Moving Average Order 1 (MA(1)) to WV

This function computes the WV (haar) of a Moving Average order 1 (MA1) process.

ma1_to_wv(theta, sigma2, tau)

Arguments

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. \(2^{\tau}\)

Value

A vec containing the wavelet variance of the MA(1) process.

Details

This function is significantly faster than its generalized counter part arma_to_wv.

Process Haar Wavelet Variance Formula

The Moving Average Order \(1\) (MA(\(1\))) process has a Haar Wavelet Variance given by: $$\nu _j^2\left( {\theta ,{\sigma ^2}} \right) = \frac{{\left( {{{\left( {\theta + 1} \right)}^2}{\tau _j} - 6\theta } \right){\sigma ^2}}}{{\tau _j^2}}$$

See also

arma_to_wv, arma11_to_wv