deriv_dr: Analytic D matrix for Drift (DR) Process

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

Description

Obtain the first derivative of the Drift (DR) process.

Usage

deriv_dr(omega, tau)

Arguments

omega	A double that is the slope of the drift.
tau	A vec containing the scales e.g. 2^tau

Value

A matrix with the first column containing the partial derivative with respect to omega.

Process Haar WV First Derivative

Taking the derivative with respect to omega yields:

d/domega nu[j]^2 (omega) = (tau[j]^2 * omega)/8

Note: We are taking the derivative with respect to omega and not omega^2 as the omega relates to the slope of the process and not the processes variance like RW and WN. As a result, a second derivative exists and is not zero.

Author(s)

James Joseph Balamuta (JJB)

Examples

deriv_dr(5.3, 2^(1:5))

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