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Selecting seasonal filters in X-13-ARIMA via cross-validation

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  • Ollech, Daniel

Abstract

Official statistics routinely employs the X-13-ARIMA method to seasonally adjust economic time series. A key step is choosing the length of the seasonal moving av- erage. Traditionally, this choice relies on ad hoc criteria and expert judgement. We propose a cross-validation-based filter selection scheme that offers greater flexibility, including the possibility of incorporating novel filters. This approach is particularly promising for the seasonal adjustment of weekly, daily, and high-frequency time series. We demonstrate how to integrate cross-validation into the X-13-ARIMA method and discuss the advantages of various implementation options. Evaluation on monthly and quarterly time series demonstrates that this selection method performs at least as well as, and often better than, conventional selection criteria.

Suggested Citation

  • Ollech, Daniel, 2026. "Selecting seasonal filters in X-13-ARIMA via cross-validation," Discussion Papers 16/2026, Deutsche Bundesbank.
    • Handle: RePEc:zbw:bubdps:341639
    DOI: 10.71734/DP-2026-16
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    References listed on IDEAS

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    1. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 127-152, April.
    2. Daniel Ollech & Deutsche Bundesbank, 2023. "Economic analysis using higher-frequency time series: challenges for seasonal adjustment," Empirical Economics, Springer, vol. 64(3), pages 1375-1398, March.
    3. Kasun Bandara & Rob J. Hyndman & Christoph Bergmeir, 2025. "MSTL: a seasonal-trend decomposition algorithm for time series with multiple seasonal patterns," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 52(1), pages 79-98.
    4. Kirchner, Robert, 1999. "Auswirkungen des neuen Saisonbereinigungsverfahrens Census X-12-ARIMA auf die aktuelle Wirtschaftsanalyse in Deutschland," Discussion Paper Series 1: Economic Studies 1999,07, Deutsche Bundesbank.
    5. Racine, Jeff, 2000. "Consistent cross-validatory model-selection for dependent data: hv-block cross-validation," Journal of Econometrics, Elsevier, vol. 99(1), pages 39-61, November.
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    Keywords

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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