DOI: doi.org/10.71734/DP-2026‑7

How can we improve the quality of seasonally adjusted estimates obtained with up-to-date methods tailored to the complexities of modern daily and weekly economic data? This study revisits the classical data-driven selection of seasonal filters in the popular X-11 method and proposes a generic redesign for a recent X-11 modification. A crucial step is the proper treatment of superimposed seasonal dynamics often displayed in daily economic time series. By addressing this and other challenges, the present research offers a robust strategy for improving seasonal adjustment adequacy for real-time economic data with potentially complex seasonality.

Seasonal adjustment is a cornerstone of economic data analysis, enabling policymakers and researchers to identify more clearly underlying long-term trends and sudden short-term changes by removing recurring sub-annual patterns. The X-11 method for monthly and quarterly data, introduced in 1967, has been a foundational tool in this domain, evolving through various extensions such as X-12-ARIMA and X-13ARIMA-SEATS. Its most recent modification, which is available in the JDemetra+ time series software for official statistics and described in Webel and Smyk (2024), enables seasonal adjustment of time series with any seasonal periodicity but does not inherit the classical method’s popular mechanism for a data-driven selection of seasonal filters. To fill this gap, this study proposes a generic redesign of this legacy mechanism. Real-time macroeconomic data for Germany, covering quarterly gross domestic product (GDP), monthly industrial production, and daily realised electricity consumption, are used to illustrate one specific redesigned selection rule.

Leaning on the legacy approach to data-driven seasonal filter selection

The proposed redesign builds on the ideas of Lothian (1978), who developed a framework for automatically picking the most appropriate X-11 seasonal filter given the time series characteristics. His approach is based upon the moving seasonality ratio (MSR) that measures the strength of the seasonal dynamics relative to the irregular ones in the detrended observations. He originally suggested two selection rules, but those have gradually morphed into a single rule that is currently implemented in virtually all seasonal adjustment programs containing the classical X-11 method. Along this path, several (sparsely documented) changes have been made with respect to the candidate filters and certain thresholds controlling both the filter selection and the potential MSR recalculation from suitably shortened detrended observations.

This study expands the current implementation of Lothian’s ideas in three respects. First, the set of candidate seasonal filters is larger. Second, the asymmetric filters required near the sample boundaries are derived according to the exact same principle for each candidate filter. Third, the recalculation thresholds that have been introduced somewhat mysteriously in the classical X-11 method are now obtained in a more transparent way. To this end, multiple Lothian-type selection rules are considered, each of which utilising a specific derivation principle for all asymmetric seasonal filters. The obtained rules are finally averaged, which not only stabilises the final filter choice but also produces the recalculation thresholds naturally through intersections.

Avoiding biased filter selection for time series with complex seasonality

A specific redesigned selection rule based upon threshold quartiles is empirically assessed using real-time data for three German macroeconomic time series. The examples on quarterly GDP and monthly industrial production demonstrate that the classical and redesigned rules often selected the same seasonal filters, but the latter occasionally favours slightly longer filters, leading to more frequent revisions. Accordingly, both approaches produce similar real-time seasonally adjusted estimates.

The example on daily electricity consumption underscores the importance of recognising the coexistence of multiple seasonal patterns in modern economic time series, as neglecting these complexities can lead to systematic seasonal adjustment inadequacy. More specifically, ignoring the day-of-the-year movements in the data will inevitably inflate the irregular volatility in Lothian’s modelling framework and hence increase the probability of designating an overly long seasonal filter for extracting the day-of-the-week dynamics, causing a systematic residual seasonality issue. Incorporating an intermediate step to disentangle the two seasonal patterns during the MSR calculation results in the consistent data-driven selection of shorter and more appropriate seasonal filters.

References

Lothian, J. (1978), “The Identification and Treatment of Moving Seasonality in the X-11 Seasonal Adjustment Method”, Research Paper 78‑10‑004, Statistics Canada.

Webel, K. and A. Smyk (2024), “Seasonal Adjustment of Infra-Monthly Time Series with JDemetra+”, Journal of Official Statistics 40(4): 783–828.

Webel, K., (2026), Redesigning the classical automatic selection of X-11 seasonal filters, Bundesbank Discussion Paper, No 07/2026