Zero sample correlation does not necessarily mean there is no linear relationship - page 49

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C-4:


In general, yes, it's like that. But with the only exception that I need methods that allow to determine the relationship, not using the assumption that there is such a relationship a priori. For example, I read an article on regression analysis on wikipedia:

OK, so before we can use the same regression analysis, we have to identify the relationship. But how do we identify it? Regression analysis is impossible as it is a consequence of the relationship, correlation is also impossible as QC itself does not talk about cause-effect relationships, cross-correlation? - seems better, but that's where my knowledge ends...

No big deal. Modern "correlation traders" - there are even posts like that, so they are called - they start from the "null" hypothesis that EVERYTHING IS RELATED, and then by enumeration they calculate the strength of that connection - of everything - to everything.

Here, found in the archives, guardian.co.uk has a blog about financiers. And there are some great articles there about the real work of a trader in a big bank or hedge fund there. They can hunt for correlations for up to TWO WEEKS, then the trader checks it all in some math lab, gives a presentation to his bosses, and then the bank opens a hedged position for something like 100 million.

http://www.guardian.co.uk/commentisfree/joris-luyendijk-banking-blog/2012/apr/02/quantatitive-prop-trader-voices-of-finance

There's a lot of interesting stuff for pro traders on the blog.

 
anonymous:

The best known approach is the Granger causality test. You can also look at the transfer entropy

Where can I find documentation on them and in which R-packages can these tests be consulted?
 
C-4:
And where can I find documentation on them and in which R-packages can I find these tests?


library(MSBVAR); ?granger.test

There are no packages for transfer entropy, but it's not hard to query them yourself.

 
Is there no one willing to write this Granger on the emcool?
 
GaryKa: Dear visitors, what data for the price time series (FX) do you use when drawing conclusions about stationarity, distributions, ergodicity, correlation and other statistical things? The question is without a quibble. Just often taking one of the bestband readings quantified by astronomical time? But that is ... how shall I put it... unacceptable. It makes sense to analyse the sequence of price readings from "real" trades, taking into account real volumes. Maybe that's the point - to prepare the data for analysis.

Read the definitions in any textbook and get the gist. It makes no difference at all whether you use bid/ask/midprice. The numerical characteristics may be slightly different, but the conclusions about stationarity will be the same.

The question is somewhat broader and involves several sub-questions:


  • (1) What is the price reading on the actual trades?

bid and ask are just the best offers and, . and then what. Can they change when there is no actual trade? Yes, they can. Can they remain unchanged in the presence of a trade? Yes, absolutely (partially executed). Midprice! What about times when the spread increases several times, what about midprice or best band?

  • (2) What are the volume readings on real trades?
Here's an example, again contrived (the picture is taken from the first post of the branch)


The correlation is zero throughout the range, although the entire trade is concentrated in areas where the correlation is significant.
It's obvious that deals of one lot are not equivalent to trades of 100 lots. And meanwhile, price data of such micro transactions make a significant contribution into calculations of selective characteristics. Knowing real volumes, we could perform "weighted averages" that would be more adequate.
  • (3) How to quantize data
Take the first difference between the candles, it's not HP BP. And why should it be normally distributed if one candle has X trades and the other 100X trades and all with different volumes. Digging into tick history, level II history? The deeper it goes, the more differences there are between brokers.
 
C-4: I(0) is simply the first differences of I(1).

That's logical, no argument there. But the truth is actually different: I(1) is the "integral" of I(0) - from the process that is defined from the beginning. It is not I(0) that is defined through I(1), but vice versa.

I(1) properties could be anything, it could be SB, it could be a real market with a non-normal distribution, temperature dynamics in Lisbon, whatever.

Sorry, but that's not quite right. You have to start from I(0), which should always be stationary and no other. Successive "integrations" of the I(0) process lead to different I(n).

I(1) can in no way be real quotes, because the process of differences of these quotes is not stationary, i.e. cannot be I(0). So, originally it (the quotes) was not I(1).

 

Horror.

With all due respect, I cannot understand why statistics should be applied to processes whose essence is explainable and descriptible.

Here, I have developed something. No one knows whether it is good or bad. Turn on the statistics - it will decide. When no one knows!

 
hMathemat:

That's logical, no argument there. But the truth is actually different: I(1) is the "integral" of I(0) - of the process that is defined from the beginning. It is not I(0) that is defined through I(1), but vice versa.

Sorry, but that's not quite right. You have to start from I(0), which must always be stationary and no other. Successive "integrations" of the I(0) process result in different I(n).

I(1) can in no way be real quotes, because the process of differences of these quotes is not stationary, i.e. cannot be I(0). So, originally it (the quotes) was not I(1).

Suppose MQ has decided to release MetaTrader 6 where instead of classic charts in the form of bars and candlesticks we are given only price increments. The market is still not normal, but now we use and rely on I(0).

Both processes in the image above are of the order I(0), but the first one is a classical normal distribution and the second one is a real and non-stationary RTS market. If the bottom picture is not a process of order I(0), then what order is it and what should we call it?

 
Integer:
Is there no one willing to emulate this Granger on the emculus?

It would be nice to know how it works, for a start.

Does anyone have Granger's 1969 book"Investigating Causal Relations by Econometric Models and Cross-Spectral Methods"?)

And also, to be honest, I still don't understand who is more to blame for the Israel-Polestine conflict? The Jews? The Arabs?

There's just a special dataset called IsraelPalestineConflicte that goes with the test, looked like this:

You can see that the data is tightly correlated, but you can't see who is to blame, and what Granger is saying is not clear.

 
C-4: If the bottom picture is not an order I(0) process, then what order is it and what do you call it?
I don't know, we have to check it. Here let faa check for unidirectional roots.
1...424344454647484950515253545556...60
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