Cross-Sectional Dimensions and BY Groups

Often, time series in a collection are related by a cross sectional dimension. For example, the national average U.S. consumer price index data shown in the previous example can be disaggregated to show price indexes for major cities. In this case, there are several related time series: CPI for New York, CPI for Chicago, CPI for Los Angeles, and so forth. When these time series are considered as one data set, the city whose price level is measured is a cross sectional dimension of the data.

There are two basic ways to store such related time series in a SAS data set. The first way is to use a standard form time series data set with a different variable for each series.

For example, the following statements read CPI series for three major U.S. cities:

```data citycpi;
input date : monyy7. cpiny cpichi cpila;
format date monyy7.;
datalines;
nov1989  133.200  126.700  130.000
dec1989  133.300  126.500  130.600
jan1990  135.100  128.100  132.100

... more lines ...

```

The second way is to store the data in a time series cross-sectional form. In this form, the series for all cross sections are stored in one variable and a cross section ID variable is used to identify observations for the different series. The observations are sorted by the cross section ID variable and by time within each cross section.

The following statements indicate how to read the CPI series for U.S. cities in time series cross-sectional form:

```data cpicity;
length city \$11;
input city \$11. date : monyy. cpi;
format date monyy.;
datalines;
New York       JAN1990   135.100
New York       FEB1990   135.300
New York       MAR1990   136.600

... more lines ...

```
```proc sort data=cpicity;
by city date;
run;
```

When processing a time series cross sectional form data set with most SAS/ETS procedures, use the cross section ID variable in a BY statement to process the time series separately. The data set must be sorted by the cross section ID variable and sorted by date within each cross section. The PROC SORT step in the preceding example ensures that the CPICITY data set is correctly sorted.

When the cross section ID variable is used in a BY statement, each BY group in the data set is like a standard form time series data set. Thus, SAS/ETS procedures that expect a standard form time series data set can process time series cross sectional data sets when a BY statement is used, producing an independent analysis for each cross section.

It is also possible to analyze time series cross-sectional data jointly. The PANEL procedure (and the older TSCSREG procedure) expects the input data to be in the time series cross-sectional form described here. See Chapter 20: The PANEL Procedure, for more information.