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Producer Price Indexes

Seasonal Adjustment in the PPI ‐ Additional Information

Direct Adjustment

To estimate seasonal factors, PPI uses X-13 ARIMA (X-13), a software package published by the U.S. Census Bureau. X-13 employs moving averages over historical time series data to estimate the trend and seasonal components of a series. PPI generally uses 8 years of historical data to estimate seasonal factors. Series are directly adjusted by dividing the unadjusted index value (at time t) by the seasonal factor (at time t) and multiplying that result by 100.

In addition to the estimation of seasonal factors, PPI also uses X-13 to test the series that are eligible for direct seasonal adjustment for the presence of seasonality. Ultimately, only series that are found to exhibit statistically significant seasonality are seasonally adjusted. The PPI utilizes three primary measures, known as quality control (QC) statistics, to determine whether a particular index should be seasonally adjusted:

  • F(s)— a measure of stable seasonality;
  • M7— the amount of moving seasonality relative to the amount of stable seasonality; and
  • Q— a weighted average of several diagnostic statistics.

Seasonally adjusted indexes are only produced for series in which all three QC statistics indicate the presence of seasonality. As with seasonal factors, QC statistics are re-estimated annually based on data from the most recent 8 years, and the decision whether or not to calculate seasonally adjusted indexes for a given series is revisited.

Intervention Analysis

Intervention analysis involves estimating and removing the effects of certain, important non-seasonal events from the movement of an index prior to testing the series for seasonality and developing seasonal factors. The goals of intervention analysis are to determine whether a seasonal pattern exists and to correctly estimate seasonal factors in spite of non-seasonal distortions that might disturb the normal seasonal pattern.

To conduct intervention analysis, PPI again utilizes the Census Bureau's X-13 ARIMA package. Intervention analysis entails estimating regression models for the intervention series that include pre-specified intervention variables. The intervention variables measure the effects of non-seasonal events on the movements of the time series. For example, an intervention variable to estimate the effects of a hurricane on a gasoline price index may be included in the gasoline series regression model. The PPI employs three types of intervention variables: outliers, level shifts, and ramps. Typically, outliers are used to account for a sudden change in the level of a series that affects one period only; level shifts are used to represent sudden, permanent change in the level of a series; and ramps are used to control for a gradual, linear change in the level of a series that, after a certain period, becomes permanent.

After the regression model is estimated, the effects of the non-seasonal event or events are removed from the original time series. Subsequent to the process of removing these effects, the standard direct seasonal adjustment methods described earlier are applied to the indexes to test for seasonality and to develop seasonal factors. The PPI conducted intervention analysis on unleaded regular gasoline in 2018.

The PPI tests approximately fifteen hundred commodity indexes on an annual basis for the presence of seasonality. However, because intervention analysis is a time consuming process, the PPI cannot feasibly conduct intervention analysis on all of these series. To determine the series on which to conduct an intervention analysis, PPI examines all commodity indexes that account for more than one percent of major FD-ID indexes annually. (Major FD-ID indexes include final demand goods, final demand services, processed goods for intermediate demand, unprocessed goods for intermediate demand, and final demand services.) If seasonal adjustment experts and industry analysts determine non-seasonal events are inhibiting the accurate estimation of seasonal factors for any of these indexes, intervention analysis is performed on those indexes. The set of intervention analysis series can therefore vary from year to year, but in practice stays relatively stable. Once a series is added as an intervention series, a somewhat more stringent criterion is used to determine whether that series is seasonal. In addition to the three QC statistics described earlier, a fourth QC statistic, F(m), a measure of moving seasonality, is also analyzed to determine whether an index should be seasonally adjusted.

Currently, BLS adjusts 69 series using Intervention Analysis Seasonal Adjustment, including selected foods and beverages, fuels, electricity, vehicles, and healthcare.

Coordination with the Consumer Price Index Program on Intervention Analysis

Some PPI series exhibit a great deal of similarity to Consumer Price Index (CPI) series. For these series, seasonal adjusters from the programs meet to compare and discuss their intervention models. The goal is to coordinate intervention decisions between the two programs for similar series. Communication also allows the programs to benefit from each other's expertise and helps to avoid large discrepancies in modeling decisions. Such discrepancies can lead to situations in which similar series exhibit consistent unadjusted movements but different seasonally adjusted movements. More detail on this coordination process, see


Last Modified Date: February 14, 2023