Sets up the necessary backend for the GM process.

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).

## 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)

## 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.

## 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)