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X-13ARIMA-SEATS Seasonal Adjustment Program

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Modeling Time-Varying Trading-Day Effects in Monthly Time Series

William R. Bell(1) and Donald E. K. Martin(2)


Trading-day effects reflect variations in monthly time series due to the changing composition of months with respect to the numbers of times each day of the week occurs in the month. A relevant question regarding trading-day effects is whether they remain constant over time? This is especially pertinent for retail sales data in which trading-day effects presumably depend on consumers’ shopping patterns and on hours that retail stores are open, two things that have changed over time in the U.S. Seasonal adjustment practitioners sometimes deal with this issue by restricting the length of the series to which the trading-day model is fit. However, this can provide only a crude approximation to trading-day effects that vary through time. In this paper we explore some alternative models for time-varying trading-day effects and investigate possible time variation in trading-day effects in some Census Bureau monthly time series.


ARIMA models, unobserved components, time-varying regression

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

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

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