GM {simts} | R Documentation |
Create a Gauss-Markov (GM) Process
Description
Sets up the necessary backend for the GM process.
Usage
GM(beta = NULL, sigma2_gm = 1)
Arguments
beta |
A |
sigma2_gm |
A |
Details
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.
Value
An S3 object with called ts.model with the following structure:
- process.desc
Used in summary: "BETA","SIGMA2"
- theta
\beta
,\sigma ^2_{gm}
- plength
Number of parameters
String containing simplified model
- desc
"GM"
- obj.desc
Depth of parameters e.g. list(1,1)
- starting
Guess starting values? TRUE or FALSE (e.g. specified value)
Note
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})
.
Author(s)
James Balamuta
Examples
GM()
GM(beta=.32, sigma2_gm=1.3)