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I'd like to know if there is a standard way of creating a matrix like the one shown below using the R programming language.

$$ \begin{bmatrix} 1 & \rho & \rho^2 & \cdots & \rho^{T-1}\\ \rho & 1 & \rho & \cdots & \rho^{T-2}\\ \rho^2 & \rho & 1 & \cdots & \rho^{T-3}\\ \vdots &\vdots &\vdots & \ddots & \vdots\\ \rho^{T-1} & \rho^{T-2} & \rho^{T-3} & \cdots & 1 \end{bmatrix} $$

The code I've been using to create matrices like this one is shown below.

For illustrative purposes, let rho = 0.8 and T = 20.

rho <- 0.8
t   <- 20
toeplitz(c(1, poly(rho, t-1, raw=TRUE)))

Although the output of this code does, indeed, produce the matrix of interest, I get the feeling that there's probably a better way of doing it.

Can this code snippet be improved - in the sense that there is a more elegant, more standard, more correct, or more efficient way of creating the matrix?

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In this case, poly is probably too much trouble. You can just calculate the polynomial yourself with rho^seq.int(0, t-1). Altogether that gives

toeplitz(rho^seq.int(0, t-1))
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