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The EXPAND Procedure |

The spline functions fit by the EXPAND procedure are very good at approximating continuous curves within the time range of the input data but poor at extrapolating beyond the range of the data. The accuracy of the results produced by PROC EXPAND may be somewhat less at the ends of the output series than at time periods for which there are several input values at both earlier and later times. The curves fit by PROC EXPAND should not be used for forecasting.

PROC EXPAND normally avoids extrapolation of values beyond the time range of the nonmissing input data for a series, unless the EXTRAPOLATE option is used. However, if the start or end of the input series does not correspond to the start or end of an output interval, some output values may depend in part on an extrapolation.

For example, if FROM=YEAR, TO=WEEK, and OBSERVED=BEGINNING, the first observation output for a series is for the week of 1 January of the first nonmissing input year. If 1 January of that year is not a Sunday, the beginning of this week falls before the date of the first input value, and therefore a beginning-of-period output value for this week is extrapolated.

This extrapolation is made only to the extent needed to complete the terminal output intervals that overlap the endpoints of the input series and is limited to no more than the width of one FROM= interval or one TO= interval, whichever is less. This restriction of the extrapolation to complete terminal output intervals is applied to each series separately, and it takes into account the OBSERVED= option for the input and output series.

When the EXTRAPOLATE option is used, the normal restriction on extrapolation is overridden. Output values are computed for the full time range covered by the input data set.

For the SPLINE method, extrapolation is performed by a linear projection of the trend of the cubic spline curve fit to the input data, not by extrapolation of the first and last cubic segments.

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