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

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.