X-12-ARIMA

Comparing Automatic Modeling Procedures of TRAMO and X-12-ARIMA, an Update

Kathleen M. McDonald-Johnson⁽¹⁾, Catherine C. Harvill Hood,⁽²⁾, Brian C. Monsell⁽³⁾, Chak Li⁽⁴⁾

ABSTRACT:

The U. S. Census Bureau's enhanced X-12-ARIMA seasonal adjustment program includes the automatic ARIMA (Autoregressive Integrated Moving Average) model selection procedure developed by Statistics Canada and a second procedure based on the automatic procedure of TRAMO (Time series Regression with ARIMA noise, Missing observations and Outliers), a modeling package developed by Victor Gómez and Agustín Maravall. Each program has automatic identification of key regressors, allowing for full automatic selection of a regARIMA model (regression with an underlying ARIMA process). X-12-ARIMA's procedure differs from TRAMO's in a number of ways. Our study updates previous work as we compared the procedures again using improved versions of the two programs. We applied the procedures to a set of Census Bureau time series and simulations. When model choices differed, we compared standard modeling diagnostics to look for a consistent preference for either procedure. As in the previous study, we found that X-12-ARIMA still seems to choose trading day effects more appropriately than TRAMO. However, we found that X-12-ARIMA inaccurately identifies Easter effects more often than TRAMO. Overall, we found that the diagnostics for the X-12-ARIMA models were at least as good as the diagnostics from TRAMO models.

KEYWORDS:

Time series, Seasonal adjustment, Trading day effect

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⁽¹⁾ Kathleen M. McDonald-Johnson is Mathematical Statistican, Office of Statistical Methods and Research for Economic Programs, U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : kathleen.m.mcdonald.johnson@census.gov

⁽²⁾ Catherine C. H. Hood is currently a consultant. email : cath@catherinechhood.net

⁽³⁾ Brian C. Monsell is Mathematical Statistician, Center for Statistical Research and Methodology, U.S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : brian.c.monsell@census.gov.

⁽⁴⁾ Chak Li was a student intern at the Census Bureau.