
1. 
What
is an economic time series? 
2. 
What
is seasonal adjustment? 
3. 
Why
do you seasonally adjust data? 
4. 
In
the original (unadjusted) series, this year's April value is larger
than the March value. But the seasonally adjusted series shows
a decrease from March to April this year. What does this discrepancy
mean? 
5. 
What
kinds of seasonal effects are removed during seasonal adjustment?

6. 
What
is the seasonal adjustment process? 
7. 
What
are trading day effects and trading day adjustments? 
8. 
How
is the seasonal adjustment derived? 
9. 
What
is X12ARIMA? 
10. 
What
diagnostics do you publish? 
11. 
What
indicates a good quality seasonal adjustment? 
12. 
Why
do you revise seasonal factors? 
13. 
What
is an annual rate? Why are seasonally adjusted data often
shown as annual rates? 
14. 
Why
can't I get the annual total by summing the seasonally adjusted
monthly values (or by summing the annual rates for each month
(quarter) of the year and dividing by 12 (4))? 
15. 
How
do I get seasonally adjusted quarterly data when you publish monthly
seasonal adjustments (or rates)? 
16. 
What
is an indirect adjustment? Why is it used? 
1. 
What is
an economic time series? 

An economic
time series is a sequence of successive measurements of an economic
activity (that is, variable) obtained at regular time intervals (such
as every month or every quarter). The data must be comparable over
time, so they must be consistent in the concept being measured and
the way that concept is measured.

2. 
What is
seasonal adjustment? 

Seasonal
adjustment is the process of estimating and removing seasonal effects
from a time series in order to better reveal certain nonseasonal
features. Examples of seasonal effects include a July drop in automobile
production as factories retool for new models and increases in heating
oil production during September in anticipation of the winter heating
season.(Seasonal effects are defined more precisely in 5.
and 6. below.) Sometimes we also estimate and remove
trading day effects and moving holiday effects (see 7.
below) during the seasonal adjustment process.

3. 
Why do
you seasonally adjust data? 

Seasonal
movements are often large enough that they mask other characteristics
of the data that are of interest to analysts of current economic trends.
For example, if each month has a different seasonal tendency toward
high or low values it can be difficult to detect the general direction
of a time series' recent monthly movement (increase, decrease, turning
point, no change, consistency with another economic indicator, etc.).
Seasonal adjustment produces data in which the values of neighboring
months are usually easier to compare. Many data users prefer seasonally
adjusted data because they want to see those characteristics that
seasonal movements tend to mask, especially changes in the direction
of the series.

4. 
In the
original (unadjusted) series, this year's April value is larger than
the March value. But the seasonally adjusted series shows a decrease
from March to April this year. What does this discrepancy mean? 

This difference
in direction can happen only when the seasonal factor for April is
larger than the seasonal factor for March, indicating that when the
underlying level of the series isn't changing, the April value will
typically be larger than the March value. This year, the original
series' April increase over the March value must be smaller than usual,
either because the underlying level of the series is decreasing or
because some special event or events abnormally increased the March
value somewhat, or decreased the April value somewhat. (When trading
day or moving holiday effects are present and are being adjusted out,
other explanations are possible.)

5. 
What kinds
of seasonal effects are removed during seasonal adjustment? 

Seasonal
adjustment procedures for monthly time series estimate effects that
occur in the same calendar month with similar magnitude and direction
from year to year. In series whose seasonal effects come primarily
from weather (rather than from, say, Christmas sales or economic activity
tied to the school year or the travel season), the seasonal factors
are estimates of average weather effects for each month, for example,
the average January decrease in new home construction in the Northeastern
region of the U.S. due to cold and storms. Seasonal adjustment does
not account for abnormal weather conditions or for yeartoyear changes
in weather. It is important to note that seasonal factors are estimates
based on present and past experience and that future data may show
a different pattern of seasonal factors.
Back to question 2 
6. 
What is
the seasonal adjustment process? 

The mechanics
of seasonal adjustment involve breaking down a series into trendcycle,
seasonal, and irregular components.
TrendCycle: 
Level
estimate for each month (quarter) derived from the surrounding
yearortwo of observations. 
Seasonal
Effects: 
Effects
that are reasonably stable in terms of annual timing, direction,
and magnitude. Possible causes include natural factors (the
weather), administrative measures (starting and ending dates
of the school year), and social/cultural/religious traditions
(fixed holidays such as Christmas). Effects associated with
the dates of moving holidays like Easter are not seasonal in
this sense, because they occur in different calendar months
depending on the date of the holiday. 
Irregular
Component: 
Anything
not included in the trendcycle or the seasonal effects (or
in estimated trading day or holiday effects). Its values
are unpredictable as regards timing, impact, and duration.It
can arise from sampling error, nonsampling error, unseasonable
weather, natural disasters, strikes, etc. 
Back to question 2 
7. 
What are
trading day effects and trading day adjustments? 

