arma11_to_wv: ARMA(1,1) to WV

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

Description

This function computes the WV (haar) of an Autoregressive Order 1 - Moving Average Order 1 (ARMA(1,1)) process.

Usage

arma11_to_wv(phi, theta, sigma2, tau)

Arguments

phi	A double corresponding to the autoregressive term.
theta	A double corresponding to the moving average term.
sigma2	A double the variance of the 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 ARMA(1,1) process.

Process Haar Wavelet Variance Formula

The Autoregressive Order 1 and Moving Average Order 1 (ARMA(1,1)) process has a Haar Wavelet Variance given by:

nu[j]^2 (phi, theta, sigma2) = (-2*sigma2*((-(theta + phi))*(1 + theta*phi)*(3 - 4*phi^(tau[j]/2) + phi^tau[j]) - 0.5*(1 + theta)^2*(-1 + phi^2)*tau[j])) / ((-1 + phi)^3*(1 + phi)*tau[j]^2)

Haar Wavelet Derivation Information

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

See Also

arma_to_wv

Examples

ntau = 7
tau = 2^(1:ntau)
wv.theo = arma11_to_wv(0.3, 0.1, 1, tau)

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