Zero sample correlation does not necessarily mean there is no linear relationship - page 26
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Here ' s a thoughtful commentary on a good article.
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Now the premise of your research is clear. Do I understand correctly that in order to increase the efficiency of pair trading, you have decided to try to include (investigate for the possibility of including in the combination) all tradable instruments (as hinted at in the cited forum)?
Now I understand the background to your research. Do I understand correctly, that to increase effectiveness of pair trading, you decided to try to include all traded instruments into combination (as it was hinted at on cited forum)?
Yes, only my bicycle was based on an intuitive understanding of the right and wrong ways. I began to get the mathematical foundations after I had written it.
Yes, only my bicycle was based on an intuitive understanding of the right and wrong ways. I learned the mathematical basics after I wrote it.
Here we come to where the dog is in the hole.....
"Shares of a company in the same industry should, according to this theory, react equally to external background unless it directly affects only one of them." is a quote from the cited article; it is repeated twice in the text. Do you understand the meaning of my highlighted condition?
Look at the publication date of this article and my fake.
If there is a correlation between financial instruments, the dummy will find it and show it. And it does not care whether the companies are related to the same industry or to different ones.
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If there is a correlation between financial instruments, the tool will find it and show it. And it does not care whether the companies are related to the same industry or to different ones.
What does the date have to do with it?
Essentially:
So, let's take an example: there are a lot of people; everyone throws a coin "eagle/rice"; after 100 rounds, we look at the recorded results of each of the throws, and applying mathematical methods find that between say, T and P there is a high correlation. (We do not discuss what mathematical methods are used for the analysis, but assume that the figures in the output show the interrelation). Accordingly, if there is a relationship, then you can safely bet on the prediction of the next result P for the next result T...... It is clear, that such an inference is defective because there is no cause-and-effect relation between the results of P and T. I.e. we should speak not about interrelation/dependence, but about coincidence (I will apply such non-mathematical term). And this means that in the next series of 100 shots we may find complete absence of any mathematical proof of dependence (and consequently the bet will be hopelessly lost) ......
The caveat in the phrase "Shares of a company in the same industry should, according to this theory, react in the same way to the external background...." means that the causal link of the same reaction is one industry - as a single valuation basis for the shares. If we find the same response of oil company shares and c\x company shares, it would be a simple coincidence. So when you say that you don't care about the "basis" (i.e. the existence of a causal relationship of the identified identical movement), then your piece of work will simply show the number\of coincidences that are there today and may not be there tomorrow... Why? Because there is no correlation of such identical motion....
The caveat in the phrase "Shares of a company in the same industry should, according to this theory, react in the same way to external background.... " means that the causal link of the same response is one industry - as a single stock valuation basis. If we find the same response of oil company shares and c\h company shares, it would be a simple coincidence.
If by coincidence you mean that tomorrow the link could be broken, then by coincidence you can interpret everything. And the linking of stocks of companies in the same industry. For example, at least look at the relationship between Russian oil companies before and during the Yukos events.
So when you say that you don't care about "basis" (i.e. whether there is a causal relationship of the identified same movement), then your craft will simply show the number/quality of coincidences that are there today and may not be there tomorrow... Why? Because there is no correlation of such identical movement....
We always have a finite amount of data to analyze. So the correlations found may not work tomorrow. And this is normal.
Another thing is that you can estimate the characteristics of change in the links. For example, if you look at how the linear relationship between GBPUSD, USDJPY and GBPJPY changes, you will see that no matter what interval you measure, the linear relationship is the same everywhere.
The more stable the relation is over time, the more you can trust it (or not). And if there is a stable linear relationship between the granny's blood pressure and the behavior of GBPJPY over the longitudinal section of the study, then I will use that relationship if it is possible.
You cannot draw any conclusions with coins on 100 laps. Do at least 10,000 laps. Then apply Recycle and see that there is no stable connection.
There is a section in the product description that analyses its performance and draws short conclusions...
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And if there is a stable linear relationship between granny's blood pressure and GBPJPY behaviour in the longitudinal section of the study, then I will use that relationship if it is possible to do so.
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Why so abstract? You can use the tester to find optimal parameters of intersecting MAs which will give wonderful results on a very long history; plus a priori between the price and MAs from the price the linear relationship will be revealed (and it cannot be otherwise); and go - the grail is ready......:)
Banal fitting by history.... only instead of MA you propose to use a contrived "Recycle" (the principles of operation are different, but the conceptual approach is the same)
Then you've got it wrong. Your example on the MAs:
As a result we obtained N values of the optimized parameters. Now let's create Matrix Matrix, where the first row is V1, second row V2 and so on.
Each column of this matrix (of length N) will correspond to a change in one of the input parameters during optimization.
We study the nature of these columns. If the column members behave stably, everything is great. Otherwise it sucks.
So with your example, everything will suck.
Although the method of identifying TS stability shown above is universal, it cannot be applied to all TS since there are an infinite number of TS.
The situation is different with Recycle - the number of financial instruments is finite. Therefore, it is realistic to find stable situations. Recycle does not search for stable situations, it only runs steps 1-6 on all Instruments at a time, finding Matrix and visualizing it and some characteristics. And the more set of FI you give it for analysis, the more stable matrix it will give you.
Looking for stability in such a matrix is much easier.
P.S. It is impossible for me to explain in two words the difference of approaches to make it obvious.
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Examine the nature of these columns. If the column members behave stably, everything is great. Otherwise, it sucks.
So with your example of MAs, it's going to suck.
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Yep, and if you use your conditional example of Grandma's blood pressure, everything is just chocolate......:).....:)......:)