arma_to_wv_app: ARMA process to WV Approximation

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

View source: R/RcppExports.R

Description

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

Usage

1
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: blog post on SMAC group website.

See Also

ARMAtoMA_cpp, ARMAacf_cpp, acf_sum and arma_to_wv


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