arma_to_wv: ARMA process to WV

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

Description

This function computes the Haar Wavelet Variance of an ARMA process

Usage

arma_to_wv(ar, ma, sigma2, tau)

Arguments

ar	A vec containing the coefficients of the AR process
ma	A vec containing the coefficients of the MA process
sigma2	A double containing the residual variance
tau	A vec containing the scales e.g. 2^tau

Details

The function is a generic implementation that requires a stationary theoretical autocorrelation function (ACF) and the ability to transform an ARMA(p,q) process into an MA(infinity) (e.g. infinite MA process).

Value

A vec containing the wavelet variance of the ARMA process.

Process Haar Wavelet Variance Formula

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

(tau[j]*(1-rho(tau[j]/2)) + 2*sum(i*(2*rho(tau[j]/2 - i) + rho(i) - rho(tau[j] - i))))/tau[j]^2 * sigma[x]^2

where sigma[X]^2 is given by the variance of the ARMA process. Furthermore, this assumes that stationarity has been achieved as it directly

Haar Wavelet Derivation Information

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

See Also

ARMAtoMA_cpp, ARMAacf_cpp, and arma11_to_wv

Examples

# Calculates the Haar WV for an ARMA(2,3).
wv.theo = arma_to_wv(c(.23,.43), c(.34,.41,.59), 3, 2^(1:9))

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