X-13ARIMA-SEATS Seasonal Adjustment Program

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A Nonparametric Test for Assessing Spectral Peaks

Tucker S. McElroy(1) and Scott Holan(2)


Peaks in the spectrum of a stationary process are indicative of the presence of a periodic phenomenon, such as a seasonal effect or business cycle. This work proposes to measure and test for the presence of such spectral peaks via assessing their aggregate acceleration and velocity. Our method is developed nonparametrically, and thus may be useful in a preliminary analysis of a series. The technique is also useful for detecting the presence of residual seasonality in seasonally adjusted data. The diagnostic is investigated through simulation and two data examples.


seasonal adjustment, spectral density, nonparametric kernel methods

(1) Tucker S. McElroy is Mathematical Statistican, U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : Tucker.S.McElroy@census.gov

(2) Scott Holan is a professor in the Department of Statistics, University of Missouri-Columbia.

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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or x12@census.gov) |  Last Revised: August 07, 2015