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 X-13ARIMA-SEATS seasonal adjustment software. X-13ARIMA-SEATS is an extension of the
X-11 variant of the Census Method II Seasonal Adjustment methodology. In some cases, intervention analysis seasonal adjustment
is carried out using X-13ARIMA-SEATS 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 show erratic behavior due to
non-seasonal economic events (called interventions) or methodology changes. These events, which can be one-time occurrences or recurring events that happen
at infrequent and irregular intervals, adversely affect the estimate of the seasonal component of the series.
Intervention analysis seasonal adjustment allows non-seasonal economic phenomena, such as outliers and level shifts, to be factored out of indexes
before calculation of seasonal adjustment factors. (An outlier is an extreme value for a particular month. A level shift is a change or shift in the price
level of a CPI series caused by an event, such as an excise tax increase or oil embargo, occurring over one or more months.) An index series whose underlying
trend has experienced a sharp and permanent shift will generate distorted results when adjusted using the standard X-13ARIMA-SEATS procedure. X-13ARIMA-SEATS's regression techniques are used to model the distortions and account for them as part of the seasonal adjustment process. The result is an
adjustment based on a representation of the series with the seasonal pattern emphasized. Intervention analysis seasonal adjustment also makes it possible
to account for seasonal shifts, resulting in a better seasonal adjustment in the periods before and after the shift occurred. Not all CPI series are
adjusted using intervention analysis seasonal adjustment techniques. However, for affected series, the resulting seasonal factors better represent the true
seasonal pattern than factors calculated without these techniques. These seasonal factors are applied to the original unadjusted series. Level shifts and
outliers, removed in calculating the seasonal factors, remain in the resulting seasonally adjusted series.
In recent years, BLS has used intervention analysis seasonal adjustment for various indexes—gasoline, fuel oil, new vehicles, women's and girls’ apparel,
educational books and supplies, electricity, utility (piped) gas service, water and sewerage maintenance, nonalcoholic beverages and beverage materials,
and whiskey at home are examples. Series are adjusted using intervention analysis techniques when interventions are clearly identified. After a number of
years, series may revert to adjustment using standard methods. In addition, for some series, intervention analysis is used, and the resulting series does
not show a clear and stable seasonal pattern. In these cases, the series is not seasonally adjusted.
Direct and aggregative adjustment
Each year BLS seasonally adjusts eligible lower-level CPI index series directly with the X-13ARIMA-SEATS software using unadjusted indexes for the
latest five to eight calendar years. CPI index series are adjusted using the multiplicative model.
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. Each year in February, BLS recalculates and publishes revised seasonally adjusted
indexes for the previous five years. Seasonally adjusted indexes become final in the last and 5th year of revision. Seasonal factors for the past year
are used to generate seasonally adjusted indexes for the current year starting with the release of the January CPI.
Last Modified Date: February 18, 2014