Variance-covariance matrix

Hi Tsjerk,

Yes, I understand your point. Thanks for drawing my attention on that aspect.

Let me then rephrase my question.

I would need some R package function able to compute the variance-covariance matrix
for multivariate series as defined at:

        http://stattrek.com/matrix-algebra/covariance-matrix.aspx


About what outlined in the book reference I mentioned, I shall open a separate thread
in the case.

Thanks.

---

Giorgio

Genoa, Italy

From: Tsjerk Wassenaar [mailto:tsjerkw at gmail.com]
Sent: domenica 10 maggio 2015 22:31
To: Giorgio Garziano
Cc: r-help at r-project.org
Subject: Re: [R] Variance-covariance matrix

Hi Giorgio,

This is for a multivariate time series. x1 is variable 1 of the observation vector x, x2, variable 2, etc. If you need x(i) and x(i+1), etc, then you're looking for the autocovariance/autocorrelation matrix, which is a quite different thing (and David showed the way). You can easily see that you don't have N-1 degrees of freedom per entry, because you have fewer 'observations' for larger lag times.

Cheers,

Tsjerk



On Sun, May 10, 2015 at 10:25 PM, Giorgio Garziano <giorgio.garziano at ericsson.com<mailto:giorgio.garziano at ericsson.com>> wrote:
Hi Tsjerk,

Yes, seriously.

Time series:

X = [x1, x2, x3, ....,xn]

The variance-covariance matrix is V matrix:

            V    =


? x12 / (N-1)

? x1 x2 / (N-1)

. . .

? x1 xn / (N-1)

? x2 x1 / (N-1)

? x22 / (N-1)

. . .

? x2 xn / (N-1)

. . .

. . .

. . .

. . .

? xn x1 / (N-1)

? xn x2 / (N-1)

. . .

? xn2 / (N-1)




Reference: ?Time series and its applications ? with R examples?, Springer,
     $7.8 ?Principal Components? pag. 468, 469

Cheers,

Giorgio


From: Tsjerk Wassenaar [mailto:tsjerkw at gmail.com<mailto:tsjerkw at gmail.com>]
Sent: domenica 10 maggio 2015 22:11

To: Giorgio Garziano
Cc: r-help at r-project.org<mailto:r-help at r-project.org>
Subject: Re: [R] Variance-covariance matrix

Hi Giorgio,

For a univariate time series? Seriously?

data <- rnorm(10,2,1)
as.matrix(var(data))

Cheers,

Tsjerk


On Sun, May 10, 2015 at 9:54 PM, Giorgio Garziano <giorgio.garziano at ericsson.com<mailto:giorgio.garziano at ericsson.com>> wrote:
Hi,

Actually as variance-covariance matrix I mean:

        http://stattrek.com/matrix-algebra/covariance-matrix.aspx

that I compute by:

        data <- rnorm(10,2,1)
        n <- length(data)
        data.center <- scale(data, center=TRUE, scale=FALSE)
        var.cov.mat <- (1/(n-1)) * data.center %*% t(data.center)

--
Giorgio Garziano


-----Original Message-----
From: David Winsemius [mailto:dwinsemius at comcast.net<mailto:dwinsemius at comcast.net>]
Sent: domenica 10 maggio 2015 21:27
To: Giorgio Garziano
Cc: r-help at r-project.org<mailto:r-help at r-project.org>
Subject: Re: [R] Variance-covariance matrix


On May 10, 2015, at 4:27 AM, Giorgio Garziano wrote:

Hi,

I am looking for a R package providing with variance-covariance matrix computation of univariate time series.

Please, any suggestions ?

If you mean the auto-correlation function, then the stats package (loaded by default at startup) has facilities:

?acf
# also same help page describes partial auto-correlation function
#Auto- and Cross- Covariance and -Correlation Function Estimation

--

David Winsemius
Alameda, CA, USA