Why not publish the trend-cycle? The goal of publishTC is to facilitate the computation of trend-cycle component:
Using the Cascade Linear Filter (CLF) and the surrogate cut-and-normalise asymmetric filters, as done by Statistique Canada;
Using the classical Henderson symmetric filter and the surrogate Musgrave asymmetric filters, as done by Australian Bureau of Statistics (Trewin 2003);
Using a local Parametrization of the Musgrave asymmetric filters, as described in Quartier-la-Tente (2024);
Extending the Henderson symmetric fiter and the surrogate Musgrave asymmetric filters to take into account additive outliers and level shifts, as described in Quartier-la-Tente (2025).
Bibliography
Dagum, E. B., & Luati, A. (2008). A Cascade Linear Filter to Reduce Revisions and False Turning Points for Real Time Trend-Cycle Estimation. Econometric Reviews 28 (1-3): 40‑59. https://doi.org/10.1080/07474930802387837
Henderson, R. (1916). Note on graduation by adjusted average. Transactions of the actuarial society of America 17: 43‑48.
Musgrave, J. (1964). A set of end weights to end all end weights. US Census Bureau [custodian].
Trewin, D. (2003). A guide to interpreting time series - Monitoring trends. Australian Bureau of Statistics Information Paper. https://www.abs.gov.au/AUSSTATS/abs@.nsf/Lookup/1349.0Main+Features12003?OpenDocument.
Quartier-la-Tente, A. (2024). Improving Real-Time Trend Estimates Using Local Parametrization of Polynomial Regression Filters. Journal of Official Statistics, 40(4), 685-715. https://doi.org/10.1177/0282423X241283207.
Quartier-la-Tente, A. (2025). Estimation de la tendance-cycle avec des méthodes robustes aux points atypiques. https://github.com/AQLT/robustMA.