Modeling and Multivariate Methods - SAS

Chapter 14 Performing Time Series Analysis 355
Time Series Commands
Time Series Commands
Graph
The platform red triangle menu has the options described in the following sections.
The Time Series platform begins by showing a time series plot, like the one shown previously in
Figure 14.2. The Graph command on the platform popup menu has a submenu of controls for the time
series plot with the following commands.
Time Series Graph
hides or displays the time series graph.
Show Points
hides or displays the points in the time series graph.
Connecting Lines
hides or displays the lines connecting the points in the time series graph.
Mean Line
series.
hides or displays a horizontal line in the time series graph that depicts the mean of the time
Autocorrelation
The Autocorrelation command alternately hides or displays the autocorrelation graph of the sample, often
called the sample autocorrelation function. This graph describes the correlation between all the pairs of points
in the time series with a given separation in time or lag. The autocorrelation for the kth lag is
N
c k
1
r k
= ---- wherec k
= ---
c N ( y t
– y) ( y t– k
– y)
0
t = k + 1
where y is the mean of the N nonmissing points in the time series. The bars graphically depict the
autocorrelations.
By definition, the first autocorrelation (lag 0) always has length 1. The curves show twice the large-lag
standard error (± 2 standard errors), computed as
k – 1
1
SE --- k
N
1 2 r 2
= +
i
i = 1
The autocorrelation plot for the Seriesg data is shown on the left in Figure 14.3. You can examine the
autocorrelation and partial autocorrelations plots to determine whether the time series is stationary
(meaning it has a fixed mean and standard deviation over time) and what model might be appropriate to fit
the time series.
In addition, the Ljung-Box Q and p-values are shown for each lag. The Q-statistic is used to test whether a
group of autocorrelations is significantly different from zero or to test that the residuals from a model can be
distinguished from white-noise.