deriv_rw

Obtain the first derivative of the Random Walk (RW) process.

A system contains easy-to-use tools as a support for time series analysis courses. In particular, it incorporates a technique called Generalized Method of Wavelet Moments (GMWM) as well as its robust implementation for fast and robust parameter estimation of time series models which is described, for example, in Guerrier et al. (2013) <doi: 10.1080/01621459.2013.799920>. More details can also be found in the paper linked to via the URL below.

St<c3><a9>phane Guerrier

simts

Time Series Analysis Tools

Stéphane Guerrier

James Balamuta

Roberto Molinari

Justin Lee

Lionel Voirol

Yuming Zhang

Wenchao Yang

Nathanael Claussen

Yunxiang Zhang

Christian Gunning

Romain Francois

Ross Ihaka

R Core Team 

deriv_rw function

<dl><dt>tau</dt>
<dd>A <code>vec</code> containing the scales e.g. $2^{\tau}$</dd></dl>

Arguments

Taking the derivative with respect to $\gamma ^2$ yields:
$$ \frac{\partial }{{\partial {\gamma ^2}}}\nu _j^2\left( {{\gamma ^2}} \right) = \frac{{\tau _j^2 + 2}}{{12{\tau _j}}} $$

Process Haar WV First Derivative

Author

Analytic D matrix Random Walk (RW) Process — deriv_rw

<dl>

<dt>tau</dt>
<dd>A <code>vec</code> containing the scales e.g. $2^{\tau}$</dd>

</dl>

Taking the derivative with respect to $\gamma ^2$ yields:
$$ \frac{\partial }{{\partial {\gamma ^2}}}\nu _j^2\left( {{\gamma ^2}} \right) = \frac{{\tau _j^2 + 2}}{{12{\tau _j}}} $$

deriv_rw: Analytic D matrix Random Walk (RW) Process

Description

Usage

Value

Arguments

Process Haar WV First Derivative

Author