Generates a \(p \times p\) autocorrelated covariance matrix

Source: R/data-block-autocorrelation.r

This function generates a \(p \times p\) autocorrelated covariance matrix with autocorrelation parameter rho. The variance sigma2 is constant for each feature and defaulted to 1.

cov_autocorrelation(p, rho, sigma2 = 1)

Arguments

p

the size of the covariance matrix
rho

the autocorrelation parameter. Must be less than 1 in absolute value.
sigma2

the variance of each feature

Value

autocorrelated covariance matrix

Details

The autocorrelated covariance matrix is defined as: The \((i,j)\)th entry of the autocorrelated covariance matrix is defined as: \(\rho^{|i - j|}\).

The value of rho must be such that \(|\rho| < 1\) to ensure that the covariance matrix is positive definite.