Estimation of Seasonal Effects
From the BLS Handbook of Methods
Bulletin 2490, April 1997
Chapter 17, The Consumer Price Index, "Estimation of Price Change", p. 192
Seasonal adjustment Seasonal adjustment removes the estimated effect of changes that normally
occur at the same time every year (such as price movements resulting from changing climatic
conditions, production cycles, model changeovers, holidays, sales, etc.). CPI series are
selected for seasonal adjustment if they pass certain statistical criteria and if there is an
economic rationale for the observed seasonality. Seasonal factors used in computing the
seasonally adjusted indexes are derived using the ARIMA option of the X-11 variant of the Census
Method II Seasonal Adjustment Program. In some cases, intervention analysis seasonal adjustment
is carried out using X-12-ARIMA to derive more accurate seasonal factors. Consumer price indexes
may be adjusted directly or aggregatively depending on the level of aggregation of the index,
and the behavior of the component series.
Intervention analysis seasonal adjustment Some index series that show occasional erratic
behavior known as a 'trend shift," which can cause problems in making an accurate seasonal
adjustment. An index series whose underlying trend has experienced a sharp and permanent shift
will generate distorted results when put through the X-11 ARIMA procedure. Trend shifts have
been observed, for example, when gasoline prices have reacted to major changes instituted by the
Organization of Petroleum Exporting Countries cartel—a recurring event which happens at
infrequent and irregular intervals. Another kind of distorting change may occur when the
seasonal pattern itself changes.
In order to compensate for those instances in which such distortions (called interventions) are
both substantial and identifiable, regression techniques are used to model the distortions and
account for them as part of the seasonal adjustment process. Intervention analysis seasonal
adjustment is performed using X-12-ARIMA seasonal adjustment software. X-12-ARIMA, developed by
the Bureau of the Census, is an extension of the X-11 methodology which allows the use of
regression-ARIMA models for more sophisticated time series analysis. In recent years, BLS has
used intervention analysis seasonal adjustment for various indexes—gasoline, fuel oil, new
vehicle, women's apparel, and tobacco and smoking products.
Direct and aggregative adjustment Each year BLS seasonally adjusts eligible lower level CPI
index series independently with the X-11-ARIMA multiplicative model on to data for the latest 5
to 8 calendar years. This product's seasonal factors that will be used to generate seasonal
adjusted indexes for the current year. BLS recalculates and publishes seasonally adjusted
indexes for the previous 5 years.
Most higher level index series are adjusted by the indirect, or aggregative, method, which is
more appropriate for broad categories whose component indexes show strongly different seasonal
patterns. Under the aggregative method, direct adjustment is first applied to indexes at lower
levels of detail, and thereafter the adjusted detail is aggregated up to yield the higher level
seasonally adjusted indexes. If intervention analysis is indicated, it will be used in adjusting
selected lower level indexes prior to aggregation. For those series which have not been selected
for seasonal adjustment, the original, unadjusted data are used in the aggregation process.
Revision The seasonal factors are updated annually. BLS recalculates and publishes
seasonally adjusted indexes for the previous 5 years.
Last Modified Date: February 19, 2003