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July, 2001, Vol. 124, No. 7

A state space model-based method of seasonal adjustment

Raj K. Jain

The Bureau of Labor Statistics publishes a very large number of economic
time series such as the Consumer Price Index, the Producer Price Index, employment and unemployment statistics and many more. Most of these series are published as seasonally unadjusted series as well as seasonally adjusted ser
ies. More often, however, it is the seasonally adjusted data series that the business community and government agencies use in evaluating the economic situation. There are several reasons given for the use of seasonally adjusted series. It is suggested that the presence of seasonality1 in time series obscures the stage of the business cycle that the economy is in. In addition, it obscures the effects of interventions,2 such as a rapid cut in oil production, on a series. At the present time, BLS uses the Census X-11/X-12 ARIMA methods to seasonally adjust BLS indexes and series that have seasonality.3 In the last 20 years or so, several ARIMA model-based methods have been proposed for seasonal adjustment.4

This article presents a structural model based method of seasonal adjustment called the state space model-based method.5 This article presents research conducted on this method and illustrates the advantages of the method. The research is part of the Bureau's ongoing efforts to explore relevent measurement issues of interest to the wider statistical community.

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1 Ted Jaditz, "Seasonality: economic data and model estimation," Monthly Labor Review, 1994, pp. 17–22. Jaditz has discussed the factors that give rise to seasonality and the rationale of seasonally adjusting the economic time series.

2 Interventions resulting from external events such as an opec decision to reduce total production of crude oil at a point in time that will almost immediately, or with a slight lag time, affect the retail prices and hence, the CPI of the gasoline at that time. Unless the effect of this intervention is separated from other components, the decomposition of the time series would produce components, which would include some effect of the intervention and hence be misleading. The approach to separating the effects of interventions at a certain point in time is called intervention analysis.

3 x-12 ARIMA Reference Manual (Washington, DC, Time Series Staff, Bureau of the Census, 1999) and E. B. Dagum, The x-11ARIMA/88 Seasonal Adjustment Method – Foundations And User’s Manual (Time Series Research and Analysis Division Statistics Canada, Ottawa, Canada, 1988).

4 J. P. Burman, "Seasonal Adjustment by Signal Extraction," Journal of the Royal Statistical Society, 1980, series A, vol. 143, pp. 321–37 and S. C. Hillmer, and G. C. Tiao, "An arima-Model-Based Approach to Seasonal Adjustment," Journal of the American Statistical Association, 1982, vol. 77, pp. 63–70.

5 R. K., Jain, "A State Space Modeling Approach to the Seasonal Adjustment of the Consumer Price and other bls Indexes: Some Empirical Results," BLS Working Paper, no. 229 (Bureau of Labor Statistics, 1992) and "Structural Model-Based Seasonal Adjustment of the Bureau of Labor Statistics Series," bls Working Paper no. 236 (Bureau of Labor Statistics, 1992).

Related BLS programs

Consumer Price Indexes

Related Monthly Labor Review articles

Seasonal adjustment of quarterly consumer expenditure series.Dec. 1994.
Seasonality: economic data and model estimation.Dec. 1994.

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