarily a dependence on previous values of the series. Dependence on the starting point in time (as in the definition of stationarity and non-stationarity). For example, if trades turn out to be dependent, it doesn't mean that the market remembers their values or consistency but they just fell in time into a certain phase of the governing process development (up-trend, for example). I.e. dependence manifests itself by the fact that sometimes the series is distributed quite differently and this can last for quite a long time. And many people perceive it as in the case of dependent trades - that two losing trades will most probably be followed by a profitable one, though it is usually a random arrival at a certain phase of the managing process and not necessarily this time-synchronization with it will happen again in the future.
In fact any TS looks for the moments when the distribution is stationary at its maximum and has a positive mo
I read your topic and did not understand anything.
But I understood how to get a stationary series. I ran the first time around zero and it fluctuates.
The second, third, fourth, twentieth - I copied the loop in the program...
Fluctuations rise in sum and don't change much in appearance.
A few bounces show up, they are constant in time. The rest are similar to each other.
What is the meaning of this? ).
Did the opposite, inverse conversion to stationary.
Started copying cycles too.
On 21 got the price series I started with.
At 22 I got a hyperbola.
It is also unclear how to understand it.
I've read your topic, I don't understand anything.
But I understand how to get a stationary series. I ran the first time around zero and it fluctuates.
The second, third, fourth, twentieth - I copy the cycle in the program...
Fluctuations rise in sum and don't change much in appearance.
A few bounces show up, they are constant in time. The rest are similar to each other.
What is the meaning of this? ).
Did the opposite, inverse conversion to stationary.
Started copying cycles too.
On 21 got the price series I started with.
At 22 I got a hyperbola.
I do not understand it either.
I do not really understand what you mean either. What are the cycles, how did you get the series, etc. And what it was done for in principle.
1) Let's not wiggle from side to side and give out such series as "It assumes that it assumes nothing". Well if you have decided to take fire on yourself (not just to fluff, really), then the question of proving local regularities on random wandering passes to you.
2) Well, and for those in the tank, for me it has already been handed over 500 times. the answer is "yes" - I can.
1. Too bad you don't understand the difference between the two statements: "the shape and parameters of the distribution do not give an unambiguous answer that there are no dependencies" and "the shape and parameters of the distribution indicate that there are local regularities". But that's your problem.
2. Well, since you said "A", go ahead and say it. Prove it.
3. This is an interesting situation. On the one hand you can prove that there are no local regularities on the random walk. This obviously implies that there are no global patterns at all. That is, there is definitely nothing to make money on. On the other hand, you are present on this forum and probably on forex. A logical question: what are you doing here? :-)
to Yurixx
Yura, hello!
And you, if memory serves me correctly, are the Father, Son and Holy Spirit of the idea of residualization (or, bringing to a normal form) of RRR from price VR. Maybe you can give voice to the basic idea. Can you put some order into my inflamed brain?
Why Sergey? Why ! :-)
When did I put forward such ideas? Well, unless I was unconscious.
You and I have long ago moved away from trying to fit price BP to beautiful model series of probability theory - stationary, normally distributed, etc. To be precise, I was focused on the dynamic approach from the beginning. And after Pastukhov, I finally confirmed myself in it.
To this your passage I have nothing to add:
The first-difference series (FDR) from the price series is not stationary in any sense. It has the most unpredictable MO variation (albeit around zero), forcing us to "see" an uptrend in the price GP when MO RRR>0, a downtrend when MO<0 and a flat when MO->0. It has a standard deviation (volatility) with a diurnal period. I don't understand why and how do we need to restate it? Do we want to get from it a SV with normal distribution with zero MO and variance equal to a constant? Even if we get it by some unknown method, what should we do with this "miracle"?
I can accept the idea of residuals only in this form.
If there is some model of price VR, then we can construct a series of residuals, that is, differences between the real price and the model price. If this residual series is stationary and normally distributed, then the model can be considered adequate.
Here I want to note that this adequacy is not all that is needed to be happy. The variance of this series of residues, even if it is stationary, can be so big, that the model will not only be non-profitable, but even unprofitable. Therefore this variance can be a measure of model adequacy. That is, to be fully happy the variance of the residuals series needs to be less than some critical value corresponding to the zero profitability of the model.
What are you doing, Sergei? What for! :-)
When did I ever come up with such ideas? Well, unless I was unconscious.
You and I have long ago moved away from trying to fit price BP to beautiful model series of probability theory - stationary, normally distributed, etc. To be precise, I was focused on the dynamic approach from the beginning. And after Pastukhov I finally confirmed myself in it.
I can only accept the idea of residualization in this form.
If there is some model of price BP, then we can construct a series of residuals, that is, differences between the real price and the model price. If that series of residuals is stationary and normally distributed, then the model can be considered adequate.
Thanks, friend!
I really feel relieved. Otherwise I found myself in a situation when the smart half of the forum is seriously discussing the important thing, while I can't understand what's clear to everybody, and I even can't see the subject of the discussion.
I'm sure, that now it is possible to close a theme for absence of practical utility of the discussed question.
:-)
It would be interesting to hear the opinion of forum participants. The presence of an adequate pricing model will allow us to understand the hidden mechanisms of exchange rate dynamics, which means there is a non-zero probability of profitable exploitation.
Neutron писал(а) >>
Suppose we have an arbitrary TS that trades according to the most general algorithm.
The block of analysis:
1. determines the point of entering the market and the direction of the position to be opened;
2. determines the exit point, i.e., it closes the open position.
It is clear that upon such a trade algorithm definition we break down the price TP into time-isolated parts where we are in the market. Let's call the TS optimality parameter - k the ratio of the number of payments of DC commissions to the number of completed transactions. In this case it is evident that k=1 always and the series of transactions contains any long unidirectional series. We will call an "optimal" TS the one that minimizes the parameter k.
It turns out that there's no need to close and open one-directional consecutive positions losing the spread at each step. Consecutive unidirectional transactions can be combined by "not exiting" the market and losing one spread at each "virtual" transaction series instead of each series member that will lead to minimization of the optimization parameter. Now k<=1.
Such an TS, all other conditions being equal (when one and the same analytical control unit works for different TS), will give the maximum possible return defined as points per one transaction (on average) and will be optimal in the stated sense.
Now, if you turn on your "artistic" imagination, you can see in front of your eyes a flipping TS that is always in the market. Which is what was needed to prove.
And what, the parameter "ratio of the number of payments of DC commissions to the number of transactions made" is really a good parameter? And we are looking for the minimum value, as I understand it. And what is meant by commission? The brokerage companies for forex declare it virtually as zero, some brokerage companies "squeeze" the spread. Or is it just a spread? If we mean spread, it seems to be always available (it is said that there are some brokerage companies that trade without spread). Or does it mean the profit? But in this case its also a very doubtful parameter.
to Yurixx, Neutron
What are you doing, Sergey? What for ? :-)
When did I ever express such ideas? Unless I was unconscious ...
Thanks, man.
I'm really relieved. And then I found myself in a situation, when the intelligent half of the forum is discussing some significant thing, and I can't understand what is clear to everybody, and I even can't see the subject of the discussion.
I am sure that the topic may be closed now for lack of practicality of the issue under discussion.
You're a baker (in a good sense of the word) :o) Colleagues, it is possible to get such a conversion, with some limitations, of course. And what it is needed for - the answer is very simple, it gives an opportunity to apply the maximum likelihood method.