1. Real-Time Signalextraction An Application of Customized Estimation Criteria

2. Real-Time Estimation:KOF-economic barometer

3. GDP and old KOF-economic barometer (ex post) Standardized growth rates 3 3 2 2 GDP 1 1 0 0 -1 -1 -2 -2 KOF-Barometer -3 -3 84 86 88 90 92 94 96 98 00 02 04

4. `Old´ KOF-economic barometer (real time) 1.5 0 -1.5 2001 2002 2003

5. Problems • Real-time estimates lag • Delay • Real-time estimates are noisy • Unreliability • Purpose of TP-criterion • Reduce delay and improve reliability, SIMULTANEOUSLY!

6. Signal Definition Customization

7. Definition • Signal: match intention of researcher/user • KOF economic barometer: • Eliminate short-term (periodicity < 1.5 years) fluctuations from a leading indicator of GDP • Transfer function of the filter • Symmetric filter

8. Business-cycle frequencies,cutoff: 1.5 years

9. Symmetric MA-filter

10. Customization • Specify a smoothing process that fits your intention • Signal • Estimate that signal properly in real-time • Concurrent filter (completely asymmetric) • Customized estimation criteria

11. Research Focus • Business cycle analysis • Trading, climatology, linguistics • Detection of turning-points • Local extrema of the (previous) trend component • Experience: these TP‘s are informative about the future dynamics of the series • Convey a strong prospective content

12. Real-time estimation problem Traditional MBA (level) Methodological issues

13. Traditional MBA • X-12, X-11 ARIMA, TRAMO/SEATS • Identify a time series model for the DGP • Forecast the future • Apply the symmetric filter to the extended time series • Criterion • One-step ahead mean-square performance • Multi-step ahead forecasts needed • Mismatch because models are misspecified

14. TRAMO: heavy misspecification(120 Obs.) • Business survey data: bounded time series

15. Conclusions • Statistics based on one-step ahead forecasts • Estimation, Identification (AIC/BIC, unit-roots tests,…), Diagnostics (Box-Pierce, Ljung-Box) • Cannot detect misspecification related to mid-or long-term dynamics • Conflict one vs. multi-step ahead forecasting performances • Consequences • Inefficient real-time filters • Unnecessarily large time delays • TP cannot be accounted for explicitly

16. Customized criteria Level Turning Point (TP)

17. Material • Paper • Book • Marc.wildi@zhawin.ch • Software • R-package: signalextraction • CRAN (ETHZ, Zurich)

18. Empirical results TP‘s (Part 1) Simple level criteria (Benchmarks)

19. Criteria (Level) • Customization: WYOIWYG

20. Simple designs • Optimal (mean-square) real-time level filter • L-L filter • TP: local extrema • Optimal (mean-square) real-time level filter in first differences • L-D Filter • TP: crossings of the zero-level line

21. L-L and L-D filters

22. TP‘s: identification in real-time

23. Conclusions • Level-Filter for original data (L-L-Filter) • Faster • Noisier • Classical trade-off • Next steps: improve • Speed • Speed AND reliability

24. Empirical results TP‘s (Part 2) Improving speed An explicit focus towards TP‘s

25. Characteristics of previous level filters

26. Controlling the time delay • λ>1: emphasize the time delay in the pass-band • λ=1: best level filter • Issues are detailed in paper/book

27. Empirical results part 2 • Two competing designs • Optimal real-time level filters in first differences • λ=1: mean-level performance • λ=6: SELECTIVE mean-level performance

28. L-L (black) vs. L-D (λ=1: red and λ=6: brown) • Rate of false alarms: 9.1%(λ=6), 12.4% (λ=1),15% (level)

29. Filter characteristics

30. Selectivity: improved performance in TP‘s

31. Selectivity: improved performance in TP‘s • Mean-square filter errors • Selectivity-effect • Obtained without knowledge of location of TP‘s • Due to stylized fact: second derivative large (in absolute value) in TP‘s

32. Empirical results TP‘s (Part 3) Improving speed and reliabilitySIMULTANEOUSLY Research Projects

33. Customization: Controlling time delay and high-frequency damping • Stronger damping of high-frequency noise in stop-band • Smaller time delays in pass-band • W(ω) is monotonic (increasing) and λ>1

34. Competing Designs • Fast real-time level filter in first differences • λ=6 • Logit-model • New TP-filter

35. Comparison: TP-filter vs fast (λ=6) level-filter

36. TP-filter vs. logit-model

37. Performances • Rate of undesirable errors: • TP: 4.1% (IN REAL-TIME) • Logit: 9.1% • λ=6: 9.1%

38. Amplitude DFA TP-filter vs. DFA level filter (KOF-Economic Barometer)

39. Delay TP-filter vs. level filter(KOF-Economic Barometer)

40. Conclusions • TP-filter is both fast and reliable • There is a trade-off! • But optimal filter designs can significantly improve upon • Traditional level filters • Logit models • Traditional level- and TP-criteria are incongruent • Generalization of level-criterion • Improved level performance in TP‘s

41. Economic Sentiment Indicator (ESI) for the euro area, published monthly by DG ECFIN. DFA vs Dainties

42. In the past (DFA: fast and reliable)

43. Towards the current boundary

44. Leading Indicator for German GDP Research Project with the Bundesministerium für Wirtschaft und Technologie

45. GDP and fastest (real-time) series

46. Comparison: symmetric trend and real-time output

47. Conclusions

48. Optimization criteria • Very often ML does not fit the intention of the researcher/user • Model misspecification: functions of ML-estimates are not ML-estimates of these functions • Example: multi-step ahead forecasts • Customization • Define and implement criteria that match the intention of the researcher • Very often: generalization of ML

49. Outcome • New estimation criteria • Level/TP’s • Estimate parameters of real-time filter directly • New diagnostics • Verify characteristics of real-time filter directly • New filter constraint test • Generalizes unit root tests to problems involving one- and multi-step ahead forecasts

50. New Results/Work in Progress • Trading filters • Non-linear Filters • Asymmetric cycles • Multivariate filters