FitAR (version 1.94)

SiddiquiMatrix: Covariance Matrix of MLE Parameters in an AR(p)

Description

A direct method of computing the inverse of the covariance matrix of p successive observations in an AR(p) with unit innovation variance given by Siddiqui (1958) is implemented. This matrix, divided by n = length of series, is the covariance matrix for the MLE estimates in a regular AR(p).

Usage

SiddiquiMatrix(phi)

Arguments

phi

coefficients in a regular AR(p)

Value

Matrix, covariance matrix of MLE estimates

References

Siddiqui, M.M. (1958) On the inversion of the sample covariance matrix in a stationary autoregressive process. Annals of Mathematical Statistics 29, 585-588.

Pagano, M. (1973), When is an autoregressive scheme stationary? Communications in Statistics A 1, 533-544.

See Also

FitAR

Examples

#compute the inverse directly and by Siddiqui's method and compare:
phi<-PacfToAR(rep(0.8,5))
A<-SiddiquiMatrix(phi)
B<-solve(toeplitz(TacvfAR(phi, lag.max=length(phi)-1)))
max(abs(A-B))