ma1_to_wv {simts}

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

Description

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

Usage

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}

Details

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

Value

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

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}}