Nothing
ar1est0 <-
function (z)
{
n <- length(z)
stopifnot(n > 3)
a <- sum(z^2)
b <- sum(z[-1] * z[-n])
c <- sum(z[c(-1, -n)]^2)
i <- complex(1, 0, 1)
x <- ((-16) * b^3 + 18 * a * b * c + 24 * b^3 * n -
27 * a * b * c * n - 9 * b * c^2 * n - 12 * b^3 *
n^2 + 9 * a * b * c * n^2 + 27 * b * c^2 * n^2 +
2 * b^3 * n^3 - 18 * b * c^2 * n^3)
y <- (-b^2 * (-2 + n)^2 + 3 * c * (-1 + n) * (-a - c *
n))
f <- complex(1, x^2 + 4 * y^3, 0)
z <- (x + sqrt(f))^(1/3)
g <- x^2 + 4 * y^3
z1 <- (x + (-g)^(1/2) * i)^(1/3)
part1 <- (n - 2) * b/(3 * c * (n - 1))
part2 <- (1 - sqrt(3) * i) * y/(3 * 2^(2/3) * c * (n -
1) * z)
part3 <- (1 + sqrt(3) * i) * z/(6 * 2^(1/3) * c * (n -
1))
Re(part1 + part2 - part3)
}
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