Modeling and Multivariate Methods - SAS

Chapter 14 Performing Time Series Analysis 359
Time Series Commands
Angular Frequency is the angular frequency of the harmonic, 2πf i .
Sine is the Fourier sine coefficients, a i .
Cosine is the Fourier cosine coefficients, b i .
Periodogram is the periodogram, I(f i ).
Spectral Density
is the spectral density, a smoothed version of the periodogram.
Number of Forecast Periods
Difference
The Number of Forecast Periods command displays a dialog for you to reset the number of periods into
the future that the fitted models will forecast. The initial value is set in the Time Series Launch dialog. All
existing and future forecast results will show the new number of periods with this command.
Many time series do not exhibit a fixed mean. Such nonstationary series are not suitable for description by
some time series models such as those with only autoregressive and moving average terms (ARMA models).
However, these series can often be made stationary by differencing the values in the series. The differenced
series is given by
w t
= ( 1 – B) d ( 1 – B s ) D y t
where t is the time index and B is the backshift operator defined by By t = y t-1 .
The Difference command computes the differenced series and produces graphs of the autocorrelations and
partial autocorrelations of the differenced series. These graphs can be used to determine if the differenced
series is stationary.
Several of the time series models described in the next sections accommodate a differencing operation (the
ARIMA, Seasonal ARIMA models, and some of the smoothing models). The Difference command is useful
for determining the order of differencing that should be specified in these models.
The Differencing Specification dialog appears in the report window when you select the Difference
command. It allows you to specify the differencing operation you want to apply to the time series. Click
Estimate to see the results of the differencing operation. The Specify Differencing dialog allows you to
specify the Nonseasonal Differencing Order, d, the Seasonal Differencing Order, D, and the number of
Periods Per Season, s. Selecting zero for the value of the differencing order is equivalent to no differencing of
that kind.