Data Examples {vstdct}

Data Examples

Description

example1, example2 and example3 generate i.i.d. vectors from a given distribution with different Toeplitz covariance matrices. The covariance function \sigma of the Toeplitz covariance matrix of

• example1: has a polynomial decay, \sigma(\tau)= sd^2(1+|\tau|)^{-gamma},

• example2: follows an ARMA(2,2) model with coefficients (0.7,-0.4,-0.2,0.2) and innovations variance sd^2,

• example3: yields a Lipschitz continuous spectral density f that is not differentiable, i.e. f(x)= sd^2({|\sin(x+0.5\pi)|^{gamma}+0.45})

Usage

example1(p, n, sd, gamma, family = "Gaussian")

example2(p, n, sd, family = "Gaussian")

example3(p, n, sd, gamma, family = "Gaussian")

Arguments

p

vector length

n

sample size

sd

standard deviation

gamma

polynomial decay of covariance function for example1 resp. exponent for example3

family

distribution of the simulated data. Available distributions are "Gaussian", "Gamma", "Uniform". The default is "Gaussian".

Value

A list containing the following elements:

• Y: pxn dimensional data matrix

• sdf: true spectral density function

• acf: true covariance function

Examples

example1(p=10, n=1, sd=1, gamma=1.2, family="Gaussian")
example2(p=10,n=1,sd=1,family="Gaussian")
example3(p=10, n=1, sd=1, gamma=2,family="Gaussian")