The EXPAND Procedure

The EXPAND procedure converts time series from one sampling interval or frequency to another and interpolates missing values in time series. A wide array of data transformations is also supported. Using PROC EXPAND, you can collapse time series data from higher frequency intervals to lower frequency intervals, or expand data from lower frequency intervals to higher frequency intervals. For example, quarterly values can be aggregated to produce an annual series, or quarterly estimates can be interpolated from an annual series.

Time series frequency conversion is useful when you need to combine series with different sampling intervals into a single data set. For example, if you need as input to a monthly model a series that is only available quarterly, you might use PROC EXPAND to interpolate the needed monthly values.

You can also interpolate missing values in time series, either without changing series frequency or in conjunction with expanding or collapsing the series.

You can convert between any combination of input and output frequencies that can be specified by SAS time interval names. (See Chapter 5: Date Intervals, Formats, and Functions, for a complete description of SAS interval names.) When the FROM= and TO= options are used to specify from and to intervals, PROC EXPAND automatically accounts for calendar effects such as the differing number of days in each month and leap years.

The EXPAND procedure also handles conversions of frequencies that cannot be defined by standard interval names. Using the FACTOR= option, you can interpolate any number of output observations for each group of a specified number of input observations. For example, if you specify the option FACTOR=(13:2), 13 equally spaced output observations are interpolated from each pair of input observations.

You can also convert aperiodic series, observed at arbitrary points in time, into periodic estimates. For example, a series of randomly timed quality control spot-check results might be interpolated to form estimates of monthly average defect rates.

The EXPAND procedure can also change the observation characteristics of time series. Time series observations can measure beginning-of-period values, end-of-period values, midpoint values, or period averages or totals. PROC EXPAND can convert between these cases. You can construct estimates of interval averages from end-of-period values of a variable, estimate beginning-of-period or midpoint values from interval averages, or compute averages from interval totals, and so forth.

By default, the EXPAND procedure fits cubic spline curves to the nonmissing values of variables to form continuous-time approximations of the input series. Output series are then generated from the spline approximations. Several alternate conversion methods are described in the section Conversion Methods. You can also interpolate estimates of the rate of change of time series by differentiating the interpolating spline curve.

Various transformations can be applied to the input series prior to interpolation and to the interpolated output series. For example, the interpolation process can be modified by transforming the input series, interpolating the transformed series, and applying the inverse of the input transformation to the output series. PROC EXPAND can also be used to apply transformations to time series without interpolation or frequency conversion.

The results of the EXPAND procedure are stored in a SAS data set. No printed output is produced.