arma_to_wv: ARMA process to WV

Description Usage Arguments Details Value Process Haar Wavelet Variance Formula See Also

View source: R/RcppExports.R

Description

This function computes the Haar Wavelet Variance of an ARMA process

Usage

1
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

See Also

ARMAtoMA_cpp, ARMAacf_cpp, and arma11_to_wv


wv documentation built on Jan. 17, 2020, 1:07 a.m.