arma_to_wv_app: ARMA process to WV Approximation

In schoi355/gmwm: Generalized Method of Wavelet Moments

ARMA process to WV Approximation

Description

This function computes the (haar) WV of an ARMA process

Usage

arma_to_wv_app(ar, ma, sigma2, tau, alpha = 0.9999)

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
alpha	A double indicating the cutoff.

Details

This function provides an approximation to the arma_to_wv as computation times were previously a concern. However, this is no longer the case and, thus, this has been left in for the curious soul to discover...

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, acf_sum and arma_to_wv

Examples

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

schoi355/gmwm documentation built on April 11, 2022, 1:21 a.m.