pldinverse {pcme}R Documentation

Compute autocovariances from periodic partial autocorrelations

Description

Compute periodic autocovariances from periodic partial autocorrelations using the inverse periodic Levinson-Durbin algorithm.

Usage

pldinverse(beta)

Arguments

beta numeric matrix, containing the periodic partial autocorrelations for lags 0, 1, ..., ncol(beta)-1, see pcme-package for details.

Value

A list containing the following components:

R numeric matrix with the autocovariances.
Af numeric matrix with the periodic filter coefficients.
sigma2f numeric vector with the forward error variances.

Note

The signs of the coefficients of the filter are as in Lambert-Lacroix (2005).

Author(s)

Sophie Lambert-Lacroix

References

Boshnakov, Georgi and Lambert-Lacroix, Sophie (2009?) Maximum entropy for periodically correlated processes from nonconsecutive autocovariance coefficients. J. Time Series Anal. (to appear)

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

LD

Examples

#Ex
beta <- matrix(c(3,2,0.6,0,0.85,0,-0.55,0,-0.55,0),nrow=2)
pldinverse(beta)

#Ex for ME method with gaps
#Ex1: We consider a PAR(1,2). The acf is computed for lag 0:3.
#We consider only one gap at season = 1 and lag = 2.
#By construction, we know that the solution is the one
#of the begining.
beta <- matrix(c(1,1,0.5,0.3,0,-0.3,0,0),nrow=2)
R1 <- pldinverse(beta)$R
gaps1 <- matrix(1,2,4)
gaps1[1,3] <- 0

#Ex2
beta <- matrix(c(1,1,0.9,0.3,0,-0.3,0,0),nrow=2)
R2 <- pldinverse(beta)$R
gaps2 <- matrix(1,2,4)
gaps2[1,3] <- 0

#Ex3: exemple nearly to the singularity
beta <- matrix(c(1,1,0.999999,0.3,0,-0.3,0,0),nrow=2)
R3 <- pldinverse(beta)$R
gaps3 <- matrix(1,2,4)
gaps3[1,3] <- 0

#Ex4: We consider a PAR(1,2) with singularity (one pacf coefficient equal
#to 0) and  compute the acf for lag 0:3.
#We consider only one gap at season = 1 and lag = 2.
#demontrer que la solution ME est bien degeneree
beta <- matrix(c(1,1,0.5,0.3,0,1,0,0),nrow=2)
R4 <- pldinverse(beta)$R
gaps4 <- matrix(1,2,4)
gaps4[1,3] <- 0

#Ex5: We construct one example for which there does not exist solution.
beta <- matrix(c(1,1,2,0.3),nrow=2)
R5 <- pldinverse(beta)$R
R5 <- cbind(R5,c(0.7,0.8),c(0.9,0.9))
gaps5 <- matrix(1,2,4)
gaps5[2,3] <- 0

[Package pcme version 0.51 Index]