pldinverse {pcme} | R Documentation |
Compute periodic autocovariances from periodic partial autocorrelations using the inverse periodic Levinson-Durbin algorithm.
pldinverse(beta)
beta |
numeric matrix, containing the periodic partial
autocorrelations for lags 0, 1, ..., ncol(beta)-1 ,
see pcme-package for details.
|
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. |
The signs of the coefficients of the filter are as in Lambert-Lacroix (2005).
Sophie Lambert-Lacroix
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.
#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