Covariance

Hi,

quick question: can someone confirm that Matlab doesn't give back correct results for 'cov ? Example is here: http://www.mathworks.ch/help/techdoc/ref/cov.html

I calculated by hand and excel. I think there's something. Need the covariance for the financial toolbox.

Thanks a lot Ben

[David Young]

If you think the example has the wrong result, what do you think the correct result should be, according to your hand calculation and excel?

[David Young]

Thanks for the information (though perhaps better to edit the question than to add an answer). I think Oleg has the explanantion.

Answer 1

[nor]

Matrix A in the example has 3 rows which represents 3 observations. In your case,if you use: a) cov(A) this command will divide by 2 i.e (N-1), giving you 10.3333 for the first element in the covariance matrix.

b)cov(A,1) this command will divide by 3 i.e (N), giving you the same result as you obtain in Excel. Hope this helps.

Answer 2

[Oleg Komarov]

You should read the documentation thoroughly:

cov(A,1)

is the population covariance (divides by N), while

cov(A)

is the sample covariance (divides by N-1)

By default, the functions cov, var and std compute the sample statistic.

Answer 3

[Sean Lawson]

I used MATLAB cov and don't experience a wrong answer. Maybe you could post your example here if you cannot find anything wrong.

[David Young]

This strikes me as a comment on the question, rather than an answer to it.

Answer 4

[Benjamin]

For the matrix: A = [-1 1 2 ; -2 3 1 ; 4 0 3] Matrix gives result ans =

   10.3333   -4.1667    3.0000
   -4.1667    2.3333   -1.5000
    3.0000   -1.5000    1.0000

just like the Example given in the link. With Excel and its covariance function (data analysis add-in), I receive this result 6.888888889 -2.777777778 2 -2.777777778 1.555555556 -1 2 -1 0.666666667

and by hand just for the very first element: Cov(1,1)=(-1-1/3)^2+(-2-1/3)^2+(4-1/3)^2 = 20.666/3 = 6.88889 But it seems that Matlab devides 20,666/2 = 10.333

What am I doing wrong? Thanks

[Benjamin]

Here again the excel result, hopefully in the right format:

6.8888 -2.77777 2.0000

-2.7777 1.5555 -1.0000

2.0000 -1.0000 0.6666

Answer 5

[Chinmayee L M]

I didn't quite understand the terminology used in the documentation. Could someone clarify?

The documentation reads:

"If A is a matrix whose columns represent random variables and whose rows represent observations, C is the covariance matrix with the corresponding column variances along the diagonal."

If I have 10 time series with 400 samples, how should the matrix be organised before taking covariance?

a. 10 x 400

b. 400 x 10

Thanks

[Chinmayee L M]

Figured it out.

Input to cov function should be a 10 x 400 matrix.