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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 X-12-ARIMA:

  1. How many years of data are needed to detect Easter holiday effects with high reliability?
  2. How many years of data are needed to obtain useful estimates of the Easter effect (estimates that improve the seasonal adjustment)?
  3. 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?
  4. How often does X-12-ARIMA misidentify the Easter effect length, e.g. select easter[15] when the true effect is easter[8]?
  5. How does the estimation of trading day effects affect Easter effect detection?

These questions were investigated using synthetic series with Easter effects constructed to conform to the models assumed by X-12-ARIMA.


moving holiday effects, revisions, outliers, seasonal adjustment

(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 : david.f.findley@census.gov

(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 : brian.c.monsell@census.gov

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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or x12@census.gov) |  Last Revised: November 19, 2012