Impacts of natural disasters on a dynamic economy

Transcription

1 Impacts of natural disasters on a dynamic economy Andreas Groth Ecole Normale Supérieure, Paris in cooperation with Michael Ghil, Stephane Hallegatte, Patrice Dumas, Yizhak Feliks, Andrew W. Robertson Seminar at the Potsdam Institute for Climate Impact Research February 5, 213 Supported by a grant from

2 Outline 1 Singular spectrum analysis 2 Macroeconomic activity business cycles 3 International business cycles 4 Oscillatory climate modes 5 Conclusions and discussion Andreas Groth, ENS, Paris Natural disasters (2) on a dynamic economy PIK seminar 2 / 36

3 Outline 1 Singular spectrum analysis 2 Macroeconomic activity business cycles 3 International business cycles 4 Oscillatory climate modes 5 Conclusions and discussion Andreas Groth, ENS, Paris Natural disasters (3) on a dynamic economy PIK seminar 3 / 36

4 Motivation Observation Short multivariate time series Deterministic behavior is mixed with random fluctuations 1 2 Time series Time Andreas Groth, ENS, Paris Natural disasters (4) on a dynamic economy PIK seminar 4 / 36

5 Motivation Observation Short multivariate time series Deterministic behavior is mixed with random fluctuations Objective Spatio-temporal dynamics Regular/recurrent behavior in time Spatial clustering Discriminate deterministic behavior from stochastic fluctuations Time series Time Andreas Groth, ENS, Paris Natural disasters (4) on a dynamic economy PIK seminar 4 / 36

6 Motivation Observation Short multivariate time series Deterministic behavior is mixed with random fluctuations Objective Spatio-temporal dynamics Regular/recurrent behavior in time Spatial clustering Discriminate deterministic behavior from stochastic fluctuations Singular spectrum analysis Time series Time Andreas Groth, ENS, Paris Natural disasters (4) on a dynamic economy PIK seminar 4 / 36

7 Singular spectrum analysis (SSA) Idea: Reconstruct dynamics from time-delayed embedding (Mañé-Takens) Andreas Groth, ENS, Paris Natural disasters (5) on a dynamic economy PIK seminar 5 / 36

8 Singular spectrum analysis (SSA) Idea: Reconstruct dynamics from time-delayed embedding Data: Multivariate time series x(n) = {x d (n)} (Mañé-Takens) d = 1... D channels of length n = 1... N Andreas Groth, ENS, Paris Natural disasters (5) on a dynamic economy PIK seminar 5 / 36

9 Singular spectrum analysis (SSA) Idea: Reconstruct dynamics from time-delayed embedding Data: Multivariate time series x(n) = {x d (n)} (Mañé-Takens) d = 1... D channels of length n = 1... N Embedding: M-dimensional time-delayed embedding of each channel ( ) X d (n) = x d (n), x d (n + 1),..., x d (n + M 1) Andreas Groth, ENS, Paris Natural disasters (5) on a dynamic economy PIK seminar 5 / 36

10 Singular spectrum analysis (SSA) Idea: Reconstruct dynamics from time-delayed embedding Data: Multivariate time series x(n) = {x d (n)} (Mañé-Takens) d = 1... D channels of length n = 1... N Embedding: M-dimensional time-delayed embedding of each channel ( ) X d (n) = x d (n), x d (n + 1),..., x d (n + M 1) Concatenate channels gives full augmented trajectory matrix ) (X 1 X 2... X D X = of size N D M Andreas Groth, ENS, Paris Natural disasters (5) on a dynamic economy PIK seminar 5 / 36

11 Singular spectrum analysis How to extract information from X = (X 1 X 2... X D )? Andreas Groth, ENS, Paris Natural disasters (6) on a dynamic economy PIK seminar 6 / 36

12 Singular spectrum analysis (X 1 X 2... X D ) How to extract information from X =? Apply Principal Component Analysis (PCA) to X 1 Compute covariance matrix C = X X 2 Eigendecomposition Λ = E C E gives diagonal matrix Λ of eigenvalues λ k orthogonal matrix E of eigenvectors e k 3 Projection of X onto E gives principal components (PCs) 4 Reconstruction of x gives reconstructed components (RCs) (Broomhead&King 1986; Vautard&Ghil 1989) Andreas Groth, ENS, Paris Natural disasters (6) on a dynamic economy PIK seminar 6 / 36

13 Singular spectrum analysis (X 1 X 2... X D ) How to extract information from X =? Apply Principal Component Analysis (PCA) to X 1 Compute covariance matrix C = X X 2 Eigendecomposition Λ = E C E gives diagonal matrix Λ of eigenvalues λ k orthogonal matrix E of eigenvectors e k 3 Projection of X onto E gives principal components (PCs) 4 Reconstruction of x gives reconstructed components (RCs) (Broomhead&King 1986; Vautard&Ghil 1989) (Ghil et al., Advanced spectral methods for climatic time series, Reviews of Geophysics, 22) SSA software toolkit from the UCLA: Andreas Groth, ENS, Paris Natural disasters (6) on a dynamic economy PIK seminar 6 / 36

14 Simulation experiment Time series: composite of 4 harmonic oscillations + AR(1) noise Time series Time Andreas Groth, ENS, Paris Natural disasters (7) on a dynamic economy PIK seminar 7 / 36

