gmwm (version 2.0.0)

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.

Examples

deriv_2nd_ar1(.3, 1, 2^(1:5))