ARMA process to WV
This function computes the Haar Wavelet Variance of an ARMA process
arma_to_wv(ar, ma, sigma2, tau)
ar |
A |
ma |
A |
sigma2 |
A |
tau |
A |
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(infinity) (e.g. infinite MA process).
A vec containing the wavelet variance of the ARMA process.
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
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