This function computes the Haar Wavelet Variance of an ARMA process

arma_to_wv(ar, ma, sigma2, tau)

## Arguments

ar A vec containing the coefficients of the AR process A vec containing the coefficients of the MA process A double containing the residual variance A vec containing the scales e.g. $$2^{\tau}$$

## Value

A vec containing the wavelet variance of the ARMA process.

## 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($$\infty$$) (e.g. infinite MA 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: $$\frac{{{\tau _j}\left[ {1 - \rho \left( {\frac{{{\tau _j}}}{2}} \right)} \right] + 2\sum\limits_{i = 1}^{\frac{{{\tau _j}}}{2} - 1} {i\left[ {2\rho \left( {\frac{{{\tau _j}}}{2} - i} \right) - \rho \left( i \right) - \rho \left( {{\tau _j} - i} \right)} \right]} }}{{\tau _j^2}}\sigma _X^2$$ where $$\sigma _X^2$$ is given by the variance of the ARMA process. Furthermore, this assumes that stationarity has been achieved as it directly

ARMAtoMA_cpp, ARMAacf_cpp, and arma11_to_wv