Some Issues in Seasonal Adjustment When Modeling Interventions

James A. Buszuwski and Stuart Scott

1. Introduction

This paper presents examples to illustrate that

intervention analysis, while beneficial to seasonal

adjustment, raises statistical issues deserving further

attention. As described in Buszuwski and Scott (1988), a

sharp drop in prices in early 1986 distorted seasonal

adjustment of the U.S. Producer Price Index (PPI) for

Gasoline. Modeling a ramp intervention across a threemonth period, plus other intervention effects, led to a

seasonal adjustment which (1) showed improved

diagnostics and (2) gave seasonal factors more in accord

with past history and analysts' expectations. Since its first

use in energy series in January 1988, X-11 seasonal

adjustment with intervention analysis has expanded to

about 20 Producer Price Index series and 30 Consumer

Price Index series in the areas of energy, transportation,

apparel, and tobacco. In turn, these series affect many

indexes at higher levels of aggregation, where indirect

seasonal adjustments are calculated.

The types of interventions we consider are additive

outlier (AO), level shift (LS), ramp (level shift spread

linearly across two or more months), and Burman's

seasonal shift (SS). Software developed at BLS

(Buszuwski, 1989), to support these activities, utilizes the

program developed by Burman (1980) for estimating

seasonal ARIMA models with interventions. The

intervention effects from the model are used to compute

prior adjustment factors for seasonal adjustment with the

1980 version of X-11-ARIMA for seasonal adjustment.

Findley et al (1988) and Bruce and Jurke (1992) have

also found benefits in applying intervention analysis to

seasonal adjustment with preliminary versions of Census'

X-12-ARIMA. This software is convenient and flexible

for modeling interventions, and can identify and estimate

intervention effects in an automatic mode. Burman and

Otto (1988) found only small gains from intervention

analysis, but stimulated subsequent work at Census and

the Bureau of Labor Statistics.

After six years of experience, we still find that

difficulties arise in the process. Examples show that

many intervention effects may be needed for a single

series, a departure from usual notions of desired

parsimony. Choosing a set of interventions can be labor

intensive and somewhat subjective. Caution is warranted

in modeling interventions near the end of a series, since a

wrong decision can lead to a poor seasonal adjustment. It

is hoped that the examples will stimulate more work on

intervention analysis in the context of seasonal

decomposition.

2. Parsimony

The issues will be illustrated with three series,

beginning with PPI Unleaded Gasoline (057104), shown

in Figure. 1. Part of the reason that difficulties arise is

the fact that many price index series have mild

seasonality, which can be overshadowed by large trend or

irregular movements. PPI gasoline prices, like consumer

gasoline prices, tend to rise during spring, level off

through summer and fall, and decline in winter. While

most might agree that seasonality is present in the series,

some might reasonably question whether the seasonality

is identifiable, i.e., can be estimated reliably.

 FIGURE 1

 FIGURE 2

Figure 2 is a spectral plot of (1) B01, the prior

adjusted series, divided by D12, the trend estimate from

X-11's decomposition, vs. (2) D13, the irregular from X11's decomposition. This graph indicates that seasonality

is present, and that it is effectively removed by X-11-

ARIMA. Figure 3 compares the official seasonal factors

for 1992 to those with no prior adjustment. The pattern

without prior adjustment is quite different and not in

accord with analysts' notions of seasonality in the series.

We take the position that with intervention analysis, X-11

seasonal adjustment is satisfactory, but without it it is not.
 FIGURE 3

Returning to Figure 1, the most prominent features are

trend movements, the sharp decline in early 1986, an

exceptional rise and fall during the latter half of 1990 and

early 1991, and, to a lesser extent, another rise and fall in

1989. These three behaviors correspond to, respectively,

(1) increased production following a dispute among oilproducing nations, (2) the Persian Gulf war, and (3) the

Alaskan oil spill. Also unusual are (1) very low values in

July and August, 1986 and (2) a sharp January increase in

1990. These are more evident from a graph of first

differences, grouped by month.

