Example 31.1 The Airline Series Revisited

The series in this example, the monthly airline passenger series, has already been discussed earlier; see the section A Seasonal Series with Linear Trend. Recall that the series consists of monthly numbers of international airline travelers (from January 1949 to December 1960). Here additional output features of the UCM procedure are illustrated, such as how to use the ESTIMATE and FORECAST statements to limit the span of the data used in parameter estimation and forecasting. The following statements fit a BSM to the logarithm of the airline passenger numbers. The disturbance variance for the slope component is held fixed at value 0; that is, the trend is locally linear with constant slope. In order to evaluate the performance of the fitted model on observed data, some of the observed data are withheld during parameter estimation and forecast computations. The observations in the last two years, years 1959 and 1960, are not used in parameter estimation, while the observations in the last year, year 1960, are not used in the forecasting computations. This is done using the BACK= option in the ESTIMATE and FORECAST statements. In addition, a panel of residual diagnostic plots is obtained using the PLOT=PANEL option in the ESTIMATE statement.

data seriesG;
   set sashelp.air;
   logair = log(air);
run;

ods graphics on;
proc ucm data = seriesG;
   id date interval = month;
   model logair;
   irregular;
   level;
   slope var = 0 noest;
   season length = 12 type=trig;
   estimate back=24 plot=panel;
   forecast back=12 lead=24 print=forecasts;
run;

The following tables display the summary of data used in estimation and forecasting (Output 31.1.1 and Output 31.1.2). These tables provide simple summary statistics for the estimation and forecast spans; they include useful information such as the beginning and ending dates of the span, the number of nonmissing values, etc.

The following tables display the fixed parameters in the model, the preliminary estimates of the free parameters, and the final estimates of the free parameters (Output 31.1.3, Output 31.1.4, and Output 31.1.5).