Sets up the necessary backend for the ARIMA process.

`ARIMA(ar = 1, i = 0, 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.

- i
An `integer`

containing the number of differences to be done.

- 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 ARIMA process.

## 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)

## Details

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

## Note

We consider the following model: $$\Delta^i X_t = \sum_{j = 1}^p \phi_j \Delta^i X_{t-j} + \sum_{j = 1}^q \theta_j \varepsilon_{t-j} + \varepsilon_t$$, where \(\varepsilon_t\) is iid from a zero
mean normal distribution with variance \(\sigma^2\).

## Examples

```
# Create an ARMA(1,2) process
ARIMA(ar=1,2)
# Creates an ARMA(3,2) process with predefined coefficients.
ARIMA(ar=c(0.23,.43, .59), ma=c(0.4,.3))
# Creates an ARMA(3,2) process with predefined coefficients and standard deviation
ARIMA(ar=c(0.23,.43, .59), ma=c(0.4,.3), sigma2 = 1.5)
```