deriv_dr: Analytic D matrix for Drift (DR) Process

In SMAC-Group/simts: Time Series Analysis Tools

Analytic D matrix for Drift (DR) Process

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:

\frac{\partial }{{\partial \omega }}\nu _j^2\left( \omega \right) = \frac{{\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)

SMAC-Group/simts documentation built on Sept. 4, 2023, 5:25 a.m.