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

## Description

Definition of an ARMA(1,1)

## Usage

 1 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 = φ X_{t-1} + θ_1 \varepsilon_{t-1} + \varepsilon_t,

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

James Balamuta

## Examples

 1 2 3 4 5 # 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 Nov. 16, 2018, 8:05 a.m.