X-12-ARIMA

New ARIMA Models for Seasonal Time Series and Their Application to Seasonal Adjustment and Forecasting

John A.D. Aston⁽¹⁾, David F. Findley⁽²⁾, Tucker S. McElroy⁽³⁾, Kellie C. Wills⁽⁴⁾, Donald E. K. Martin⁽⁵⁾

ABSTRACT:

Focusing on the widely-used Box-Jenkins "airline" model, we show how the class of seasonal ARIMA models with a seasonal moving average factor can be parsimoniously generalized to model time series with heteroskedastic seasonal frequency components. Our frequency-specific models decompose this factor by associating one moving average coefficient with a proper subset of the seasonal frequencies 1, 2, 3, 4, 5 and 6 cycles per year and a second coefficient with the complementary subset. A generalization of Akaike's AIC is presented to determine these subsets. Properties of seasonal adjustment filters and adjustments obtained from the new models are examined as are forecasts.

KEYWORDS:

Airline model; Frequency-Specific Model; Generalized Airline Model; Model selection; AIC; F-AIC

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⁽¹⁾ John A.D. Aston is currently at the University of Warwick. email : j.a.d.aston@warwick.ac.uk

⁽²⁾ David F. Findley was the Senior Mathematical Statistican for Time Series and is now a consultant, U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : david.f.findley@census.gov

⁽³⁾ Tucker S. McElroy is Mathematical Statistican, Center for Statistical Research and Methodology U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : Tucker.S.McElroy@census.gov

⁽⁴⁾ Kellie C. Wills is currently a doctoral student.

⁽⁵⁾ Donald E. K. Martin is currently a professor at North Carolina State University.