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gmwm (version 2.0.0)

deriv_rw: Analytic D matrix random walk process

Description

Analytic D matrix random walk process

Usage

deriv_rw(tau)

Arguments

tau
A vec that contains the scales to be processed (e.g. 2^(1:J))

Value

A matrix with the first column containing the partial derivative with respect to $gamma[0]^2$.

Details

The haar wavelet variance is given as $nu^2(tau) = (2*tau^2+1)*gamma^2 / (24*tau)$. Taking the first derivative with respect to $gamma_0^2$ yields: $$\frac{{{\partial ^2}}}{{\partial \gamma _0^4}}{\nu ^2}\left( \tau \right) = 0$$ The second derivative derivative with respect to $gamma[0]^2$ is then: $$\frac{{{\partial ^2}}}{{\partial \sigma_0^4}}{\nu ^2}\left( \tau \right) = 0$$.

Examples

Run this code
deriv_rw(2^(1:5))

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