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toeplitz(x), x a REAL vector.

Keywords: matrix algebra
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