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 $$\sigma^2$$.

James Balamuta

## 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)