Modeling and Multivariate Methods - SAS

Chapter 14 Performing Time Series Analysis 365
ARIMA Model
Iteration History
The model parameter estimation is an iterative procedure by which the log-likelihood is maximized by
adjusting the estimates of the parameters. The iteration history for each model you request shows the value
of the objective function for each iteration. This can be useful for diagnosing problems with the fitting
procedure. Attempting to fit a model which is poorly suited to the data can result in a large number of
iterations that fail to converge on an optimum value for the likelihood. The Iteration History table shows
the following quantities:
Iter
lists the iteration number.
Iteration History
lists the objective function value for each step.
Step
lists the type of iteration step.
Obj-Criterion
lists the norm of the gradient of the objective function.
Model Report Options
The title bar for each model you request has a popup menu, with the following options for that model:
Show Points
hides or shows the data points in the forecast graph.
Show Confidence Interval
hides or shows the confidence intervals in the forecast graph.
Save Columns
creates a new data table with columns representing the results of the model.
Save Prediction Formula
saves the data and prediction formula to a new data table.
Create SAS Job
creates SAS code that duplicates the model analysis in SAS.
Submit to SAS submits code to SAS that duplicates the model analysis. If you are not connected to a SAS
server, prompts guide you through the connection process.
Residual Statistics controls which displays of residual statistics are shown for the model. These displays
are described in the section “Time Series Commands” on page 355; however, they are applied to the
residual series.
ARIMA Model
An AutoRegressive Integrated Moving Average (ARIMA) model predicts future values of a time series by a
linear combination of its past values and a series of errors (also known as random shocks or innovations). The
ARIMA command performs a maximum likelihood fit of the specified ARIMA model to the time series.
For a response series { y i
}, the general form for the ARIMA model is:
φ( B) ( w t
– μ) = θ( B)a t
where
t is the time index