Comparison of X-12-ARIMA Trading Day and Holiday Regressors With Country Specific Regressors Christopher G. Roberts,∗ Scott H. Holan yand Brian Monsellz University of Missouri-Columbia and U.S. Census Bureau Abstract Several methods exist which can adjust for trading day and holiday effects in monthly economic time series. This paper reviews and compares two such methodologies for conducting proper adjustments. The two methodologies are based upon the U.S. Census Bureau's X-12-ARIMA method and one developed by the Statistical Offices of the European Communities, commonly referred to as Eurostat. Three different methods are used to compare the U.S. Census Bureau procedure and the Eurostat-inspired procedure. These methods are spectral analysis, sample- size corrected AIC comparisons, and examination of out-of-sample forecast errors. Finally, these comparisons are conducted using nearly 100 U.S. Census Bureau time series of manufacturing data, retail sales, and housing starts. This empirical study is the first of its kind and therefore provides an important contribution to the seasonal adjustment community. Keywords: Eurostat; Holiday effect; Model selection; RegARIMA model; Trading day effect; X-12-ARIMA. Disclaimer This paper is released to inform interested parties of ongoing research and to encour- age discussion of work in progress. The views expressed are those of the authors and not necessarily those of the U.S. Census Bureau. 1 Introduction Many time series are reported on a monthly basis and represent an aggregation of unobserved daily values. Since the daily values are unobserved, these particular time series often contain various ∗Department of Statistics, University of Missouri-Columbia, 146 Middlebush Hall, Columbia, MO, 65211-6100,
[email protected] y(to whom correspondence should be addressed) Department of Statistics, University of Missouri-Columbia, 146 Middlebush Hall, Columbia, MO, 65211-6100,
[email protected] zStatistical Research Division, U.S.