Modeling and Multivariate Methods - SAS

Chapter 14 Performing Time Series Analysis 367
Seasonal ARIMA
The Confidence Intervals box allows you to set the confidence level between 0 and 1 for the forecast
confidence bands. The Intercept check box determines whether the intercept term μ will be part of the
model. If the Constrain fit check box is checked, the fitting procedure will constrain the autoregressive
parameters to always remain within the stable region and the moving average parameters within the
invertible region. You might want to uncheck this box if the fitter is having difficulty finding the true
optimum or if you want to speed up the fit. You can check the Model Summary table to see if the resulting
fitted model is stable and invertible.
Seasonal ARIMA
In the case of Seasonal ARIMA modeling, the differencing, autoregressive, and moving average operators
are the product of seasonal and nonseasonal polynomials:
w t
= ( 1 – B) d ( 1 – B s ) D y t
ϕ( B) = ( 1 – ϕ 11 , B – ϕ 1, 2 B 2 – … – ϕ 1, p B p )( 1 – ϕ 2, s B s – ϕ 2, 2s B 2s – … – ϕ 2, Ps B Ps )
θ( B) = ( 1 – θ 1, 1 B – θ 1, 2 B 2 – … – θ 1, q B q )( 1 – θ 2, s B s – θ 22s , B 2s – … – θ 2, Qs B Qs )
where s is the number of periods in a season. The first index on the coefficients is the factor number (1
indicates nonseasonal, 2 indicates seasonal) and the second is the lag of the term.
The Seasonal ARIMA dialog appears when you select the Seasonal ARIMA command. It has the same
elements as the ARIMA dialog and adds elements for specifying the seasonal autoregressive order (P),
seasonal differencing order (D), and seasonal moving average order (Q). Also, the Periods Per Season box
lets you specify the number of periods per season (s). The seasonal ARIMA models are denoted as Seasonal
ARIMA(p,d,q)(P,D,Q)s.