X12ARIMA

X12ARIMA, also written X-12-ARIMA, is a statistical software package used for seasonal adjustment of univariate time series. It is part of the X-11 family of seasonal adjustment methods and was developed by the U.S. Census Bureau as an extension of X-11-ARIMA. The program combines ARIMA modeling with the traditional X-11 decomposition to separate a series into trend, seasonal, and irregular components with improved robustness. Key features include automatic outlier detection and adjustment, the inclusion of regressors for trading-day and holiday effects, and support for user-specified regressors. It can operate with additive or multiplicative decompositions and produces outputs such as the seasonally adjusted series, the seasonal factors, the trend-cycle component, the irregular component, and various diagnostic statistics.

X12ARIMA operates by applying an ARIMA model to the irregular component and incorporating regression terms to account for calendar-related effects. This approach allows for more flexible adjustments, particularly for series with irregular patterns or influential calendar events. The software is used to produce seasonally adjusted data that feed into a wide range of economic indicators and analyses, enabling comparisons across time free of regular seasonal fluctuations.

Legacy and status: In many statistical agencies, X-13ARIMA-SEATS has largely supplanted X12ARIMA, offering a unified framework that combines X-13’s tools with SEATS’ theoretical basis. Nevertheless, X12ARIMA remains part of historical practice and continues to be used in some contexts, including legacy analyses and workflows that depend on its outputs.