# ARMA: Create an Autoregressive Moving Average (ARMA) Process In SMAC-Group/simts: Time Series Analysis Tools

 ARMA R Documentation

## Create an Autoregressive Moving Average (ARMA) Process

### Description

Sets up the necessary backend for the ARMA process.

### Usage

ARMA(ar = 1, ma = 1, sigma2 = 1)


### Arguments

 ar A vector or integer containing either the coefficients for \phi's or the process number p for the Autoregressive (AR) term. ma A vector or integer containing either the coefficients for \theta's or the process number q for the Moving Average (MA) term. sigma2 A double value for the standard deviation, \sigma, of the ARMA process.

### 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

AR*p, MA*q

theta

\sigma

plength

Number of Parameters

print

String containing simplified model

obj.desc

y desc replicated x times

obj

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

starting

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

### Note

We consider the following model:

X_t = \sum_{j = 1}^p \phi_j X_{t-j} + \sum_{j = 1}^q \theta_j \varepsilon_{t-j} + \varepsilon_t

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

James Balamuta

### Examples

# Create an ARMA(1,2) process
ARMA(ar=1,2)
# Creates an ARMA(3,2) process with predefined coefficients.
ARMA(ar=c(0.23,.43, .59), ma=c(0.4,.3))

# Creates an ARMA(3,2) process with predefined coefficients and standard deviation
ARMA(ar=c(0.23,.43, .59), ma=c(0.4,.3), sigma2 = 1.5)


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