The X12 Procedure

Overview: X12 Procedure

The X12 procedure is an adaptation of the U.S. Bureau of the Census X-12-ARIMA Seasonal Adjustment program (U.S. Bureau of the Census, 2010). The X-12-ARIMA program was developed by the Time Series Staff of the Statistical Research Division, U.S. Census Bureau. The X-12-ARIMA seasonal adjustment program contains components developed from Statistics Canada’s X-11-ARIMA program. The X-12-ARIMA automatic modeling method is based on the work of Gómez and Maravall (1997a, 1997b).

The version of PROC X12 documented here was produced by converting the U.S. Census Bureau’s FORTRAN code to the SAS development language and adding typical SAS procedure syntax. This conversion work was performed by SAS and resulted in the X12 procedure. Although several features were added during the conversion, credit for the statistical aspects and general methodology of the X12 procedure belongs to the U.S. Census Bureau.

The X12 procedure seasonally adjusts monthly or quarterly time series. The procedure makes additive or multiplicative adjustments and creates an output data set that contains the adjusted time series and intermediate calculations.

The X-12-ARIMA program combines the capabilities of the X-11 program (Shiskin, Young, and Musgrave, 1967) and the X-11-ARIMA/88 program (Dagum, 1988) and also introduces some new features (Findley et al., 1998). One of the main enhancements involves the use of a regARIMA model, a regression model with ARIMA (autoregressive integrated moving average) errors. Thus, the X-12-ARIMA program contains methods developed by both the U.S. Census Bureau and Statistics Canada. In addition, the X-12-ARIMA automatic modeling routine is based on the TRAMO (time series regression with ARIMA noise, missing values, and outliers) method (Gómez and Maravall, 1997a, 1997b). The four major components of the X-12-ARIMA program are regARIMA modeling, model diagnostics, seasonal adjustment that uses enhanced X-11 methodology, and post-adjustment diagnostics. Statistics Canada’s X-11 method fits an ARIMA model to the original series, and then uses the model forecasts to extend the original series. This extended series is then seasonally adjusted by the standard X-11 seasonal adjustment method. The extension of the series improves the estimation of the seasonal factors and reduces revisions to the seasonally adjusted series as new data become available.

Seasonal adjustment of a series is based on the assumption that seasonal fluctuations can be measured in the original series, ${O_{t}}$, $t = 1,$ …, $n$, and separated from trend cycle, trading day, and irregular fluctuations. The seasonal component of this time series, ${S_{t}}$, is defined as the intrayear variation that is repeated consistently or in an evolving fashion from year to year. The trend cycle component, ${C_{t}}$, includes variation due to the long-term trend, the business cycle, and other long-term cyclical factors. The trading day component, ${D_{t}}$, is the variation that can be attributed to the composition of the calendar. The irregular component, ${I_{t}}$, is the residual variation. Many economic time series are related in a multiplicative fashion (${O_{t}=S_{t}C_{t}D_{t}I_{t}}$). Other economic series are related in an additive fashion (${O_{t}=S_{t} + C_{t} + D_{t} + I_{t}}$). A seasonally adjusted time series, ${C_{t}I_{t}}$ or ${C_{t} + I_{t}}$, consists of only the trend cycle and irregular components. For more details about seasonal adjustment with the X-11 method, see Ladiray and Quenneville (2001).

Graphics are now available with the X12 procedure. For more information, see the section ODS Graphics.