pld {pcme}R Documentation

Compute partial autocorrelations, forward variances and their derivatives.

Description

Compute partial autocorrelations, forward variances, and their first and second derivatives using the periodic Levinson Durbin algorithm.

Usage

LD(R, Tau)
LDgrad(R, Tau)
LDhessian(R, Tau)

Arguments

R autocovariances, see details
Tau a matrix indicating which lags aregiven, see details

Details

R is a matrix of periodic autocovariances such that R_k(l) is the (k,l+1)th entry of the matrix R, see pcme-package for full description.

Tau is a matrix of the same size as R. It specifies the missingness status of the elements of R. Tau[k,l] = 1 if R_k(l-1) is given, Tau[k,l] = 0 if R_k(l-1) is missing and (k,l-1) is a gap, and Tau[k,l] = 1 if R_k(l-1) is missing but (k,l-1) is not a gap. See pcme-package for the terminology and Boshnakov and Lambert-Lacroix (2009?) for details.

Value

For LD, a list with components R, Beta, and sigma2f, see the description below.
For LDgrad, a list with components gradsigma2f and sigma2f.
For LDhessian, a list with components sigma2f, gradsigma2f, and grad2sigma2f.

R matrix of autocovariances, R[k,l]=R_k(l-1).
Beta matrix of partial autocorrelations, Beta[k,l]=β_k(l-1).
sigma2f The forward prediction variances.
gradsigma2f The gradient of the forward prediction variances
grad2sigma2f The Hessian of the forward prediction variances

Note

The filter coefficients have the signs used by Lambert-Lacroix (2005).

R_k(l) is set to 0 for l>p_k (??? check this!)

Unlike higher level functions like pcme, the argument tau here has a rigid format and gaps cannot be specified by NA's in R.

Author(s)

Sophie Lambert-Lacroix

References

Lambert-Lacroix, Sophie (2005) Extension of autocovariance coefficients sequence for periodically correlated processes. Journal of Time Series Analysis, 26, No. 6, 423-435.

See Also

pldinverse

Examples

# From file LD.R
R <- matrix(c(1,1,2,0.9,0.8,0.7,0.4,0.5,0.6,0.9,0.9,0.9),nrow=3)
Tau <- matrix(c(1,1,1,1,0,0,1,1,2,1,2,2),nrow=3)
R[Tau==2] <- 0
LD(R,Tau)

R[,1]<-R[,1]+1
LD(R,Tau)

# From file LDgrad.r
R <- matrix(c(1,1,2,0.9,0.8,0.7,0.4,0.5,0.6,0.9,0.9,0.9),nrow=3)
Tau <- matrix(c(1,1,1,1,0,0,1,1,2,1,2,2),nrow=3)
R[,1]<-R[,1]+1
LD(R,Tau)

R <- matrix(c(1,1,2,0.9,0.8,0.7,0.4,0.5,0.6,0.9,0.9,0.9),nrow=3)
Tau <- matrix(c(1,1,1,0,1,1,1,1,1,0,2,2),nrow=3)
R[,1]<-R[,1]+1
LD(R,Tau)

# From file LDhessian.r
R <- matrix(c(1,1,2,0.9,0.8,0.7,0.4,0.5,0.6,0.9,0.9,0.9),nrow=3)
Tau <- matrix(c(1,1,1,1,0,0,1,1,2,1,2,2),nrow=3)
R[,1]<-R[,1]+1
LDhessian(R,Tau)

R <- matrix(c(1,1,2,0.9,0.8,0.7,0.4,0.5,0.6,0.9,0.9,0.9),nrow=3)
Tau <- matrix(c(1,1,1,0,1,1,1,1,1,0,2,2),nrow=3)
R[,1]<-R[,1]+1
LD(R,Tau)

[Package pcme version 0.51 Index]