X-13ARIMA-SEATS Seasonal Adjustment Program

Modeling and Model Selection for Moving Holidays

Raymond J. Soukup ⁽¹⁾ and David F. Findley ⁽²⁾

ABSTRACT:

Moving holidays such as Easter, Thanksgiving, and Labor Day, can affect the monthly values of economic time series in a way that varies with the date of the holiday. Their effects impede economic analysis and seasonal adjustment unless they are first estimated. Bell and Hillmer (1983) showed how this can be done successfully with the aid of regressors determined by the length of the time interval over which the holiday effect occurs. It is ordinarily necessary to compare the fits or forecast performance of several models with different regressors for the holiday effects, a model selection problem involving non-nested models. We present results concerning estimation of moving holiday effects for time series published by the U.S. Census Bureau. For the comparison of competing models, we employ two techniques: 1) comparison of AIC values, and 2) analysis of out-of-sample forecast errors. The first technique allows for a simple decision rule for selecting the preferred model for the logged original series. The second technique is not always decisive, but it is usable for all comparisons,including the comparison of models for the logarithms with models for the irregulars.

KEYWORDS:

calendar effects, holiday effects, out-of-sample forecast errors, retail Sales, model selection

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⁽¹⁾ Raymond J. Soukup is currently a statistican at the Naval Research Laboratories.

⁽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