Lppl models MiFIT 2013: Vyacheslav Arbuzov

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Lppl models MiFIT 2013: Vyacheslav Arbuzov

  1. 1. Thefreedictionary.com2Mr. GreenspanCharles Kindleberger, MITProfessor J.Barley Rosser, James Madison University
  2. 2. 3• 1585 – 1650 Netherlands• Creating futures and options on the tulips• The fall is 100 times
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  9. 9. 12AuthorsA.Johansen, O.Ledoit, D.Sornette (JLS)First publicationLarge financial crashes (1997)Famous bookDidier SornetteWhy Stock Markets Crash (2004)
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  13. 13. 16m = 0.3m = 0.01m = 0.9 m = 1.7
  14. 14. 17 = 3  = 7 = 30 = 15
  15. 15. 18 = 7  = 9.5
  16. 16. 19First modelSecond model
  17. 17. John von Neumann20
  18. 18. 21122lnlnlni i ii i i i i ii i i i i iA N f g pB f f g f p fC g f g g p g                               
  19. 19. 22 Splitting the tolerance values ​​on the grid Finding the grid parameters providing a minimum sum of squared residuals Optimizing found on the grid parameters using the Newton-Gauss
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  21. 21. 24V.Filimonov and D.SornetteA Stable and Robust Calibration Schemeof the Log-Periodic Power Law Model(29 aug 2011)
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  23. 23. 26
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  25. 25. 28The procedure for estimationof parameters0tctmABln[ ( )]p tFilter
  26. 26. 290 10 20 30 40050100150LOMB PERIODOGRAMomegaP(omega)m
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  29. 29. 32D.Fantazzini, P.Geraskin,Everything You Always Wanted to Knowabout Log Periodic PowerLaws for Bubble Modelling but Were Afraid to Ask (2011)
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  33. 33. The practical task № 7. Estimate LPPL modelCommands to help :help(nsl)TASK :a. Download Index Data(ticker: “MICEX”) from 2001 to 2009b. Estimate parameters of model LPPLMODEL LPPL:
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