Summary Measures for Evaluating the Quality of the Seasonal Adjustment of
M3 Series

The measures shown in table G-1 through G-6 in the printed report were used
in evaluating the current seasonal adjustment procedure. A brief
description of these measures is included below.

The average absolute percentage change without regard to sign is the
average of the absolute percentage changes between all pairs of adjacent
months; it is one measure of variability.

The "O" is the average month-to-month percentage change, without regard to
sign, in the original series. The "CI" is the same for the seasonally
adjusted series. The "C" is the same for the cyclical component which is a
smooth, flexible moving average of the seasonally adjusted series. The "I"
is the same for the irregular component, which is obtained by dividing the
cyclical component into the seasonally adjusted series.

The "IC" is the average relative month-to-month change, without regard to
sign, of the irregular component divided by the average relative month-to-
month change, without regard to sign, of the cyclical component. It serves
as an indication of the series' relative irregularity.

The measures of relative contributions of the component series to the
variation in the original series can be interpreted as measures of the
absolute importance of each component. The percentages shown are actually
the percentages of the total variance obtained by adding up the variances
of the individual components and may differ from those using the variance
computed directly from the original series. The I is the irregular
component; C is the trend component; and S, the seasonal component. A value
of I greater than 30 usually indicates that the erratic movements in the
series will significantly diminish the ability of X-11 to identify the
seasonal movements in the data. Values of S less than 50 suggest that the
seasonal movements are difficult to quantify.

The F value presented here measures the presence of stable seasonality.
It is the quotient of two variances: (1) the between months variance, which
is mainly due to seasonal, and (2) the residual variance, which is mainly
due to irregular. A value of 7.0 or greater is used as an indicator of the
presence of stable seasonality.

The Q value is a weighted average of 11 different quality control
statistics concerned variously with the irregular movements of the series
and with seasonal patterns changing too rapidly to be identifiable,
particularly in recent years. A value greater than 1.2 is unacceptable;
whereas, values less than 0.8 often indicate an acceptable adjustment. With
values between 0.8 and 1.2, other measures must be consulted to determine
if the seasonal movement in the series can be adequately quantified by the
X-11 program.

The SFR and MMR are diagnostics from the sliding spans tests. The SFR
measures the amount of revision in a seasonal factor for a specific
observation which occurs as the specific years included in the seasonal
adjustment analysis change. For example, for most series in this
publication a 14-year series is examined as four 11-year spans: 1982-1992,
1983-1993, 1984-1994, and 1985-1995. For the SFR, it is considered
acceptable if no more than 25 percent of the seasonal factors are revised
by more than 3 percent for Q values less than or equal to 0.8; for Q values
< 0.8; for Q values between 0.8 and 1.2,>between 0.8 and 1.2, the SFR
should be no more than 15 percent.

The MMR is a measure of the revision in the month-to-month percent change
for specific observations, as the years included in the span are changed.
It is considered acceptable if no more than 40 percent of the observations
are revised by more than 3 percent.

The ratio of maximum to minimum seasonal factor gives the ratio of the
largest downward adjustment to the largest upward adjustment and,
therefore, measures the extent of the seasonal movements estimated by
the program. An NS in the last column indicates a series is not seasonally
adjusted in this publication. The information in the other columns for
these series is the measures produced in X-11 ARIMA and sliding spans runs
to determine the presence of quantifiable seasonality. For series which are
not seasonally adjusted in this publication, the original unadjusted values
are included in both the seasonally adjusted and unadjusted
totals.