The X11 Procedure

Overview: X11 Procedure

The X11 procedure, an adaptation of the U.S. Bureau of the Census X-11 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 X11 procedure also provides the X-11-ARIMA method developed by Statistics Canada. This 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.

The X11 procedure incorporates sliding spans analysis. This type of analysis provides a diagnostic for determining the suitability of seasonal adjustment for an economic series.

Seasonal adjustment of a series is based on the assumption that seasonal fluctuations can be measured in the original series, ${O_{t}}$, $t = 1,\ldots ,n$, 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 (${O_{t}=S_{t}C_{t}D_{t}I_{t}}$). A seasonally adjusted time series, ${C_{t}I_{t}}$, consists of only the trend cycle and irregular components.