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X-13ARIMA-SEATS Seasonal Adjustment Program

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X-12-ARIMA and its Application to Some Italian Indicator Series

David F. Findley (1) and Catherine C. H. Hood (2)

Introduction and Overview:

X-12-ARIMA is the Census Bureau's new seasonal adjustment program. It belongs to the methodological lineage of the Census Bureau's X-11 program (Shiskin, 1967) and Statistics Canada's X-11-ARIMA and X-11-ARIMA/88 (Dagum, 1988) programs. These methods estimate seasonality mainly by applying moving average filters to a possibly modified version of the input series. The modifications might include adjustments for extreme values, trading day effects, or holiday effects also estimated by the program. The filters are chosen from a fixed set of filters, partially or - in X-11-ARIMA/88 and X-12-ARIMA, possibly completely - automatically, on the basis of certain signal-to-noise ratios.

The major improvements in X-12-ARIMA fall into four general categories:

  1. new modeling capabilities using regARIMA models-regression models with ARIMA error-for estimating other calendar or disturbance effects with built-in or user-defined regressors;
  2. new diagnostics for modeling, model selection, adjustment stability, and for the quality of indirect as well as direct seasonal adjustment;
  3. additional capabilities to make it easier to adjust large numbers of series and determine which have problematic adjustments; and
  4. a new user interface.

The article by Findley, Monsell, Bell, Otto, and Chen (1998) gives a detailed overview.

At times, we will compare the results from X-12-ARIMA to results from the programs TRAMO (Time series Regression with ARIMA noise, Missing observations, and Outliers) and SEATS (Signal Extraction in ARIMA Time Series) by Gomez and Maravall (1997a, 1997b). These are linked programs for seasonally adjusting time series using ARIMA model-based signal extraction techniques.

We begin by discussing the diagnostics we used in this paper to judge the quality of the X-12-ARIMA adjustment. We will then discuss some of the results from the default runs of both X-12-ARIMA and TRAMO/SEATS. Then we will discuss some of the options in X-12-ARIMA that help us deal with the problems we found in the series. We will contrast the available diagnostics and the available options in X-12-ARIMA with the diagnostics and options available in TRAMO/SEATS.

(1) David F. Findley was the Senior Mathematical Statistican for Time Series and is now retired from the U. S. Census Bureau.

(2) Catherine C. H. Hood is a consultant. email :

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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or |  Last Revised: September 01, 2015