deriv_2nd_ar1: Analytic second derivative matrix for AR(1) process
Description
Analytic second derivative matrix for AR(1) process
Usage
deriv_2nd_ar1(phi, sig2, tau)
Arguments
phi
A double corresponding to the phi coefficient of an AR(1) process.
sig2
A double corresponding to the error term of an AR(1) process.
tau
A vec that contains the scales to be processed (e.g. 2^(1:J))
Value
A matrix with the first column containing the second partial derivative with respect to $sigma^2$ and the second column contains the second partial derivative with respect to $sigma^2$
Details
The haar wavelet variance is given as $See PDF Manual for equation$
Note: $phi = rho$ and $V[0]^2 = sigma[0]^2$.
Due to length, the analytical derivations of the AR(1) haar wavelet variance are given in a supplied file within vignette.