Extreme events : Causes and consequences WP2

1
Extreme events Causes and consequencesWP2

• M. AUSLOOS
• SUPRATECS, B-4000 Liège, Euroland
• Email marcel.ausloos_at_ulg.ac.be

2
Extreme events Causes and consequences

• Introduction
• Objectives
• Tasks
• Conclusions

3
Objectives

• To provide a library of data series
• and of PDF evaluation methods
• To compare the ability of the different PDF
  evaluation methods
• To develop new ones
• based on the findings from previous comparisons

4
Objectives

• To provide a library of data series
• and of PDF evaluation methods
• To compare the ability of the different PDF
  evaluation methods
• To develop new ones
• based on the findings from previous comparisons

5
Objective 1

• To provide a library of data series
• and of
• PDF evaluation methods

• Financial data
• Currency exchanges
• Financial indices
• Gross domestic product
• Geophysics data
• Climatology
• Meteorology
• Earthquakes
• Sociological data
• Sales

6
Objective 1

• To provide a library of data series
• and of
• PDF evaluation () methods
• () tail characterization

• Ranking (Zipf) method
• Spectral analysis
• Moving Average analysis
• Rescaled Range analysis
• Detrended Fluctuation anal.
• Recurrence Plots Recurr. Quantification
  analysis

7
Objective 1 examples
Ranking (Zipf) method
8
Objective 1 examples
Ranking (Zipf) method
9
Objective 1 examples
Spectral analysis
10
Objective 1 examples
Detrended Fluctuation analysis
Rescaled Range analysis
11
Objective 1 examples

• El nino (SOI)
• Z (monthly variability) for DP
• Tsallis distr.
• NAO
• Crossover 152 m
• (0.54 0.30)

12
Objectives

• To provide a library of data series
• and of PDF evaluation methods
• To compare the ability of the different PDF
  evaluation methods
• To develop new ones
• based on the findings from previous comparisons

13
Objective 2

• To compare the ability of the different PDF
  evaluation methods

• Financial data
• Currency exchanges
• Financial indices
• Gross domestic product
• Geophysics data
• Climatology
• Meteorology
• Earthquakes
• Sociological data
• Sales shocks
• Airplane crashes

14
Objective 2 examples

• To compare the ability of the different PDF
  evaluation methods
• Financial data
• Currency exchanges
• Financial indices
• Gross domestic product
• N.B. Time window size effects on averages
• network stylization

UMLP Discrete distance
BMLP Discrete distance
15
Objective 2 examples

• To compare the ability of the different PDF
  evaluation methods
• Geophysics data
• Climatology
• Meteorology
• Earthquakes
• N.B. Time window size effects on averages !!!

16
Objective 2 examples

• To compare the ability of the different PDF
  evaluation methods
• Sociological data
• Sales shocks
• Airplane crashes
• N.B. Time window size effects on averages
• network stylization

17
Objectives

• To provide a library of data series
• and of PDF evaluation methods
• To compare the ability of the different PDF
  evaluation methods
• To develop new ones
• based on the findings from previous comparisons

18
Objective 3

• To develop new ones
• based on the findings from previous comparisons

• Financial data
• Currency exchanges
• Financial indices
• Gross domestic product
• Geophysics data
• Climatology
• Meteorology
• Earthquakes
• Sociological data
• Sales

19
Objective 3

• To develop new ones
• based on the findings from previous comparisons

• Financial data
• Geophysics data
• Sociological data
• Fractional Brownian Motions
• Delayed Verhulst Evolutions
• Bak-Sneppen Evolutions

20
Tasks

• 2a.1. To develop a set of time series to test the
  skill of analysis and prediction methods
• 2a.2. To develop a library of the different PDF
  evaluation methods and spectral estimation
• 2a.3. To develop new methods for estimation and
  prediction

21
Task 2a.1

• To develop a set of time series to test the skill
  of analysis and prediction methods

• New artificial time series ?
• Fractional Brownian Motions
• Delayed Verhulst Evolutions
• Bak-Sneppen Evolutions
• Multivariate series ?

22

• Fractional Brownian Motion (1D)

(not really new)
Berry Lewis, 1980
23
x(t1) r x(t)1-x(t)
x(t1) r x(t)1-x(t-T)

• Delayed Verhulst Evolutions
• vs. BDE

x(t1) r Fx(t) G1-x(t-T)
24
x(t1) r x(t)1-x(t)
x(t1) r x(t)1-x(t-T)

• Delayed Verhulst Evolutions

x(t1) r Fx(t) G1-x(t-T)
25

• Bak-Sneppen Evolutions

bubble
26

• Multivariate series ?

cf. fBM
27

• Fractional Brownian Motions (2D)

D2.2 M8 g1.2
D2.5 M8 g1.5

28
Task 2a.2

• To develop a library of the different PDF
  evaluation methods and spectral estimation

• Ranking (Zipf) method
• Spectral analysis
• Moving Average analysis
• Rescaled Range analysis
• Detrended Fluctuation analysis
• Recurr. Plots Recurr. Quantification analysis

29
Task 2a.2

• To develop a library of the different PDF
  evaluation methods and spectral estimation

• Ranking (Zipf) method
• Spectral analysis
• Moving Average analysis
• Rescaled Range analysis
• Detrended Fluctuation analysis
• Recurr. Plots Recurr. Quantification analysis

30

• Moving Average analysis

Crossing of ..
r (1/T2)DT (1-DT)H-1
T2 80
gt H(t)
31

• Moving Average analysis

spectrum of ..
pre-crash
32

• Recurr. Plots Recurr. Quantification analysis

Log periodicity
bubble
33
Task 2a.3

• To develop new methods for estimation and
  prediction
• Precursors
• Change in trends
• Clustering

• Search for log periodicity
• Use recurrence plots quantification analysis
• Distance analysis
• Network evolution cluster percolation
• Multifractality ?

34
Hamiltonian / Langevin physics

• H H0 H1 H2
• with H0 E0
• H1 - Si Hi.Si
• H2 - Sij Jij Si.Sj

35
Thanks for your attention
36
(No Transcript)