# johnramey

Don't think. Compute.

## Autocorrelation Matrix in R

I have been simulating a lot of data lately  with various covariance (correlation) structures, and one that I have been using is the autocorrelation (or autoregressive) structure, where there is a “lag” between variables. The matrix is a v-dimension matrix of the form

$$\begin{bmatrix} 1 & \rho & \rho^2 & \dots & \rho^{v-1}\\ \rho & 1& \ddots & \dots & \rho^{v-2}\\ \vdots & \ddots & \ddots & \ddots & \vdots\\ \rho^{v-2} & \dots & \ddots & \ddots & \rho\\ \rho^{v-1} & \rho^{v-2} & \dots & \rho & 1 \end{bmatrix}$$,

where $$\rho \in [-1, 1]$$ is the lag. Notice that the lag decays to 0 as v increases.

My goal was to make the construction of such a matrix simple and easy in R.  The method that I used explored a function I have not used yet in R called “lower.tri” for the lower triangular part of the matrix.  The upper triangular part is referenced with “upper.tri.”

My code is as follows:

 autocorr.mat

I really liked it because I feel that it is simple, but then I found Professor Peter Dalgaard’s method, which I have slightly modified. It is far better than mine, easy to understand, and slick. Oh so slick. Here it is:

 autocorr.mat

Professor Dalgaard’s method puts mine to shame. It is quite obvious how to do it once it is seen, but I certainly wasn’t thinking along those lines.

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Written by ramhiser

December 26th, 2010 at 4:55 am

Posted in r,statistics

Tagged with , ,

• fabians

I can do better:

rho^(as.matrix(dist(1:p)))

;P

• fabians

or even:
rho ^ abs(outer(1:p,1:p,”-”))