The X11 Procedure

Prior Daily Weights and Trading-Day Regression

Suppose that a detailed examination of retail sales at ZXY Company indicates that certain days of the week have higher amounts of sales. In particular, Thursday, Friday, and Saturday have approximately twice the amount of sales as Monday, Tuesday, and Wednesday, and no sales occur on Sunday. This means that months with five Saturdays would have higher amounts of sales than months with only four Saturdays.

This phenomenon is called a calendar effect; it can be handled in PROC X11 by using the PDWEIGHTS (prior daily weights) statement or the TDREGR=option (trading-day regression). The PDWEIGHTS statement and the TDREGR=option can be used separately or together.

If the relative weights are known (as in the preceding) it is appropriate to use the PDWEIGHTS statement. If further residual calendar variation is present, TDREGR=ADJUST should also be used. If you know that a calendar effect is present, but know nothing about the relative weights, use TDREGR=ADJUST without a PDWEIGHTS statement.

In this example, it is assumed that the calendar variation is due to both prior daily weights and residual variation. Thus both a PDWEIGHTS statement and TDREGR=ADJUST are specified.

Note that only the relative weights are needed; in the actual computations, PROC X11 normalizes the weights to sum to 7.0. If a day of the week is not present in the PDWEIGHTS statement, it is given a value of zero. Thus sun=0 is not needed.

proc x11 data=sales;
   monthly date=date tdregr=adjust;
   var sales;
   tables a1 a4 b15 b16 C14 C15 c18 d11;
   pdweights mon=1 tue=1 wed=1 thu=2 fri=2 sat=2;
   output out=x11out a1=a1 a4=a4 b1=b1 c14=c14
                     c16=c16 c18=c18 d11=d11;

Tables of interest include A1, A4, B15, B16, C14, C15, C18, and D11. Table A4 contains the adjustment factors derived from the prior daily weights; Table C14 contains the extreme irregular values excluded from trading-day regression; Table C15 contains the trading-day-regression results; Table C16 contains the monthly factors derived from the trading-day regression; and Table C18 contains the final trading-day factors derived from the combined daily weights. Finally, Table D11 contains the final seasonally adjusted series.