Intervention treatment greatly improves stationarity,

as seen in the prior adjusted series in Figure 1. In all, for

the eight-year span, 1983-90, the set of interventions used

for official adjustment of this series consists of four

ramps, (1/86-4/86, 12/86-2/87, 6/89-8/89, and 7/90-

10/90), one level shift (4/89), and five AO's (7/86, 8/86,

3/89, 10/89, and 12/90). Modeling diagnostics with a

(310) (011)12 seasonal model are acceptable; t-statistics

for intervention parameters are above 3, except for one

2.4 value. Stable F and Q values from X-11-ARIMA are

17.0 and .79.

The intervention model uses 14 parameters and affects

16 out of 96 points. This does not appear to be

parsimonious. Is there a simpler set of interventions

which might be used? After some experimentation, a

simpler model was tried with 2 ramps and 4 AO's

involving 10 out of 96 points. The parameter estimates

and the common intervention effects are very similar to

the official model. One of the omitted ramps has little

impact, since X-11-ARIMA adjusts both months in the

ramp in the same direction as the intervention analysis.

The major omission is treatment of the oil spill in mid1989. X-11 recognizes May, 1989 as an extreme value

both in Table C17 (Irregular Component) and Table D9

(extreme SI ratio replacement). In spite of this, the

seasonal pattern is magnified, as seen in Figure 4. The

peak shifts toward May and June. In particular, June

values for 1989 and 1990 are 105.5, compared to 102.0

and 102.1 in the official adjustment. A moving-F statistic

of 4.6 also argues against the quality of this seasonal

adjustment. The oil spill appears to affect seasonal

adjustment with the simple model more than we might

prefer.

 FIGURE 4

3. Sensitivity

For nonseasonal models, it is sometimes said that

outliers are unlikely to have great impact, except near the

end of the series. Many points are near the ends of

monthly subseries. Our feeling is that seasonal

decomposition is much more sensitive.

3.1 Different ramp start

The price decline in early 1986 shows the persistent

effects of a trend intervention. Excluding a single month

from a ramp can impact estimation of the seasonal

component. The series moves downward after December,

1985. Since the January decrease is not very different

from usual behavior, the official adjustment uses a ramp

from 1/86 to 4/86. Like level shifts, ramp effects are

considered part of the trend-cycle component. Starting

the ramp in December, i.e., including January as part of

the intervention period, makes a difference. The

modeling deteriorates, shrinking to a (210) (000)12, with

a failing Box-Ljung statistic. This exhibits sensitivity in

the sense that a complex set of interventions can be very

close to satisfactory without the diagnostics giving

positive indications. It helps explain that we find

ourselves going through numerous iterations before

settling on an intervention set. In this case, as well as

affecting the modeling, the December start impacts the

seasonal adjustment. The chart compares January

seasonal factors.

January

1986 1990

Official 96.0 96.7

Dec start 98.3 97.6

The 1986 value increases by 2.3. By 1990, the two

patterns are similar, although the difference for January is

nearly 1. Thus, treating one month differently has a

measurable effect on the seasonal adjustment.

3.2. Extra level shift

A second example involves an upward level shift in

January, 1990. This is part of the officially selected set of

interventions for the 1984-91 and 1985-92 spans.

However, it was initially discarded for 1983-90, due to

poor modeling results. The AR parameter estimates are

very similar, but the model shrinks to a monthly means

model and has a failing Box-Ljung statistic (33.5).
Somewhat surprisingly, the official factor for January

1990 is lower. What brings them together is that X-11-

ARIMA replaces the 1/90 unmodified SI ratio of 103.2

with 97.2. This again suggests that the extra January shift

is justified. Thus, the modeling results more favorable to

omitting this level shift are puzzling. Perhaps, we simply

haven't found quite the right combination of

interventions. In any case, this illustrates sensitivity on

the modeling side, and inconsistency between modeling

and X-11-ARIMA results.

