pld {pcme} | R Documentation |
Compute partial autocorrelations, forward variances, and their first and second derivatives using the periodic Levinson Durbin algorithm.
LD(R, Tau) LDgrad(R, Tau) LDhessian(R, Tau)
R |
autocovariances, see details |
Tau |
a matrix indicating which lags aregiven, see 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.
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 |
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
.
Sophie Lambert-Lacroix
Lambert-Lacroix, Sophie (2005) Extension of autocovariance coefficients sequence for periodically correlated processes. Journal of Time Series Analysis, 26, No. 6, 423-435.
# 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)