Creating an n x n autocorrelation matrix

Walking around in old Lisbon.

Between covid-19 news and announcements of imminent Russia-Ukraine wars I needed a bit of a distraction. Sooo, here it is how to create an n x n autocorrelation matrix based on a correlation rho, with a simple 5 x 5 example in R:

This produces the following output:

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A 5 x 5 autocorrelation matrix

How does this work? Starting from defining n as 5, and the basic rho correlation as 0.9, then mat <- diag(n) creates a diagonal matrix—a square matrix with ones in the diagonal and zeros elsewhere—with 5 rows and 5 columns.

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Diagonal matrix

Looking at the final line of code, we have that row(mat) and col(mat) create matrices with the row or col coordinates for each location:

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Output of the row() and col() functions

Then abs(row(mat) - col(mat)) is telling us how far is each cell in the matrix from the diagonal. We use that distance as an exponent for rho (0.9 in our example).

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Distances from the diagonal

Putting it all together, rho^abs(row(mat) - col(mat)) produces:

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n x n autocorrelation matrix

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