# ARMA11: Definition of an ARMA(1,1) In SMAC-Group/simts: Time Series Analysis Tools

 ARMA11 R Documentation

## Definition of an ARMA(1,1)

### Description

Definition of an ARMA(1,1)

### Usage

ARMA11(phi = NULL, theta = NULL, sigma2 = 1)


### Arguments

 phi A double containing the parameter \phi _1 (see Note for details). theta A double containing the parameter \theta _1 (see Note for details). sigma2 A double value for the parameter \sigma^2 (see Note for details).

### Details

A variance is required since the model generation statements utilize randomization functions expecting a variance instead of a standard deviation like R.

### Value

An S3 object with called ts.model with the following structure:

process.desc

AR1, MA1, SIGMA2

theta

\phi, \theta, \sigma^2

plength

Number of Parameters: 3

print

String containing simplified model

obj.desc

Depth of Parameters e.g. list(c(1,1,1))

starting

Guess Starting values? TRUE or FALSE (e.g. specified value)

### Note

We consider the following model:

X_t = \phi X_{t-1} + \theta_1 \varepsilon_{t-1} + \varepsilon_t,

where \varepsilon_t is iid from a zero mean normal distribution with variance \sigma^2.

James Balamuta

### Examples

# Creates an ARMA(1,1) process with predefined coefficients.
ARMA11(phi = .23, theta = .1, sigma2 = 1)

# Creates an ARMA(1,1) process with values to be guessed on callibration.
ARMA11()


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