3.3. Dropping marginal AO

Another illustration of sensitivity comes from

dropping one of the AO's, October 1989, which from the

graphs appears only marginally atypical. The X-11-

ARIMA statistics and the seasonal adjusment are very

similar, although October moves 0.3 in the expected

direction. The impact on modeling, however, is

significant. The model shrinks to a (210) (011)12, with a

failing Box-Ljung value (39.8). In this case, the

sensitivity lies in the modeling more than in the X-11

adjustment.

Unleaded Gasoline illustrates that series with mild

seasonality and volatile movements may require

substantial treatment for interventions, leading us away

from usual notions of parsimony. Both the modeling and

the seasonal adjustment results may be sensitive to

intervention specifications.

4. Seasonal Change Identification

In this section we discuss the benefits and pitfalls in

modeling interventions for the seasonal component of a

time series. An example of this type of intervention is the

Consumer Price Index (CPI) series for Women's

Separates and Sportswear (CUUR0000SE3803). A twocycle seasonal pattern that corresponds to the springsummer and fall-winter fashion seasons characterizes this

and several other apparel series (see Figure 5).

Pitfalls arise when an intervention may seem to be

associated with the seasonal component, but is more

appropriately modeled by a few additive outliers. An

example of this is the Producer Price Index (PPI) series

for Passenger Cars (141101) which is discussed in section

4.2.

4.1 Modeling Alternative Intervention Specifications

The major intervention affecting the Separates series

corresponds to a change in CPI data collection

methodology. This change, introduced in 1990, permitted

earlier pricing of spring season items, in response to

earlier introduction of these items in stores. As Figure 5

shows, February is a trough in the seasonal pattern (with

January nearby) for most years in the sample up to 1989.

The effect of the change in data collection methodology

is clear in the graph, when beginning in 1990, January

becomes a distinct trough in the seasonal pattern. Thus,

this series contains an abrupt change in the seasonal

pattern that becomes permanent. The CPI currently

models this as a negative seasonal shift at 1/90. January's

seasonal factor decreases relative to February's factor.

(The seasonal change model appearing in Bell (1983)

works nearly as well for this intervention).

 FIGURE 5

In the case of the Separates series, CPI analysts had

good information concerning the nature and timing of the

seasonal shift intervention. Unfortunately, the analyst

does not usually have such exact information available

and a considerable amount of speculation often enters the

analysis. Depending on the nature of the available

information, and how the analyst weighs this information,

the analysis may proceed in alternative directions.

For instance, if we envision ourselves as conducting

the analysis for the 1983-90 data span, and we see the

atypical winter trough for 1990, we might decide that

2/90 represents an additive outlier. Estimation of the

intervention in the modeling stage of the analysis would

produce a negative adjustment to the observed value for

2/90. The 1990 winter trough would then appear similar

to those of previous years. In this case the analyst is

maintaining the historical seasonal pattern in the data.

Situations can arise where the analyst is uncertain as

to how to model an apparent intervention. Prior

information concerning the series may be unavailable or

unreliable. A conservative approach to modeling under

this type of uncertainty is not modeling the intervention

until future data reveals its true nature. For instance, if in

the winter of 1991 the seasonal pattern reverts to its old

behavior then the analyst can be confident that 2/90 is an

isolated incident and therefore an additive outlier.

The advantage that not modeling the suspected

intervention offers is that the resulting seasonal factors

partially adapt. Often, seasonal factors are estimated that

are intermediate to those obtained by the seasonal shift

and additive outlier scenarios. The estimates of the

seasonal factors will not be optimal in this case.

However, "doing nothing" (DN) is less susceptible to the

large revisions liable to occur when an intervention is

modeled one way the first year and another way the next

year.

Continuing with the CPI's Separates series we model

each of the three alternative approaches to the winter

1990 intervention. Three 8-year spans of data are used

for the analysis. Table 1 defines the alternative
intervention sets and presents modeling and seasonal

adjustment results.

