X-11 Census Method II Seasonal Adjustment - The Census II Method

The basic method for seasonal decomposition and adjustment outlined in Basic Ideas and Terms can be refined in several ways. In fact, unlike many other time-series modeling techniques (e.g., ARIMA) that are grounded in some theoretical model of an underlying process, the X-11 variant of the Census II method simply contains many ad hoc features and refinements, that over the years have proven to provide excellent estimates for many real-world applications (see Burman, 1979, Kendall & Ord, 1990, Makridakis & Wheelwright, 1989; Wallis, 1974). Some of the major refinements are listed below.

Element Name Description
Trading-day adjustment Different months have different numbers of days, and different numbers of trading-days (i.e., Mondays, Tuesdays, etc.). When analyzing, for example, monthly revenue figures for an amusement park, the fluctuation in the different numbers of Saturdays and Sundays (peak days) in the different months will surely contribute significantly to the variability in monthly revenues. The X-11 variant of the Census II method allows the user to test whether such trading-day variability exists in the series, and, if so, to adjust the series accordingly.
Extreme values Most real-world time series contain outliers, that is, extreme fluctuations due to rare events. For example, a strike may affect production in a particular month of one year. Such extreme outliers may bias the estimates of the seasonal and trend components. The X-11 procedure includes provisions to deal with extreme values through the use of "statistical control principles," that is, values that are above or below a certain range (expressed in terms of multiples of Sigma, the standard deviation) can be modified or dropped before final estimates for the seasonality are computed.
Multiple refinements The refinement for outliers, extreme values, and different numbers of trading-days can be applied more than once, in order to obtain successively improved estimates of the components. The X-11 method applies a series of successive refinements of the estimates to arrive at the final trend-cycle, seasonal, and irregular components, and the seasonally adjusted series.
Tests and summary statistics In addition to estimating the major components of the series, various summary statistics can be computed. For example, analysis of variance tables can be prepared to test the significance of seasonal variability and trading-day variability (see above) in the series; the X-11 procedure will also compute the percentage change from month to month in the random and trend-cycle components. As the duration or span in terms of months (or quarters for quarterly X-11) increases, the change in the trend-cycle component will likely also increase, while the change in the random component should remain about the same. The width of the average span at which the changes in the random component are about equal to the changes in the trend-cycle component is called the month (quarter) for cyclical dominance, or MCD (QCD) for short. For example, if the MCD is equal to 2 then one can infer that over a 2 month span the trend-cycle will dominate the fluctuations of the irregular (random) component. These and various other results are discussed in greater detail below.