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

## Description

Sets up the necessary backend for the GM process.

## Usage

 1 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 (imu, 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^{(-β)} X_{t-1} + \varepsilon_t

, where \varepsilon_t is iid from a zero mean normal distribution with variance σ^2(1-e^{2β}).

James Balamuta

## Examples

 1 2 GM() GM(beta=.32, sigma2_gm=1.3) 

SMAC-Group/simts documentation built on July 23, 2018, 1:15 a.m.