Monthly (or
quarterly) time series that are totals of daily activities can be
influenced by each calendar month's weekday composition. This influence
is revealed when monthly values consistently depend on which days
of the week occur five times in the month. For example, building permit
offices are usually closed on Saturday and Sunday. Thus, the number
of building permits issued in a given month is likely to be higher
if the month contains a surplus of weekdays and lower if the month
contains a surplus of weekend days. Recurring effects associated with
individual days of the week are called tradingday effects.
Tradingday effects can make it difficult to compare series values
or to compare movements in one series with movements in another. For
this reason, when estimates of tradingday effects are statistically
significant, we adjust them out of the series. The removal of such
estimates is called trading day adjustment.
Back to question 2 
8. 
How is
the seasonal adjustment derived? 

We use a
computer program called X12ARIMA to derive our seasonal adjustment
and produce seasonal factors.
It is difficult to estimate seasonal effects when the underlying level
of the series changes over time. For this reason, the program starts
by detrending the series with a crude estimate of the trendcycle.
It then derives crude seasonal factors from the detrended series.
It uses these to obtain a better trendcycle and detrended series
from which a more refined seasonal component is obtained. This iterative
procedure, involving successive improvements, is used because seasonal
effects make it difficult to determine the underlying level of the
series required for the first step. Crude and more refined irregular
components are used to identify and compensate for data that are so
extreme that they can distort the estimates of trendcycle and seasonal
factors.
The seasonal factors are divided into the original series to get the
seasonally adjusted series. For example, suppose for a particular
January, a series has a value of 100,000 and a seasonal factor of
0.80. The seasonally adjusted value for this January is 100,000/0.80=125,000.
If trading day or moving holiday effects are detected, their estimated
factors are divided out of the series before seasonal factor estimation
begins. The resulting seasonally adjusted series is therefore the
result of dividing by the product of the trading day, holiday, and
seasonal factors. The product factors are usually called the combined
factors, although some tables refer to them as the seasonal factors
for simplicity.

9. 
What is
X12ARIMA? 

X12ARIMA
is a seasonal adjustment program developed at the U.S. Census Bureau.
The program is based on the Bureau's earlier X11 program and the
X11ARIMA/88 program developed at Statistics Canada.
Improvements in X12ARIMA as compared to X11:
Use of ARIMA models
to forecast the series, allowing us to use better, symmetric moving
averages that give us generally smaller revisions to the seasonal
factors
New diagnostic tools
Wider variety of moving
average options
New user interface.
More information on
X12ARIMA

10. 
What diagnostics
do you publish? 

The X12ARIMA
program that we use to derive our seasonal adjustment calculates numerous
diagnostic statistics. Annually, we plan to publish at least
the statistics listed below. In this listing, the term "header"
refers to the column heading in the published table. The values of
the statistic appear under these headings. The headers themselves
refer to the series and its seasonal adjustment output:
O: 
Original series 
CI: 
Seasonally adjusted series (product of the I and C components) 
I: 
Irregular series 
C: 
TrendCycle series


Average
percent change of the original series 

Header: 
O 

Description: 
The
average monthtomonth (quartertoquarter) percentage change,
without regard to sign, of the original (not seasonally adjusted)
series. 

X12
Table: 
Table
F 2.A, Span 1


Average
percent change of the seasonally adjusted series 

Header: 
CI 

Description: 
The
average monthtomonth (quartertoquarter) percentage change,
without regard to sign, of the seasonally adjusted series. 

X12
Table: 
Table
F 2.A, Span 1


Average
percent change of the irregular component. 

Header: 
I 

Description: 
The
average monthtomonth (quartertoquarter) percentage change
of the irregular component. This component is obtained by dividing
the trendcycle component into the seasonally adjusted series. 

X12
Table: 
Table
F 2.A, Span 1


Average
percent change of the trendcycle component 

Header: 
C 

Description: 
The
average monthtomonth (quartertoquarter) percentage change
of the trendcycle component. This component is a smoothed version
of the seasonally adjusted series obtained by means of a moving
average. 

X12
Table: 
Table
F 2.A, Span 1


Ratio
of the irregular component to trendcycle component 

Header: 
I/C 

Description: 
Average
relative monthtomonth (quartertoquarter) change, without
regard to sign, of the irregular component divided by the average
relative monthtomonth (quartertoquarter) change, without
regard to sign, of the trendcycle component. The ratio serves
as an indication of the series' relative smoothness (small values)
or irregularity (large values). 

X12
Table: 
Table
F 2.E, Span 1


Measure
of the amount of moving seasonality present relative to the
amount of stable seasonality 

Header: 
M7 

Description: 
A
function of the Ftest assessing the significance of stable
seasonality and the Ftest assessing the significance of moving
seasonality. It is one of the 11 quality monitoring statistics
that X12ARIMA produces. M7 may range from 0 to 3 with an acceptance
range from 0 to 1. 

