Issues in Estimating Easter Regressors Using RegARIMA Models with X-12-ARIMA
David F. Findley(1), Kellie Wills
(2) and Brian C. Monsell(3).
The most common moving holiday effect found in U. S. economic
flow series is the Easter effect. For many retail sales series, levels
of sales are elevated in the period just before the Easter holiday
(which varies between March 22 and April 25). Because of this,
X-12-ARIMA has long had a built-in regressor corresponding to
the Easter holiday.
This study seeks to provide guidance for practical concerns analysts
have when including Easter regression effects in regARIMA
models for economic time series. We seek to answer the following
questions regarding the use of Easter regressors in reg-
ARIMA models of economic data as they are incorporated into
How many years of data are needed to detect Easter holiday
effects with high reliability?
How many years of data are needed to obtain useful estimates
of the Easter effect (estimates that improve the seasonal adjustment)?
How often does X-12-ARIMA produce “false positives,” i.e.
select an Easter effect when none exists? What is the impact
of March and April outliers on the number of false positives?
How often does X-12-ARIMA misidentify the Easter effect
length, e.g. select easter when the true effect is easter?
How does the estimation of trading day effects affect Easter
These questions were investigated using synthetic series with
Easter effects constructed to conform to the models assumed by
(1)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 :
(2)Kellie C. Wills is currently a doctoral student.
(3)Brian C. Monsell
is Mathematical Statistican, Center for Statistical Research and Methodology,
U.S. Census Bureau,
4600 Silver Hill Road, Washington, DC 20233. email :
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