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arma11_to_wv

ARMA(1,1) to WV

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)

simts

Time Series Analysis Tools

v0.1.1
AGPL-3 | file LICENSE
Authors
Stéphane Guerrier [aut, cre, cph], James Balamuta [aut, cph], Roberto Molinari [aut, cph], Justin Lee [aut], Yuming Zhang [aut], Wenchao Yang [ctb], Nathanael Claussen [ctb], Yunxiang Zhang [ctb], Christian Gunning [cph], Romain Francois [cph], Ross Ihaka [cph], R Core Team [cph]
Initial release
2019-07-21

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