Create an Autoregressive Integrated Moving Average (ARIMA) Process

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 $\sigma^2$.

Author

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)