Toep.estimator {vstdct}

Toeplitz Covariance and Precision Matrix Estimator

Description

Estimates the Toeplitz covariance matrix, the inverse matrix and the spectral density from a sample of n i.i.d. p-dimensional vectors with mean zero.

Usage

Toep.estimator(y, Te, q, method, f.true = NULL)

Arguments

y

nxp dimensional data matrix

Te

number of bins for data binning.

q

penalization order, q=1,2,3,4 are available

method

to select the smoothing parameter of the smoothing spline. Available methods are restricted maxmimum likelihodd "ML", generalized cross-validation "GCV" and the oracle versions "ML-oracle", "GCV-oracle".

f.true

Te-dimensional vector with the true spectral density function evaluated at equi-sapced points in [0,pi]. Only required, if an oracle method ("ML-oracle", "GCV-oracle") is chosen for method.

Value

A list containing the following elements:

• toep: p-dim. Toeplitz covariance matrix

• toep.inv: p-dim. precision matrix

• acf: p-dim. vector with the covariance function

• sdf: p-dim. vector with the spectral density in the interval [0,1]

Examples

#EXAMPLE 1: Simulate Gaussian ARMA(2,2)
library(nlme)
library(MASS)
p=100
n=1
Sigma=1.44*corMatrix(Initialize(corARMA(c(0.7, -0.4,-0.2, 0.2),p=2,q=2),data=diag(1:p)))
Y=matrix(mvrnorm(n, mu=numeric(p), Sigma=Sigma),n,p)
fit.toep=Toep.estimator(y=Y,Te=10,q=2,method="GCV")$toep


#EXAMPLE 2: AQUAPORIN DATA
data(aquaporin)
n=length(aquaporin$Y)
y.train=aquaporin$Y[1:(0.01*n)]
y.train=y.train-mean(y.train)
fit.toep=Toep.estimator(y=y.train,Te=10,q=1,method="ML")$toep