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X-13ARIMA-SEATS Seasonal Adjustment Program

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Determining Seasonality: A Comparison of Diagnostics From X-12-ARIMA

Demetra P. Lytras(1), Roxanne M. Feldpausch(2), William R. Bell(3)


Before a series is seasonally adjusted, it should be shown that the series is seasonal. When using X-12-ARIMA for seasonal adjustment, two diagnostics commonly used to determine seasonality are M7, a diagnostic developed at Statistics Canada for X-11-ARIMA, and the F-test for seasonality assuming stability, referred to as the D8 F-test for stable seasonality; however, the statistical properties of these are not well understood. In this paper, we examine properties of these statistics and compare them to those of two other diagnostics available in the program: the presence of seasonal peaks in the spectrum of the differenced original series, and a model-based chi-squared test of fixed seasonal effects. We also examine a modification of the chi-squared test to give the corresponding model-based F-test (FM). We use simulated nonseasonal series to determine and compare the significance levels of these diagnostics and simulated seasonal series to assess their power.


Seasonal adjustment, Diagnostics

(1) Demetra P. Lytras is Mathematical Statistican, Office of Statistical Methods and Research for Economic Programs, U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email :

(2) Roxanne M. Feldpausch is currently a consultant.

(3) William R. Bell is Senior Mathematical Statistician for Small Area Estimation, U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email :

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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or |  Last Revised: April 02, 2015