Bureau of Labor Statistics > Producer Price Indexes > Methods > Seasonal Adjustment

Producer Price Index (PPI)

To illustrate the intervention analysis process employed by the PPI, an example from the 2018 seasonal revision is presented. The example explains the intervention analysis process the PPI implemented on the series for unleaded regular gasoline during the 2018 seasonal revision.

The PPI program often performs intervention analysis on the producer price index for unleaded regular gasoline for three main reasons. First, gasoline is a heavily weighted series within PPI. As of December 2017, the relative importance of unleaded regular gasoline to the PPI for final demand was 1.326 percent. In the same period, the relative importance of unleaded regular gasoline to final demand goods was 4.107 and to processed goods for intermediate demand was 2.056. Second, gasoline likely has a demand-based seasonal pattern resulting from higher driving related demand in the summer and lower driving related demand in the winter. In general, for an index to be eligible for intervention analysis, the index should have a relatively strong seasonal component to start with like gasoline. Third, the seasonal pattern of gasoline prices is frequently distorted by non-seasonal supply shocks. Supply shocks in gasoline prices often stem from weather events, such as hurricanes that can disrupt the supply and / or ability to refine crude petroleum, or other crude petroleum related supply disruptions. For example, non-weather related supply shifts might result from wars or pricing decisions by the members of the Organization of the Petroleum Exporting Countries (OPEC).

In general, PPI conducts intervention modeling using a three step process. In the first step, the series is modeled with an initial benchmark run that includes no intervention variables. This benchmark run acts as a basis of comparison. The second step involves identifying potential non-seasonal events that might negatively affect the estimation of seasonal factors. In the final step, different intervention models are compared and a final model is selected.

Step 1- benchmark run:

PPI begins intervention analysis by performing a benchmark seasonal run on the series. For the benchmark run, QC statistics and seasonal factors are estimated without pre-adjusting the data to remove the effects of nonseasonal events. The 2018 benchmark run for unleaded regular gasoline resulted in the following QC statistics:

F(s) = 8.4
F(m) = 3.2
M7 = 0.99
Q = 0.70

In order to deem an intervention series seasonal and to seasonally adjust the series, PPI requires that all of following QC statistic thresholds are met:

F(s) ≥ 7.0
F(m) ≤ 3.0
M7 < 1.0
Q < 1.0

While three of the IASA QC statistics thresholds were met for unleaded gasoline based on the benchmark run, the threshold for F(m) ≤ 3.0 was not.¹ (See Table 1.) Based on this run, the PPI for unleaded regular gasoline would not be deemed seasonal and seasonally adjusted data would not be produced for the series. However, as mentioned earlier, the benchmark run is conducted prior to intervention work and is only used for comparison purposes, not to ultimately determine if a series is seasonal. Subsequent to intervention work, it is likely the series will be deemed seasonal.

In addition to diagnostic statistics, seasonal factors are also produced from the benchmark run. The seasonal factors for unleaded regular gasoline, presented in Figure 1, indicate that the gasoline prices are expected to rise seasonally from March through June, and decrease from July through February. However, since many non-seasonal events could be distorting the seasonal pattern that X-13 estimated for unleaded gasoline, these factors may not be entirely accurate.

Step 2- identify intervention points:

Following the benchmark run, the next step PPI employs during intervention analysis is to identify potential data points to model with intervention variables. For this process, PPI begins by employing X-13’s automatic outlier and level-shift detection function. The use of this tool provides PPI a statistically based and replicable means for identifying potential outliers. X-13, however, does not search for ramps, so PPI relies on additional analysis to identify those possible intervention points. This analysis can include graphical examination of the original time series, communication with PPI industry analysts, examination of interventions modeled in previous years, and analysis of residuals from the regression model. Potential intervention variables are tested for statistical significance using t-statistics.²

For unleaded regular gasoline, X-13 detected two potential level shifts. The first is for January 2015, when the index fell approximately 24 percent. The January decline was likely the result of growth in U.S. oil production as well as weakening outlooks for the global economy and oil demand.³ Adding to this condition was a decision by OPEC in November 2014 to maintain current oil production targets despite lower oil prices, which put additional downward pressure on prices.⁴ The second level shift detected by X-13 is for the approximate 16-percent decline in September 2015. The September decrease was likely related to falling crude petroleum prices in several of the previous months.⁵ Figure 2 presents the PPI for unleaded gasoline from January 2009 through December 2017, highlighting the level shifts detected by X-13.

After including the two level shifts identified by X-13, the QC statistics for regular unleaded gasoline are:

F(s) = 9.962
F(m) = 2.217
M7 = 0.828
Q = 0.63

All of these QC statistics indicate that the series is seasonal and should be adjusted. This result is in contrast to the benchmark model, where the F(m) statistic did not support seasonality. The model developed using auto-outlier could therefore be accepted and the series could be seasonally adjusted based on this model. However, as mentioned before, X-13 cannot be used to search for ramps and there are also several means other than X-13 outlier and level shift detection that the PPI uses for identifying potential intervention variables.

