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ar1_to_wv

AR(1) process to WV

Description

This function computes the Haar WV of an AR(1) process

Usage

ar1_to_wv(phi, sigma2, tau)

Arguments

phi

A double that is the phi term of the AR(1) process
sigma2

A double corresponding to variance of AR(1) 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 AR(1) process.

Process Haar Wavelet Variance Formula

The Autoregressive Order 1 (AR(1)) process has a Haar Wavelet Variance given by:

(2*sigma2)/((1-phi)^2*(1-phi^2)*tau[j]^2)*(4*phi^(tau[j]/2 + 1) - phi^(tau[j]+1) - .5 * phi^2 * tau[j] + tau[j]/2 - 3*phi)

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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