arma_to_wv | R Documentation |
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(\infty
) (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:
\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
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