doi.org/10.71734/DP‑2026‑32

How can classical seasonal adjustment methods for monthly and quarterly time series adapt to the complex peculiarities of modern sub-monthly economic data? This paper explores a recent modification of the famous X-11 method that, compared with its classical ancestor, contains both enhancements and simplifications. For example, while the modified method builds on rich filter families for parametric trend-cycle estimation, it lacks automatic selection procedures for trend-cycle and seasonal filters alike. Besides providing exhaustive documentation of the implemented conceptual changes, the present study empirically evaluates the modified X-11 method with regard to its current maturity level and its potential for improving seasonal adjustments of daily and weekly time series.

Seasonal adjustment has been an integral part of economic data analysis for many decades. By removing repetitive sub-annual movements from observed time series, it uncovers the actual news in the data and, hence, enables policymakers and researchers to see both underlying long-term trends and sudden short-term changes more clearly. The classical X-11 method introduced in 1967 has long been a standard tool for seasonally adjusting monthly and quarterly time series. Since the COVID‑19 pandemic outbreak, however, an increasing number of sub-monthly data displaying more complex forms of seasonal dynamics have been integrated into models for short-term economic monitoring, which in turn has sparked interest in the recent introduction of a modified X-11 method. This paper provides an exhaustive list of the implemented modifications, elaborating the first overview given in Webel and Smyk (2024). It turns out that the modified X-11 method contains both enhancements and simplifications of the classical computing routines, with unclear net effects for practitioners. For that reason, real-time macroeconomic data on the monthly industrial production of capital goods in Germany are then used to evaluate the current maturity level of the implemented modifications. To focus on the added value of enhanced options for nuanced kernel-based trend-cycle extraction, real-time weekly Google searches for unemployment and daily realised electricity consumption in Germany are considered in a final step to gauge the potential for improving the quality of benchmark seasonal adjustments that are performed using default kernel settings.

Modifications contain both enhancements and simplifications …

Owing to the iterative X-11 filtering philosophy, the implemented conceptual changes fall into four main categories: data precleaning, trend-cycle estimation from the precleaned data, replacement of extremes in the detrended precleaned data, and seasonal estimation. The most outstanding novelty is the incorporation of broad families of kernel-based trend-cycle extraction filters. These filters can be constructed from local polynomial regression models (Proietti and Luati, 2008) and from reproducing kernel Hilbert spaces (Dagum and Bianconcini, 2008). This allows greater flexibility in specifying the baseline symmetric trend-cycle filter and in deriving its companion asymmetric boundary variants. Another important innovation concerns the handling of multiple overlapping seasonal patterns with potentially fractional periodicities in the linear time series regression for data precleaning and in the filtering steps for isolating the seasonal dynamics from the detrended precleaned data.

Unfortunately, these enhancements come with trade-offs that primarily concern automatic detection and selection procedures. More specifically, the modified X-11 method lacks an equivalent of the classical data-driven selection for trend-cycle and seasonal filters based on simple noise-to-signal ratios (see Webel (2026) for a detailed discussion of the seasonal case). Other missing pieces compared to its classical ancestor are the built-in replacement of extremes in the detrended precleaned data before final estimation of the seasonal dynamics and the automatic correction of ill-specified seasonal filters for very short time series.

… that are sufficiently mature overall …

Using real-time data on monthly German capital goods production, the study finds that the modified X-11 method yields seasonally adjusted estimates that are closely aligned with the classical approach. However, undesired discrepancies may still arise due to different outcomes of the automatic routines for detecting outliers in the raw data and for correcting extremes in the detrended precleaned data. The former occurs rarely and, if so, has negligible consequences, whereas the latter occurs more frequently and tends to result in non-ignorable differences that manifest, for example, in diverging month-on-month growth rates for the seasonally adjusted time series, which is particularly frustrating towards the recent end of the sample span. Nevertheless, the maturity level of the modified X-11 routines can still be deemed acceptable.

The study then considers real-time data on weekly Google trends for the search term “unemployment” and on daily realised electricity consumption in Germany to showcase the modified X-11 method’s ability to handle more intricate seasonal movements. The two sub-monthly series contain complementary seasonal signals: while Google data typically exhibit erratic seasonality by nature, daily electricity consumption usually displays stable day-of-the-week and day-of-the-year patterns. To dig deeper into the enhanced options for kernel-based trend-cycle filtering, the study extensively analyses whether the actual filter configuration significantly affects the quality of concurrent seasonally adjusted estimates. The criteria checked include the robustness of a data-driven selection rule for seasonal filters, as suggested recently in Webel (2026), the systematic occurrence of issues related to remaining autocorrelation at seasonal lags, and short and long-term revision profiles in both level estimates and their growth rates. Besides an inflated number of filter revisions in the case of the rather unstable Google signal, the trend-cycle filter setting ultimately proves to have a limited impact on the systematic adequacy of modified X-11 seasonal adjustments.

… but would benefit from further streamlining

Overall, the modified X-11 method represents a promising step forward in the seasonal adjustment of sub-monthly time series, offering greater flexibility and adaptability to complex seasonal profiles. Notwithstanding novel approaches to parametric trend-cycle estimation, the above findings suggest that choosing an appropriate seasonal filter plays a more crucial role in terms of quality aspects and, hence, highlights once again the urgent need for implementing corresponding automatic tools. Adding the other aforementioned missing features from the classical X-11 method, enabling the configuration of period-specific seasonal filters in certain special cases of integer periodicities, and trimming the seemingly countless options for kernel-based trend-cycle filtering could help to further strengthen the method’s utility for real-time economic monitoring and policy analysis.

References

Dagum, E. B. and S. Bianconcini (2008), “The Henderson Smoother in Reproducing Kernel Hilbert Space”, Journal of Business and Economic Statistics 26(4): 536–545.

Proietti, T. and A. Luati (2008), “Real Time Estimation in Local Polynomial Regression, with Application to Trend-Cycle Analysis”, Annals of Applied Statistics 2(4): 1523–1553.

Webel, K. (2026), “Redesigning the Classical Automatic Selection of X-11 Seasonal Filters”, Discussion Paper 07/2026, Deutsche Bundesbank.

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), Some thoughts on modified X-11 seasonal adjustments for time series with complex seasonality, Bundesbank Discussion Paper, No 32/2026