deriv_ma1: Analytic D matrix for MA(1) process

In SMAC-Group/gmwm: Generalized Method of Wavelet Moments

Description

Obtain the first derivative of the MA(1) process.

Usage

deriv_ma1(theta, sigma2, tau)

Arguments

theta	A double corresponding to the theta coefficient of an MA(1) process.
sigma2	A double corresponding to the error term of an MA(1) process.
tau	A vec containing the scales e.g. 2^tau

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:

d/dtheta v[j]^2 (theta, sigma2) = (sigma2*(2*(theta+1)*tau[j]-6))/(tau[j]^2)

Taking the derivative with respect to sigma^2 yields:

d/dsigma2 v[j]^2 (theta, sigma2) = ((theta+1)^2*tau[j]-6*theta)/(tau[j]^2)

Author(s)

James Joseph Balamuta (JJB)

Examples

deriv_ma1(.3, 1, 2^(1:5))

SMAC-Group/gmwm documentation built on Sept. 11, 2021, 10:06 a.m.