covmat_ar1blocks function

Calculate Theoretical Covariance Matrix of AR(1) Blocks Process

This function allows us to calculate the theoretical covariance matrix of a non-stationary AR(1) blocks process.

covmat_ar1blocks(n_total, n_block, phi, sigma2)

Arguments

• n_total: An integer indicating the length of the whole AR(1) blocks process.
• n_block: An integer indicating the length of each block of the AR(1) blocks process.
• phi: A double value for the autocorrection parameter $phi$.
• sigma2: A double value for the variance parameter $sigma^2$.

Returns

The theoretical covariance matrix of the AR(1) blocks process.

Note

This function helps calculate the theoretical covariance matrix of a non-stationary process, AR(1) blocks. It is helpful to calculate the theoretical allan variance of non-stationary processes, which can be used to compare with the theoretical allan variance of stationary processes as shown in "A Study of the Allan Variance for Constant-Mean Non-Stationary Processes" by Xu et al., 2017, IEEE Signal Processing Letters, 24(8): 1257–1260.

Examples

covmat1 = covmat_ar1blocks(n_total = 1000, n_block = 10,
phi = 0.9, sigma2 = 1)
covmat2 = covmat_ar1blocks(n_total = 800, n_block = 20,
phi = 0.5, sigma2 = 2)

Author(s)

Yuming Zhang