X-13ARIMA-SEATS Seasonal Adjustment Program

Seasonal Heteroskedasticity in Time Series Data: Modeling, Estimation, and Testing

Thomas M. Trimbur⁽¹⁾ and William R. Bell⁽²⁾

ABSTRACT

Seasonal heteroskedasticity refers to regular changes in variability over the calendar year. Models for two different forms of seasonal heteroskedasticity were recently proposed by Proietti and by Bell. We examine use of likelihood ratio tests with the models to test for the presence of seasonal heteroskedasticity, and use of model comparison statistics (AIC) to compare the models and to search among alternative patterns of seasonal heteroskedasticity. We apply the models and tests to U.S. Census Bureau monthly time series of housing starts and building permits.

KEY WORDS: seasonal adjustment, trend, unobserved component

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⁽¹⁾ Thomas Trimbur is currently at the U. S. Federal Reserve Board email : Thomas.M.Trimbur@frb.gov

⁽²⁾ William R. Bell is Senior Mathematical Statistician for Small Area Estimation, U. S. Census Bureau, 4600 Silver Hill Road, Washington, DC 20233. email : william.r.bell@census.gov