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