X-13ARIMA-SEATS Seasonal Adjustment Program

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A Mean Squared Error Criterion for Comparing X-12-ARIMA and Model-Based Seasonal Adjustment Filters

Yea-Jane Chu(1), George C. Tiao(2), Willliam R. Bell(3)


Various authors - Cleveland and Tiao (1976), Burridge and Wallis (1984), and Depoutot and Planas (1998) - have compared weight functions from X-11 versus model-based seasonal adjustment filters. We suggest a different approach to comparing filters by computing the mean squared error (MSE) when using an X-12-ARIMA filter for estimating the underlying seasonal component from an ARIMA model-based decomposition, and comparing this to the MSE of the optimal model-based estimator. This provides a criterion for choosing an X-12 filter for a given series (model the series and pick the X-12 filter with lowest MSE), and also provides results on how much MSE increases when using an X-12 filter rather than the optimal model-based filter. Calculations for monthly time series following the airline model with various parameter values show little increase in MSE for estimating the canonical seasonal component by using the best X-12 filter instead of the optimal model-based filter, particularly for concurrent adjustment. The results are much less favorable to the X-12 filters with a uniform prior distribution on the white noise allocation in the seasonal model decomposition. Examinations of simulated series show that, for the canonical decomposition, automatic filter choices of the X-12-ARIMA program sometimes use shorter seasonal moving averages than is desirable.


Census X11, concurrent adjustment, moving averages, seasonal decomposition

(1) Yea-Jane Chu is currently employed at SPSS.

(2) George C. Tiao is W. Allen Wallis Professor of Econometrics and Statistics, University of Chicago.

(3) 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

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Source: U.S. Census Bureau | Center for Statistical Research and Methodology | (301) 763-1649 (or x12@census.gov) |  Last Revised: August 07, 2015