Modeling and Multivariate Methods - SAS

Chapter 14 Performing Time Series Analysis 363
Modeling Reports
MAE is the Mean Absolute Error, and is computed
n
1
--
n y i
– ŷ i
i = 1
–2LogLikelihood is minus two times the natural log of the likelihood function evaluated at the best-fit
parameter estimates. Smaller values are better fits.
Stable indicates whether the autoregressive operator is stable. That is, whether all the roots of
lie outside the unit circle.
Invertible indicates whether the moving average operator is invertible. That is, whether all the roots of
θ( z) = 0 lie outside the unit circle.
Note: The φ and θ operators are defined in the section “ARIMA Model” on page 365.
φ( z) = 0
Parameter Estimates Table
There is a Parameter Estimates table for each selected fit, which gives the estimates for the time series model
parameters. Each type of model has its own set of parameters. They are described in the sections on specific
time series models. The Parameter Estimates table has these terms:
Term lists the name of the parameter. These are described below for each model type. Some models
contain an intercept or mean term. In those models, the related constant estimate is also shown. The
definition of the constant estimate is given under the description of ARIMA models.
Factor (Seasonal ARIMA only) lists the factor of the model that contains the parameter. This is only
shown for multiplicative models. In the multiplicative seasonal models, Factor 1 is nonseasonal and
Factor 2 is seasonal.
Lag (ARIMA and Seasonal ARIMA only) lists the degree of the lag or backshift operator that is applied
to the term to which the parameter is multiplied.
Estimate
lists the parameter estimates of the time series model.
Std Error lists the estimates of the standard errors of the parameter estimates. They are used in
constructing tests and confidence intervals.