Modeling and Multivariate Methods - SAS

Chapter 14 Performing Time Series Analysis 373
Transfer Functions
e t represents the noise series
X 1, t–d1 indicates the series X 1 is indexed by t with a d1-step lag
μ represents the mean level of the model
ϕ(B) and θ(B) represent autoregressive and moving average polynomials from an ARIMA model
ω k (B) and δ k (B) represent numerator and denominator factors (or polynomials) for individual transfer
functions, with k representing an index for the 1 to m individual inputs.
Each polynomial in the above model can contain two parts, either nonseasonal, seasonal, or a product of the
two as in seasonal ARIMA. When specifying a model, leave the default 0 for any part that you do not want
in the model.
Select Transfer Function to bring up the model specification dialog.
Figure 14.14 Transfer Function Specification Dialog
The dialog consists of several parts.
Noise Series Orders contains specifications for the noise series. Lowercase letters are coefficients for
non-seasonal polynomials, and uppercase letters for seasonal ones.
Choose Inputs
lets you select the input series for the model.
Input Series Orders specifies polynomials related to the input series.The first three orders deal with
non-seasonal polynomials. The next four are for seasonal polynomials. The final is for an input lag.
In addition, there are three options that control model fitting.
Intercept
specifies whether μ is zero or not.
Alternative Parameterization
numerator polynomials.
specifies whether the general regression coefficient is factored out of the