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Consumer Price Index

Estimation of Seasonal Effects

From the BLS Handbook of Methods, June 2015, Chapter 17, The Consumer Price Index, "Calculation of seasonally adjusted indexes", p. 34-35

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, and sales). 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-12 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 aggregately, depending on the level of aggregation of the index and the behavior of the component series.[1]

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 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 high-level index series are adjusted by the 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 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 that 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 11, 2019

1J.A. Buszuwski and S. Scott, “On the use of intervention analysis in seasonal adjustment,” Proceedings of the American Statistical Association, Business and Economics Section. (Alexandria, VA: American Statistical Association, 1988).