Model parameter estimates have significant tstatistics, Box-Ljung statistics are acceptable for all three

approaches. AIC values are similar for SS and AO and

slightly worse for DN. However, without prior

information concerning the nature of the intervention, it

would be difficult to choose among the alternative

approaches.

X-11ARIMA quality control statistics for the "No

Prior" (NP) seasonal adjustments are also included in

Table 1. The quality control statistics improve for the

three cases where interventions are modeled relative to

the case where they are not modeled (NP). Among the

three cases where the interventions are modeled the

analyst would have a difficult time making a selection

based on these statistics.

Figure 6 illustrates the differences in seasonal factor

estimates associated with the alternative ways of

modeling the winter 1990 intervention in the Separates

series. As can be seen the January factors adapt

immediately to the seasonal shift for the SS case for all

three spans. The corresponding factors for the AO case

tend to follow the pre-1990 trend. In the first span, the

DN January factor is almost identical to the AO case, but

in subsequent spans the DN factors are between the AO

and SS estimates for recent years.

For the February factors the differences between SS

and AO are more strongly defined. It is interesting to

note that the DN factors adapt to the seasonal shift

immediately as it occurs in all three spans. However,

there are substantial differences between DN and SS prior

to 1990.

By 1992, the earlier February pricing of seasonal

items has been in effect for three years. Even without

intervention treatment, X-11 is evolving to the new

seasonal pattern. The data for these three years are in

agreement with the prior information of a seasonal

change.

4.2 The Passenger Cars Case

Seasonality in this series centers on the industry

convention of a "model year". End-of-model-year

incentives to dealers lower prices in September and new

model introductions in October raise them. During the

mid-1980's the sharpness of the September trough was

moderated by earlier end-of-model-year incentives to

dealers, mostly August but sometimes as early as July. At

the same time October evolved as a sharp peak in the

seasonal factor pattern. To model this, the official set of

interventions for the series contains seasonal shifts

beginning in 9/85 and 8/86. Other interventions include

4/89 as an additive outlier and four ramps: 1) 12/84-1/85,

2) 9/86-10/86, 3) 1/87-2/87 and 4) 2/89-3/89. The

ARIMA model is L110011.

 FIGURE 7

However, our discussion here focuses on the

Septembers of 1989 and 1990. In these years, most of the

decline occurs before September. The official adjustments

treat these Septembers as AO's, which reinforces

September as the trough. For 1991 and 1992 (not shown

in Figure 7) the September trough clearly returns. Thus

the seasonal shift approach would have been an error.

Table 2 presents the X-11ARIMA quality control

statistics for the alternative modeling approaches for the

span 1/83-12/90. The SS approach models a positive

seasonal shift at 9/89. As can be seen the quality control

statistics improve for the three cases where interventions

are modeled relative to the case where they are not

modeled (NP). However the AO case, corresponding to

the official seasonal adjustment, appears to be best.

Table 2 X-11ARIMA Quality Control Statistics for

the Passenger Cars Series, 1/83-12/90

TYPE FS FM M7 Q

 NP 34.0 2.8 0.48 0.62

 SS 65.0 1.7 0.30 0.41

 AO 113.1 1.9 0.24 0.45

 DN 81.8 0.7 0.23 0.36

Table 3 presents seasonal factors for the important

months of September and October for the last five years

in the data span. The differences between the SS and AO

cases are significant. The DN factors are intermediate for

the Septembers of recent years. On the other hand, the

October factors for DN are very close to those from AO.

