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 The EXPAND Procedure

## Frequency Conversion

Frequency conversion is controlled by the FROM=, TO=, and FACTOR= options. The possible combinations of these options are explained in the following:

None Used
If FROM=, TO=, and FACTOR= are not specified, no frequency conversion is done. The data are processed to interpolate any missing values and perform any specified transformations. Each input observation produces one output observation.

FACTOR=(n:m)
FACTOR=(n:m) specifies that n output observations are produced for each group of m input observations. The fraction m/n is reduced first: thus FACTOR=(10:6) is equivalent to FACTOR=(5:3). Note that if m/n=1, the result is the same as the case given previously under "None Used".

FROM=interval
The FROM= option used alone establishes the frequency and interval widths of the input observations. Missing values are interpolated, and any specified transformations are performed, but no frequency conversion is done.

TO=interval
When the TO= option is used without the FROM= option, output observations with the TO= frequency are generated over the range of input ID values. The first output observation is for the TO= interval containing the ID value of the first input observation; the last output observation is for the TO= interval containing the ID value of the last input observation. The input observations are not assumed to form regular time series and may represent aperiodic points in time. An ID variable is required to give the date or datetime of the input observations.

FROM=interval TO=interval
When both the FROM= and TO= options are used, the input observations have the frequency given by the FROM= interval, and the output observations have the frequency given by the TO= interval.

FROM=interval FACTOR=(n:m)
When both the FROM= and FACTOR= options are used, a TO= interval is inferred from the combination of the FROM=interval and the FACTOR=(n:m) values specified. For example, FROM=YEAR FACTOR=4 is the same as FROM=YEAR TO=QTR. Also, FROM=YEAR FACTOR=(3:2) is the same as FROM=YEAR used with TO=MONTH8. Once the implied TO= interval is determined, this combination operates the same as if FROM= and TO= had been specified. If no valid TO= interval can be constructed from the combination of the FROM= and FACTOR= options, an error is produced.

TO=interval FACTOR=(n:m)
The combination of the TO= option and the FACTOR= option is not allowed and produces an error.

ALIGN= option
Controls the alignment of SAS dates used to identify output observations. The ALIGN= option allows the following values: BEGINNING|BEG|B, MIDDLE|MID|M, and ENDING|END|E. BEGINNING is the default.

### Converting to a Lower Frequency

When converting to a lower frequency, the results are either exact or approximate, depending on whether or not the input intervals nest within the output intervals and depending on the need to interpolate missing values within the series. If the TO= interval is nested within the FROM= interval (as when converting monthly to yearly), and if there are no missing input values or partial periods, the results are exact.

When values are missing or the FROM= intervals are not nested within the TO= intervals (as when aggregating weekly to monthly), the results depend on an interpolation. The METHOD=AGGREGATE option always produces exact results, never an interpolation. However, this method cannot be used unless the FROM= interval is nested within the TO= interval.

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