# GM: Create a Gauss-Markov (GM) Process In SMAC-Group/simts: Time Series Analysis Tools

 GM 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 double value for the \beta of an GM process (see Note for details). sigma2_gm A double value for the variance, \sigma ^2_{gm}, of a GM process (see Note for details).

### 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

print

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}).

James Balamuta

### Examples

GM()
GM(beta=.32, sigma2_gm=1.3)


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