The X12 Procedure

Overview

The X12 procedure, an adaptation of the U.S. Bureau of the Census X-12-ARIMA Seasonal Adjustment program, seasonally adjusts monthly or quarterly time series. The procedure makes additive or multiplicative adjustments and creates an output data set containing 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. 1988). Thus, the X-12-ARIMA program contains methods developed by both the U.S. Census Bureau and Statistics Canada. The four major components of the X-12-ARIMA program are regARIMA modeling, model diagnostics, seasonal adjustment using enhanced X-11 methodology, and post-adjustment diagnostics. Statistics Canada's X-11 method fits an ARIMA model to the original series, then uses the model forecast 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 constantly 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_tC_tD_tI_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_tI_t or C_t + I_t , consists of only the trend cycle and irregular components.

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