deriv_ma1 {simts} | R Documentation |
Analytic D matrix for MA(1) process
Description
Obtain the first derivative of the MA(1) process.
Usage
deriv_ma1(theta, sigma2, tau)
Arguments
theta |
A |
sigma2 |
A |
tau |
A |
Value
A matrix
with the first column containing the partial derivative with respect to \theta
and the second column contains the partial derivative with respect to \sigma ^2
Process Haar WV First Derivative
Taking the derivative with respect to \theta
yields:
\frac{\partial }{{\partial \theta }}\nu _j^2\left( {\theta ,{\sigma ^2}} \right) = \frac{{{\sigma ^2}\left( {2\left( {\theta + 1} \right){\tau _j} - 6} \right)}}{{\tau _j^2}}
Taking the derivative with respect to \sigma^2
yields:
\frac{\partial }{{\partial {\sigma ^2}}}\nu _j^2\left( {\theta ,{\sigma ^2}} \right) = \frac{{{{\left( {\theta + 1} \right)}^2}{\tau _j} - 6\theta }}{{\tau _j^2}}
Author(s)
James Joseph Balamuta (JJB)