If the ACCUMULATE= option is specified in the ID statement, data set observations are accumulated within each time period. The frequency (width of each time interval) is specified by the INTERVAL= option, and the ID variable contains the time ID values. Each time ID value corresponds to a specific time period. Accumulation is particularly useful when the input data set contains transactional data, whose observations are not spaced with respect to any particular time interval. The accumulated values form the time series that is used in subsequent analyses by the ESM procedure.

For example, suppose a data set contains the following observations:

19MAR1999 10 19MAR1999 30 11MAY1999 50 12MAY1999 20 23MAY1999 20

If the INTERVAL=MONTH option is specified on the ID statement, all of the preceding observations fall within three time periods: March 1999, April 1999, and May 1999. The observations are accumulated within each time period as follows.

If the ACCUMULATE=NONE option is specified, an error is generated because the ID variable values are not equally spaced with respect to the specified frequency (MONTH).

If the ACCUMULATE=TOTAL option is specified, the resulting time series is:

O1MAR1999 40 O1APR1999 . O1MAY1999 90

If the ACCUMULATE=AVERAGE option is specified, the resulting time series is:

O1MAR1999 20 O1APR1999 . O1MAY1999 30

If the ACCUMULATE=MINIMUM option is specified, the resulting time series is:

O1MAR1999 10 O1APR1999 . O1MAY1999 20

If the ACCUMULATE=MEDIAN option is specified, the resulting time series is:

O1MAR1999 20 01APR1999 . O1MAY1999 20

If the ACCUMULATE=MAXIMUM option is specified, the resulting time series is:

O1MAR1999 30 O1APR1999 . O1MAY1999 50

If the ACCUMULATE=FIRST option is specified, the resulting time series is:

O1MAR1999 10 O1APR1999 . O1MAY1999 50

If the ACCUMULATE=LAST option is specified, the resulting time series is:

O1MAR1999 30 O1APR1999 . O1MAY1999 20

If the ACCUMULATE=STDDEV option is specified, the resulting time series is:

O1MAR1999 14.14 O1APR1999 . O1MAY1999 17.32

As can be seen from the preceding examples, even though the data set observations contained no missing values, the accumulated time series can have missing values.