X12
Table: 
Table
F 3


Overall
quality assessment statistic 

Header: 
Q 

Description: 
A
weighted average of M1M11 (quality monitoring statistics from
X12ARIMA). An indicator of the overall quality of the adjustment.
Q has an acceptance range of 0 to 1. Values from 1.0 to 1.2
may be accepted if other diagnostics indicate suitable adjustment
quality. 

X12
Table: 
Table
F 3


Ftest
statistic for stable seasonality 

Header: 
F 

Description: 
An
Ftest measure of the presence of stable seasonality. It is
the quotient of two variances: (1) the betweenmonths (betweenquarters)
variance and (2) the residual variance.


X12
Table: 
Table
D 8


11. 
What
indicates a good quality seasonal adjustment? 


No residual
seasonal effect
Once we adjust the series for seasonality, there should be no remaining
seasonal effect in the adjusted series. The seasonally adjusted series
is the combination of the trendcycle and the irregular. Neither of
these components should contain seasonality. 


Passing values
for quality assessment diagnostics
We look for M7 and Q statistics less than 1.0. (See 10.
above.) These diagnostics help us decide if X12ARIMA can adequately
adjust the series. 


Stability
(small revisions) of the estimates
X12ARIMA contains several different stability diagnostics to help
us select X12ARIMA options to keep revisions of the estimates low.
Besides selecting the best X12ARIMA options, we can also reduce
revisions by running X12ARIMA every month to get concurrent seasonal
factors and by using ARIMA forecasts that make it possible to use
symmetrical averaging formulas in the calculation of the seasonal
factors, trendcycle, and irregulars.

12. 
Why
do you revise seasonal factors? 

There
are two reasons that we revise seasonal factors: 


We revise
factors when we revise the unadjusted data to achieve a better fit
to the revised data. 


The estimate
of a seasonal factor for a given month, say January, 1995, is most
strongly influenced by the data from surrounding Januaries (especially
from 1994 and 1996). In 1999, when the January data for 2000 and later
are not available, the seasonal factor estimate for January 1999 will
be of reduced quality, unless X12ARIMA has calculated good forecasts
of data for 2000 and later years and has used them in place of the
data that is not yet available. In any case, when future data become
available, we use them to obtain improved seasonal factor estimates
for the most recent years of the series. These revised factors lead
to revised seasonal adjustments of higher quality.

13. 
What is
an annual rate? Why are seasonally adjusted data often shown as annual
rates? 

Very generally, what we call the seasonally adjusted annual rate
for an individual month (quarter) is an estimate of what the annual
total would be if nonseasonal conditions were the same all year.
This "rate" is not a
rate in a technical sense but is a level estimate.
The seasonally adjusted
annual rate is the seasonally adjusted monthly value multiplied
by 12 (4 for quarterly series). For example,
The benefit of the annual
rate is that we can compare one month's data or one quarter's data
to an annual total, and we can compare a month to a quarter.
The Bureau of Economic
Analysis (BEA) publishes quarterly estimates of the United States
gross domestic product (GDP) at an annual rate, and many of the
Census Bureau data series are inputs to GDP. Annual rates for input
series help users see the data at the same level as GDP estimates.

14. 
Why can't
I get the annual total by summing the seasonally adjusted monthly
values (or by summing the annual rates for each month (quarter) of
the year and dividing by 12 (4))? 

When seasonal
adjustment is done by dividing the time series by seasonal factors
(or combined seasonaltrading dayholiday factors) it is arithmetically
impossible for the adjusted series to have the same annual totals
as the unadjusted series (except in the uninteresting case in which
the time series values repeat perfectly from year to year). "Benchmarking"
procedures can be used to modify the adjusted series so as to force
the adjusted series to have the same totals as the unadjusted series,
but these procedures do not account for evolving seasonal effects
or for trading day differences due to the differing weekday compositions
of different years.

15. 
How do
I get seasonally adjusted quarterly data when you publish monthly
seasonal adjustments (or rates)? 

Adding the seasonally
adjusted values for each month in a quarter will produce a seasonally
adjusted value for the quarter. (Averaging the seasonally adjusted
annual rates for each month in a quarter will produce a seasonally
adjusted annual rate for that quarter.)
Calculate adjusted data
for a year in a similar way.

16. 
What is
an indirect adjustment? Why is it used? 

If an aggregate time
series is a sum (or other composite) of component series that are
seasonally adjusted, then the sum of the adjusted component series
provides a seasonal adjustment of the aggregate series that is called
the indirect adjustment. This adjustment is usually different from
the direct adjustment that is obtained by applying the seasonal
adjustment program to the aggregate (or composite) series. When
the component series have quite distinct seasonal patterns and have
adjustments of good quality, indirect seasonal adjustment is usually
of better quality. Indirect seasonal adjustments are preferred by
many data users because they are consistent with the adjustments
of the component series.
Example: United States
Total Housing Starts
United States = Northeast
Region + Midwest Region + South Region + West Region
Because seasonal patterns
are different in the different regions of the country, we can estimate
the seasonality better by adjusting at the regional level and summing
the results to obtain the seasonal adjustment for the U.S. total.

