ARMA process to WV Approximation
This function computes the (haar) WV of an ARMA process
arma_to_wv_app(ar, ma, sigma2, tau, alpha = 0.9999)
ar |
A |
ma |
A |
sigma2 |
A |
tau |
A |
alpha |
A |
This function provides an approximation to the arma_to_wv as computation times
were previously a concern. However, this is no longer the case and, thus, this has been left
in for the curious soul to discover...
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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