Publication type: Book part
Type of review: Not specified
Title: Real time trend extraction and seasonal adjustment
Authors: Wildi, Marc
DOI: 10.2785/279605
Published in: Handbook on seasonal adjustment
Page(s): 415
Pages to: 451
Issue Date: 2018
Publisher / Ed. Institution: Eurostat
Publisher / Ed. Institution: Luxembourg
ISBN: 978-92-79-80170-9
Language: English
Subject (DDC): 510: Mathematics
Abstract: Signal extraction concerns the definition, the analysis and the extraction of systematic patterns in time series. We here rely on linear filters and propose a new phenomenological approach which emphasizes filter effects. In this perspective, optimal designs are derived by tuning filter characteristics to application purposes. In essence, our approach aligns optimization criteria on problem structures and user priorities. We stress the importance of an agnostic approach whose scope generalizes classical filters as well as traditional model-based approaches. In particular, we propose customized criteria for minimizing revisions and for emphasizing timeliness and/or reliability of early (real-time) estimates. The key towards our customized approach is a thorough analysis of filter effects in the frequency domain. We identify filters with transfer functions and decompose the filter effect into amplitude and phase errors. In a real-time perspective, the resulting decomposition of the mean-square filter error enables to track simultaneously reliability/accuracy issues (noise suppression) as well as timeliness (time-shift/delay) aspects. The resulting optimality concept blends with the structure of the estimation problem and the intention of the analyst, as well. We here propose a new generalized optimization criterion which bridges the gap between the original Direct Filter Approach (DFA) and a numerically fast linear approximation I-DFA of the former. Unlike I-DFA, the resulting new estimation method is able to replicate the original DFA perfectly and it is almost as fast, in computational terms, as I-DFA.
Fulltext version: Published version
License (according to publishing contract): Licence according to publishing contract
Departement: School of Engineering
Organisational Unit: Institute of Data Analysis and Process Design (IDP)
Appears in collections:Publikationen School of Engineering

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Wildi, M. (2018). Real time trend extraction and seasonal adjustment. In Handbook on seasonal adjustment (pp. 415–451). Eurostat.
Wildi, M. (2018) ‘Real time trend extraction and seasonal adjustment’, in Handbook on seasonal adjustment. Luxembourg: Eurostat, pp. 415–451. Available at:
M. Wildi, “Real time trend extraction and seasonal adjustment,” in Handbook on seasonal adjustment, Luxembourg: Eurostat, 2018, pp. 415–451. doi: 10.2785/279605.
WILDI, Marc, 2018. Real time trend extraction and seasonal adjustment. In: Handbook on seasonal adjustment. Luxembourg: Eurostat. S. 415–451. ISBN 978-92-79-80170-9
Wildi, Marc. 2018. “Real Time Trend Extraction and Seasonal Adjustment.” In Handbook on Seasonal Adjustment, 415–51. Luxembourg: Eurostat.
Wildi, Marc. “Real Time Trend Extraction and Seasonal Adjustment.” Handbook on Seasonal Adjustment, Eurostat, 2018, pp. 415–51,

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