Linear Filters Seasonal Adjustment Methods: Census Method II and Its Variants

The best known and most often applied seasonal adjustment methods are based on smoothing linear filters or moving averages applied sequentially by adding (and subtracting) one observation at a time. This chapter discusses with details the basic properties of the symmetric and asymmetric filters of the Census Method II-X11 method which belong to this class. It also discusses the basic assumptions of its two more recent variants, X11ARIMA and X12ARIMA. The latter consists of two linked parts: the regARIMA model for estimation of the deterministic components (mainly calendar effects), and the decomposition part of the linearized series for the stochastic components (trend-cycle, seasonality, and irregulars) performed using the X11 filters combined with those of the ARIMA model extrapolations. An illustrative example of the seasonal adjustment with the X12ARIMA software default option is shown with the US New Orders for Durable Goods series. The illustrative example concentrates on the most important tables of this software that enable to assess the quality of the seasonal adjustment.