X11

The X11 method developed in the United States Census Bureau is an improved version of the Census1 method of seasonal decomposition and adjustment. The additional features include:

Working day adjustment.
Holiday adjustment.
Outlier adjustment.
Multiple adjustment related to presence of outliers and various number of working days.
Calculation of statistical criteria and resulting statistics.

NOTE. The method is supported only in Windows.

Working Day Adjustment

Months contain different numbers of working days, and it may affect the final result of time series analysis. The X11 method enables the user to take this into consideration by assigning weighted coefficients for days of the week. Weight values lie within the range [0, 10]. Sum of the weights is brought to 7.

Outliers

Most of real time series include outliers. They can distort seasonality and trend estimations. The X11 method reduces outliers effect by excluding values that lie outside the specified range from analysis, or by transforming these values. Range width is determined by the lower and the upper limit of the standard deviation (sigma).

Successive Adjustments

The user can execute adjustments associated with outliers and varying number of working days several times one after another. Each time the estimations become more accurate. Calculation is split into 7 successive stages, which are identified using the characters "A" - "G". Tables within the stages are numbered using numbers one after another. Final results are shown in the tables:

D10 - seasonal component.
D11 - seasonal adjustment.
D12 – tend-cycle component.
D13 - random component of a time series.