covMatAR {TestIndVars}

Generate a covariance matrix with Autoregressive (AR) structure.

Description

This function generates generates an Autoregressive (AR) covariance structure matrix of size p \times p based on the specified autoregressive coefficient (\rho) and variance (\sigma^2).

Usage

covMatAR(p, sigma2 = 1, rho)

Arguments

p

An integer specifying the number of dimensions of the covariance matrix.

sigma2

A numeric value specifying the variance parameter (default = 1).

rho

A numeric value specifying the autoregressive coefficient. If not provided, a random value between 0 and 1 will be generated.

The Autoregressive structure is defined as follows:

\Sigma = \Sigma_{AR} = \sigma^2 \begin{bmatrix} 1 & \rho & \rho^2 & \cdots & \rho^{\lvert p-1 \rvert} \\ \rho & 1 & \rho & \cdots & \rho^{\lvert p-2 \rvert} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ \rho^{\lvert p-1 \rvert} & \rho^{\lvert p-2 \rvert} & \rho^{\lvert p-3 \rvert} \cdots & 1 \end{bmatrix}

where \Sigma is the covariance matrix, \sigma^2 is the variance parameter, and \rho is the correlation parameter.

Value

A p \times p numeric matrix representing the Autoregressive (AR) covariance structure.

Examples

# generate a covariance matrix for \eqn{p = 5}, \eqn{\sigma^2 = 1}, and \eqn{\rho = 0.9}.
covMatAR(p = 5, rho = 0.9)

# generate a covariance matrix for \eqn{p = 5},  \eqn{\sigma^2 = 5}, and \eqn{\rho = 0.9}.
covMatAR(p = 5, sigma2 = 5, rho = 0.9)

# generate  covariance matrix for \eqn{p = 5},  and no value is considered for \eqn{\rho}
covMatAR(p = 5)