covariance between 2 ts over time

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Newuser
Newuser 2011-4-29
I havea matrix(X) with 3 vectors with 380 elements each. I want to see how the covariance of 1st vector(A) and 2(B) with TS3 (C) evolves over time (25 periods used to compute the cov)
I supposed this should be done by means of a circular loop.
The problem is that the Cov(function) gives a matrix as a result .. and this fact translates into an error in the loop procedure. does someone know if there is a fromula to compute the COV without getting all the cov matrix?
the loop code i've written is :
for i = 26:380
for u = 1:3
covaariances(i,u)= ((cov(X(i,u),x(i,3))))
end
end
this results in an error. could someone of you advise me a way to get what I am aiming for??? thank u for ur valuable time
  3 个评论
显示 1更早的评论
Walter Roberson
Walter Roberson 2011-4-30
You must still have an error: the (i.25) would not be valid. Perhaps (i+25) ?
Walter Roberson
Walter Roberson 2011-4-30
x(i:(i-25),3) would be the empty vector, as i is always going to be greater than i-25.

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采纳的回答

Oleg Komarov
Oleg Komarov 2011-4-30
EDIT
X = rand(1500,50);
% Window size
ws = 25;
% Preallocate
szX = size(X);
covC = cell(szX(1)-24,1);
covM = zeros(szX(1)-24,sx(2));
for n = 1:szX(1)-24
covC{n} = cov(X(0+n:24+n,:));
covM(n,:) = covC{n}(1,:);
end
You can also save on computations by implementing your own covariance calculation for the first series against the other 49 to get a column of values.
Or you can simply save on memory (even though covC is not more than 30 mb) by substituting the "covM line" inside the loop with:
covC{n} = covC{n}(1,:);
and calling outside of the loop:
covC = cat(1,covC{:});
  2 个评论
Newuser
Newuser 2011-4-30
Thanks for your help.
The end result I am aiming at is a matrix containing the covariances (evolving over time) of all the 50 vectors with respect to the first vector.
This would mean that the first column would be of ones (1,1,1,1,1,1,)
Newuser
Newuser 2011-4-30
I mean ... of the fist matrix covC(1,1) ... i need the first line (this would be the first row of my new matric containig the covariances)
of the secon matrix covC(2,1) ... i need the first line (this would be the second row of my new matric containig the covariances)
and so on

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更多回答（4 个）

Teja Muppirala
Teja Muppirala 2011-4-30
The COV function does return a matrix. But this is not a problem since you can just extract out the relevant pieces.
I think there are running covariance algorithms out there that do this calculation very efficiently, but even just using a plain old loop is very fast (this code is only slow because I'm plotting it).
t = 0.01*(0:379)';
X = [sin(20*t.^2) sin(5*t.^3) sin(2*t.^4)];
figure;
a1 = subplot(2,1,1);
plot(X);
legend({'X1' 'X2' 'X3'});
title('X');
blk = 25;
C = zeros(size(X,1)-blk+1,2);
a2 = subplot(2,1,2);
h = plot(C);
set(h(1),'color',[0 0.5 0]);
set(h(2),'color','r');
title('Running Covariance');
for n = 0:size(X,1)-blk
c = cov(X(n + (1:blk),:));
C(n+1,:) = c(2:3,1);
set(h(1),'Ydata',C(:,1));
set(h(2),'Ydata',C(:,2));
drawnow;
end
legend({'cov(X1 , X2)' 'cov(X1 , X3)'});
linkaxes([a1 a2],'x');
If you're really against calculating the 3x3 covariance matrix, then you could do it using the formula for covariance which you can find on Wikipedia.
  1 个评论
Newuser
Newuser 2011-4-30
Thank u for the help. Could u please suggest me some of the efficient running cov algorithms u were referring to? ...
I'm using the one u posted ... but with a X matrix of dimension (1581,500). It's taking hours for the operation

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Walter Roberson
Walter Roberson 2011-4-30
Covariance is inherently an operation that returns a matrix. It measures the correlation of every component of the first vector with every component of the second vector.
If you are looking for a single value that tells you how "similar" the two vectors are, then covariance is the wrong measure. Possibly you wish to use kstest2()
Newuser
Newuser 2011-4-30
Thank you all for the prompt and useful advices. Here is another questions for you.
If instead of 3 "assets" (vectors of the Main matrix" I were to have 350 "assets" and would like to compute the correlation/covariance between them? at each point in time, how could I do it? ... would it be possible using the algorithm postedy by Teja?
Thanks again
Newuser
Newuser 2011-4-30
Hallo!
I tried to use the Teja script ... with 50 colums vector containing each 1500 obs.
I've started the calculation 5 minutes ago ... and it's still "busy"
could someone suggest me a more efficient way ?
  2 个评论
Oleg Komarov
Oleg Komarov 2011-4-30
It takes an instant to generate all the covariance matrices! Then you can plot all at once.
Newuser
Newuser 2011-4-30
cosa intendi precisamente?

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