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Real Time Trend Extraction and Seasonal Adjustment: a Generalized Direct Filter Approach

Real Time Trend Extraction and Seasonal Adjustment: a Generalized Direct Filter Approach . ISF 2011, Prague Marc Wildi Zurich University of Applied Sciences Marc.wildi@zhaw.ch. Signalextraction vs. Forecasting. Signal. Filters:.

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Real Time Trend Extraction and Seasonal Adjustment: a Generalized Direct Filter Approach

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  1. Real Time Trend Extraction and Seasonal Adjustment: a Generalized Direct Filter Approach

    ISF 2011, Prague Marc Wildi Zurich University of Applied Sciences Marc.wildi@zhaw.ch

  2. Signalextraction vs. Forecasting

  3. Signal
  4. Filters: Ad hoc designs: no explicit modellingofthedata HP-Filter, CF-Filter, BK-Filter, Henderson Filter, … Model-baseddesigns TRAMO/SEATS, X-12-ARIMA, Stamp Non-parametricfilters (Loess) Verygeneralsetting!
  5. Real-TimeSignalextractionTime Domain
  6. Example
  7. Forecasting

  8. Frequency Domain

  9. Real-Time SignalextractionFrequency Domain
  10. Example: European IPI
  11. TRAMO/SEATS (Airline-Model in red)
  12. Forecasting
  13. Optimization Criterion: Mean-Square
  14. Choice ofSpectralEstimate Model-based: TRAMO (airline-model), X-12-ARIMA, state-space Ad-hoc: implicitmodel (HP, CF, BK, Henderson,…) Non Parametric Periodogram This choiceistosomeextentarbitrary: itdepends on thepreference/experience/expertiseoftheuser. Verygeneralsetting!
  15. GeneralizedDFA: Very General Setting! Arbitrarysignals Includingas a specialcase traditional one-stepaheadforecasting Arbitrary finite sample SpectralEstimate ad hoc, model-based, non-parametric Generalizes Ad hoc filters Model-basedfilters DFA (based on theperiodogram) Traditional (one-stepahead) ARIMA-modelling, state-spacemodelling Extendsto multivariate filtering!

  16. Frequency-Domain: Timeliness-Reliability Dilemma

  17. Control of Timeliness/Speed: Cosine Law applied to
  18. Timeliness-Criterion
  19. Emphasize Noise Rejection in Stop Band (Reliability/Smoothness)
  20. EssenceofGeneralized DFA The newoptimizationcriterion IS thetimeliness-reliability-dilemma andconversely `Philosophy’ maybecontrastedwith Maximum likelihood (particularparametricsettinglambda/expweight) Maximum entropy Contrast: Manipulate Real-Time filtercharacteristicsexplicitlyon theedgeofthe fundamental dilemma User relevant priorities (risk-aversion)
  21. Effectof `Expweight’
  22. Effectof Lambda

  23. Example : European IPI

  24. Replicate TRAMO RT-Performance:TRAMO (red) vs. Gen. DFA (blue)
  25. New Target: Customized Design Insteadof optimal mean-squareestimatetheusercouldspecify a `faster’ and/or `smoother’ real-time estimate The newestimateis still purely model-based! It IS TRAMO (itcouldbe X-12, Stamp,…) But itbecomesfaster/smoother (timeliness-reliabilitydilemma)
  26. Mean-Square vs. Enhanced TRAMO Typically, TRAMO-filter (blue) is noisy (poor noise suppression in stop-band) The `customized’ filter (green) barely loses in terms of time-shift in the pass-band. It clearly wins in terms of noise suppression in the stop-band: better compromise
  27. TRAMO (red) vs. Enhanced (green)
  28. Conclusion As expected, the `customized’ real-time filter (green) isas `fast’ asthe MS-filter by TRAMO (red) anditismuch smoother (betternoisesuppression)
  29. SA vs. Customized RT-Trend Real-time customizedtrendfilterisas fast as traditional SA-filter andmuch (much) smoother.

  30. Conclusion

  31. PhilosophyGeneralizedDFA The newcriterion IS thetimeliness-reliabilitydilemma
  32. Consequences Generalizesclassicalfilterapproaches (ad hoc, model-based) Emphasizesuser relevant prioritiesexplicitly
  33. Practicality Numerically(very) fast Closed-fromapproximation (I-DFA/open source) Fast exactoptimization (Eurostat/proprietary) Short pieceof (R-) code Couldeasily dock toany existent software/tool
  34. Web: SEFblog: http://blog.zhaw.ch/idp/sefblog USRI: http://www.idp.zhaw.ch/usri MDFA-XT: http://www.idp.zhaw.ch/MDFA-XT SEF-page: http://www.idp.zhaw.ch/sef
  35. Selected SEFBlog-Entries Forecastingthe EURO-BUND-Future (6 months, one Year) http://blog.zhaw.ch/idp/sefblog/index.php?/archives/186-Forecasting-the-EURO-Bund-Future-6-months-and-One-Year-Ahead-FirstPreliminary-Draft.html OECD-CLI: leadingindicatorforthe US http://blog.zhaw.ch/idp/sefblog/index.php?/archives/173-Tutorial-I-MDFA-Part-II-The-OECD-CLI-for-the-US.html http://blog.zhaw.ch/idp/sefblog/index.php?/archives/175-Injecting-the-ZPC-Gene-into-I-MDFA-an-Application-to-the-OECD-CLI-for-the-US.html
  36. SEFBlog-Entries Algorithmic Trading: http://blog.zhaw.ch/idp/sefblog/index.php?/archives/157-A-Generalization-of-the-GARCH-in-Mean-Model-Vola-in-I-MDFA-filter.html TutorialsUnivariate Filter: http://blog.zhaw.ch/idp/sefblog/index.php?/archives/159-I-DFA-Exercises-Part-I-Mean-Square-Criterion.html http://blog.zhaw.ch/idp/sefblog/index.php?/archives/160-I-DFA-Exercises-Part-II-Customization-SpeedReliability.html
  37. SEFBlog-Entries Tutorials Multivariate Filter: http://blog.zhaw.ch/idp/sefblog/index.php?/archives/172-Tutorial-I-MDFA-Part-I-Simulated-Time-Series.html http://blog.zhaw.ch/idp/sefblog/index.php?/archives/173-Tutorial-I-MDFA-Part-II-The-OECD-CLI-for-the-US.html
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