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.garzi...@ericsson.com> wrote: > Hi Tsjerk, > > > > Yes, seriously. > > > > Time series: > > > > X = [x1, x2, x3, ....,xn] > > > > The variance-covariance matrix is V matrix: > > > > * V* = > > Σ *x*12 / (N-1) > > Σ *x*1 *x*2 / (N-1) > > . . . > > Σ *x*1 xn / (N-1) > > Σ *x*2 *x*1 / (N-1) > > Σ *x*22 / (N-1) > > . . . > > Σ *x*2 *x*n / (N-1) > > . . . > > . . . > > . . . > > . . . > > Σ *x*n *x*1 / (N-1) > > Σ *x*n *x*2 / (N-1) > > . . . > > Σ *x*n2 / (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:tsje...@gmail.com] > *Sent:* domenica 10 maggio 2015 22:11 > > *To:* Giorgio Garziano > *Cc:* r-help@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.garzi...@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:dwinsem...@comcast.net] > Sent: domenica 10 maggio 2015 21:27 > To: Giorgio Garziano > Cc: r-help@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 > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. > > > > > > -- > > Tsjerk A. Wassenaar, Ph.D. > -- Tsjerk A. Wassenaar, Ph.D. [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