Visually, for example, it appears that the January 2015 data point that X-13 identified as a level shift could alternatively be modeled as part of a larger ramp. (Recall a ramp is used to control for a gradual, linear change in the level of a series that, after certain period, becomes permanent.) Replacing the January 2015 level shift with a ramp from November 2014 through January 2015 also results in a model with acceptable t-statistics and QC statistics. There also appears to be a potential ramp from February 2011 through May 2011. Over this period, the gasoline index increased approximately 35 percent. Attempting to model this ramp, however, did not result in an acceptable model because the t-statistic for the ramp did not indicate statistical significance.

Step 3- compare models:

In practice, the PPI examines a number of potential models for each intervention series using different combinations of intervention valuables identified in step 2. Ultimately, information criteria are relied upon to select the final model for a series. Information criteria can be used to measure the quality econometric models relative to each other for a given set of data.⁶ When comparing a set of econometric models for a given dependent variable, the model with the minimum information criteria value is determined as the highest quality model. PPI uses two separate information criteria to compare intervention models, the Akaike and Bayesian information criteria. Both criteria are analyzed during modeling, but the Bayesian is given slightly more consideration because of Akaike’s tendency to select models with too many parameters. Carefully analyzing these information criteria helps to ensure that models are not overfit, a condition that tends to make the models excessively complex and exhibit poor out-of-sample predictive performance. To a lesser extent, PPI also examines the QC stats when comparing competing models.

Table 1 presents QC statistics and information criteria for four competing unleaded regular gasoline models from the 2018 seasonal revision. The first model is the benchmark model, which includes no intervention variables. The second model includes level shifts in January and September 2015 and was developed solely using X-13 automatic outlier detection. The third model replaces the January 2015 level shift from the second model with a ramp from November 2014 through January 2015 and also includes the September 2015 level shift identified by X-13. The final model is the same as the third but adds an outlier in April 2015. The April 2015 outlier was identified using X-13 auto outlier detection in an earlier year’s seasonal revision.

Table 1: Producer Price Index Unleaded regular gasoline ARIAM models QC statistics and information criteria
Model	F(s)	F(m)	M7	Q	AIC	BIC	Pass/Fail seasonality tests
1: Benchmark	8.399	3.202	0.994	0.7	716.449	725.612	Fail
2: LS (2015:01), LS (2015:09)	9.962	2.271	0.828	0.63	695.586	712.991	Pass
3: Ramp (2014:11-2015:01), LS (2015:09)	9.929	2.329	0.839	0.62	694.466	707.874	Pass
4: Ramp (2014:11-2015:01), LS (2015:09), Out (2015:04)	10.754	2.504	0.822	0.61	688.919	704.357	Pass

Based on minimizing the Akaike and Bayesian information criteria, in 2018 the PPI decided to use the fourth model to seasonal adjust unleaded regular gasoline. Also reinforcing this choice, the fourth model exhibits the highest F(s), lowest M7, and lowest Q of the models presented in table 1.

As depicted in Figure 3, the seasonal factors in the selected 2018 model (model 4) for unleaded regular gasoline prices are somewhat similar to those in model 1 but differ in three important ways. First, while both sets of factors expect gasoline prices to rise seasonally from late winter through early summer, model 1 expects seasonal price increases from March through June, whereas model 4 expects prices to rise from February through June. Second, model 1 then expects prices to fall seasonally from July through February. Model 4 also expects prices to begin seasonal declines in July, but anticipates that they will turn up in September for one month before returning to seasonal declines through January. The anticipated September seasonal increase by model 4 may be the result of an increase in gasoline demand due to the Labor Day holiday. Third, the magnitude of the seasonal factors differ between the two models. The seasonal factors from model 1 range from 91.5 to 107.2, whereas the range from model 4 is between 93.2 and 105.9.

Footnotes

1 Note that even though the benchmark run included no intervention variables, F(m) is still analyzed to determine seasonality because subsequent analysis concluded that the series should be included in the 2018 set of intervention series.

2 T-statistics are calculated to determine the statistical significance of outlier variables. T-statistics are calculated as the ratio of the estimated regression coefficient to its standard error. As the coefficient value increases relative to its standard error, the t-statistic increases. For an intervention variable to be included the model, PPI typically requires a t-statistic with an absolute value of greater than 3, but may accept a t-statistic as low as 2.5.

3 For additional information see: www.iea.org/newsroom/news/2016/january/iea-releases-oil-market-report-for-january.html

4 For additional information see: www.reuters.com/article/us-opec-meeting/saudis-block-opec-output-cut-sending-oil-price-plunging-idUSKCN0JA0O320141128

5 From June through August 2015, the PPI for crude petroleum fell approximately 30 percent.

6 Information criteria weigh the benefits of adding variables to the model by numerically rewarding the increase in fit generated by an additional variable, while at the same time numerically penalizing the model for the loss in degrees of freedom associated with the additional parameter. Information criteria are therefore used to weight the costs and benefits of adding variables to a model.

Last Modified Date: October 22, 2019