Sets up the necessary backend for the GM process.
GM(beta = NULL, sigma2_gm = 1)A double value for the \(\beta\) of an GM process (see Note for details).
A double value for the variance, \(\sigma ^2_{gm}\), of a GM process (see Note for details).
An S3 object with called ts.model with the following structure:
Used in summary: "BETA","SIGMA2"
\(\beta\), \(\sigma ^2_{gm}\)
Number of parameters
String containing simplified model
"GM"
Depth of parameters e.g. list(1,1)
Guess starting values? TRUE or FALSE (e.g. specified value)
When supplying values for \(\beta\) and \(\sigma ^2_{gm}\), these parameters should be of a GM process and NOT of an AR1. That is, do not supply AR1 parameters such as \(\phi\), \(\sigma^2\).
Internally, GM parameters are converted to AR1 using the `freq` supplied when creating data objects (gts) or specifying a `freq` parameter in simts or simts.imu.
The `freq` of a data object takes precedence over the `freq` set when modeling.
We consider the following model: $$X_t = e^{(-\beta)} X_{t-1} + \varepsilon_t$$, where \(\varepsilon_t\) is iid from a zero mean normal distribution with variance \(\sigma^2(1-e^{2\beta})\).
GM()
GM(beta=.32, sigma2_gm=1.3)