# arma11_to_wv: ARMA(1,1) to WV In wv: Wavelet Variance

## Description

This function computes the WV (haar) of an Autoregressive Order 1 - Moving Average Order 1 (ARMA(1,1)) process.

## Usage

 `1` ```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)

`arma_to_wv`