ar1_to_wv: AR(1) process to WV

In SMAC-Group/gmwm: Generalized Method of Wavelet Moments

Description

This function computes the Haar WV of an AR(1) process

Usage

ar1_to_wv(phi, sigma2, tau)

Arguments

phi	A double that is the phi term of the AR(1) process
sigma2	A double corresponding to variance of AR(1) process
tau	A vec containing the scales e.g. 2^tau

Details

This function is significantly faster than its generalized counter part arma_to_wv.

Value

A vec containing the wavelet variance of the AR(1) process.

Process Haar Wavelet Variance Formula

The Autoregressive Order 1 (AR(1)) process has a Haar Wavelet Variance given by:

(2*sigma2)/((1-phi)^2*(1-phi^2)*tau[j]^2)*(4*phi^(tau[j]/2 + 1) - phi^(tau[j]+1) - .5 * phi^2 * tau[j] + tau[j]/2 - 3*phi)

Haar Wavelet Derivation Information

For more information, please see: Supported Haar Wavelet Formulae (Internet Connection Required).

See Also

arma_to_wv, arma11_to_wv

Examples

ntau = 7
tau = 2^(1:ntau)
wv.theo = ar1_to_wv(.63, 1, tau)

SMAC-Group/gmwm documentation built on Sept. 11, 2021, 10:06 a.m.