toeplitz(x), x a REAL vector. |

toeplitz(x) computes an n by n Toeplitz matrix from a REAL vector x of length n. After a <- toeplitz(x), a is constant on the diagonals with a[i,j] == x[|i-j| + 1]. Function toeplitz() primary use is to create a covariance matrix from an auto-correlation function. For example, if gamma0, gamma1, ... are the variance and first n-1 autocovariances of a stationary time series {x[t]}, then toeplitz(vector(gamma0, gamma1, ...)) computes the n by n covariance matrix of the vector vector(x[1], x[2], ..., x[n]), or indeed of vector(x[1+k], x[2+k], ..., x[n+k]) for any integer k. See also partacf(), yulewalker().

Gary Oehlert 2003-01-15