Table 3 Alternative Seasonal Factor Estimates for

the Passenger Cars Series

SEPTEMBER OCTOBER

SS AO DN SS AO DN

1986 95.3 94.9 95.4 103.6 103.6 103.7

1987 95.4 95.0 95.6 103.7 103.7 103.8

1988 95.5 95.0 95.7 103.9 103.8 104.0

1989 96.8 95.0 95.8 102.7 103.9 104.1

1990 96.8 95.1 95.9 102.8 104.0 104.2

The point of these exercises is that strict adherence to

modeling and seasonal adjustment quality control

statistics is not advised in deciding whether or not an

intervention represents a seasonal shift or a string of

outliers. Rather prior information is often crucial in

identifying the nature of a suspected intervention. For
instance, an abrupt change in the conventions and

practices of an industry could be the basis of a seasonal

shift. Unfortunately, information on such changes in

industry behavior may not be timely or the changes may

or may not be permanent, depending on many factors in

the marketplace.

5. Summary

This paper has emphasized technical points in

applying intervention analysis to seasonal adjustment.

Additional issues for a statistical agency include openness

to public scrutiny, reproducibility, and objectivity. Since

our methods are labor-intensive, resources are also an

issue. This means that at present only series important in

their own right or as key components to important

aggregates receive intervention treatment.

Summarizing the results of the paper, our examples

illustrate the following points:

· contrary to usual notions of parsimony, many

interventions may be needed for an effective

seasonal adjustment

· summary diagnostics are not enough; it is

important to keep track of how the seasonal

pattern is affected

· small changes in the intervention set can

significantly effect the modeling, the seasonal

adjustment, or both

· when alternate treatment interventions move the

seasonal factors in opposite directions, one of

them must be inferior; yet both can yield better

modeling and X-11 diagnostics than "doing

nothing"; economic knowledge of the series and

its seasonal pattern is needed.

6. References

Bell, William R. (1983), "A Computer Program for

Detecting Outliers in Time Series," Proceedings of the

ASA Section on Business & Economic Statistics, 634-639

Bruce, Andrew G. and Jurke, Simon R. (1992), "NonGaussian Seasonal Adjustment: X-12-ARIMA Versus

Robust Structural Models," submitted for publication

Burman, J. P. (1980), "Seasonal Adjustment by Signal

Extraction," Journal of the Royal Statistical Society A

143, 321-337

Burman, J. Peter and Otto, Mark C. (1988), "Outliers

in Time Series," Bureau of the Census Report, SRD/RR88/14

Buszuwski, James A. (1989), "RAMP Software

System for the PPI," internal BLS manual

Buszuwski, James A. and Scott, Stuart (1988), "On the

Use of Intervention Analysis in Seasonal Adjustment,"

Proceedings of the ASA Section on Business & Economic

Statistics, 337-342

Findley, David F. (1988), Monsell, Brian, Otto, Mark,

Bell, William, and Pugh, Marian, "Toward X-12-

ARIMA," Proceedings of the Bureau of the Census

Annual Research Conference, 591-622

Table 1 Results for the Separates Series

TYPE MA1 MA2 SMA1 L-B AIC FS FM M7 Q

1/83-12/90

 NP 43.0 1.8 0.379 0.60

 SS -0.28 0.41 17.2 -775 51.1 1.4 0.332 0.57

 AO -0.28 0.40 16.2 -774 49.8 1.6 0.343 0.56

 DN -0.26 0.45 17.2 -771 49.2 1.4 0.335 0.57

1/84-12/91

 NP 42.4 1.9 0.386 0.59

 SS -0.17 0.34 0.31 24.3 -797 60.1 1.8 0.319 0.51

 AO -0.19 0.34 0.30 19.8 -800 61.1 1.7 0.313 0.51

 DN -0.08 0.29 0.25 25.0 -787 57.7 1.7 0.324 0.52

1/85-12/92

 NP 57.6 2.7 0.362 0.53

 SS -0.22 0.35 0.35 23.9 -800 66.5 2.3 0.324 0.46

 AO -0.25 0.34 0.31 19.0 -801 69.3 2.1 0.311 0.46

 DN -0.12 0.29 0.27 23.3 -789 64.5 2.2 0.325 0.50

SS: DN plus 1/90(-SS)

AO: DN plus 2/90 2/91 2/92

DN: 1/84 2/84 8/89 4/92 9/92