15 Simulation experiment Time series: composite of 4 harmonic oscillations + AR(1) noise Time series MTM Power spectral estimation Time Frequency Andreas Groth, ENS, Paris Natural disasters (7) on a dynamic economy PIK seminar 7 / 36

16 Simulation experiment Time series: composite of 4 harmonic oscillations + AR(1) noise Time series MTM Power spectral estimation Time Frequency Andreas Groth, ENS, Paris Natural disasters (7) on a dynamic economy PIK seminar 7 / 36

17 Classical SSA analysis e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 e 9 e 1 e 11 e 12 e 13 e 14 e 15 e e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 e 9 e 1 e 11 e 12 e 13 e 14 e 15 e 16 T=15.9 T=11.7 T=9.1 T=7.6 T=18.8 T=27.6 T=12.2 T=8.6 T=1.8 T=31.9 T=35.1 T=19.1 T=7.2 T=5.9 T=2.8 T= Frequency Andreas Groth, ENS, Paris Natural disasters (8) on a dynamic economy PIK seminar 8 / 36

18 Classical SSA analysis e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 e 9 e 1 e 11 e 12 e 13 e 14 e 15 e e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 e 9 e 1 e 11 e 12 e 13 e 14 e 15 e 16 T=15.9 T=11.7 T=9.1 T=7.6 T=18.8 T=27.6 T=12.2 T=8.6 T=1.8 T=31.9 T=35.1 T=19.1 T=7.2 T=5.9 T=2.8 T= Frequency General problem of PCA and SSA: degenerate eigenvalues and mixed eigenvectors Andreas Groth, ENS, Paris Natural disasters (8) on a dynamic economy PIK seminar 8 / 36

19 Classical SSA analysis e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 e 9 e 1 e 11 e 12 e 13 e 14 e 15 e e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 e 9 e 1 e 11 e 12 e 13 e 14 e 15 e 16 T=15.9 T=11.7 T=9.1 T=7.6 T=18.8 T=27.6 T=12.2 T=8.6 T=1.8 T=31.9 T=35.1 T=19.1 T=7.2 T=5.9 T=2.8 T= Frequency General problem of PCA and SSA: degenerate eigenvalues and mixed eigenvectors Solution: varimax rotation of SSA eigenvectors (Groth&Ghil, PRE, 211) takes spatio-temporal structure of SSA eigenvectors into account Andreas Groth, ENS, Paris Natural disasters (8) on a dynamic economy PIK seminar 8 / 36

20 SSA analysis + varimax rotation e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 e 9 e 1 e 11 e 12 e 13 e 14 e 15 e e 1 e 2 e 3 e 4 e 5 e 6 e 7 e 8 e 9 e 1 e 11 e 12 e 13 e 14 e 15 e 16 T=inf T=15.1 T=14.5 T=7.5 T=7.5 T=9.3 T=9.2 T=29.3 T=26.3 T=21.2 T=19.8 T=6.8 T=6.8 T=2.8 T=2.8 T= Frequency Perfect separation between different oscillations Unimodal eigenvectors without mixing Simplified physical interpretation Andreas Groth, ENS, Paris Natural disasters (9) on a dynamic economy PIK seminar 9 / 36

21 Reconstruction of oscillatory behavior e 1 e 2 e 3 e 4 e 5 Eigenvectors x y z SSA eigenvectors are frequency selective filters They adapt to oscillatory behavior in terms of oscillatory pairs (Vautard&Ghil 1989; Plaut&Vautard 1994) e 6 e 7 Reconstruction with RCs 1 2 e Eigenvalues.4 λ k Andreas Groth, ENS, Paris Natural disasters (1) on a dynamic economy PIK seminar 1 / 36

22 Reconstruction of synchronization cluster ω 1 Chain of Rössler oscillators 5 uncoupled and detuned oscillator c ω 2 ω J-1 c ω J Andreas Groth, ENS, Paris Natural disasters (11) on a dynamic economy PIK seminar 11 / 36

23 Reconstruction of synchronization cluster ω 1 Chain of Rössler oscillators 5 uncoupled and detuned oscillator c e 1 x 1 y 1 z 1 x 2 y 2 z 2 x 3 y 3 z 3 x 4 y 4 z 4 x 5 y 5 z 5 ω 2 e 2 e 3 e 4 e 5 e Eigenvalues λ before rotation k λ* after rotation k e 7 e 8 ω J e 9 c Order k e ω J SSA associates to each oscillator an oscillatory pair Andreas Groth, ENS, Paris Natural disasters (11) on a dynamic economy PIK seminar 11 / 36

24 Reconstruction of synchronization cluster ω 1 c Chain of Rössler oscillators 1 coupled and detuned oscillators Reconstructed components RCs x x x x x x x x x x ω 2 RC 1 2 RC 3 4 RC 5 6 RC 7 8 RC 9 1 RC ω J-1 c RC RC ω J RC RC Andreas Groth, ENS, Paris Natural disasters (12) on a dynamic economy PIK seminar 12 / 36

25 Reconstruction of synchronization cluster ω 1 c Chain of Rössler oscillators 1 coupled and detuned oscillators Reconstructed components RCs x x x x x x x x x x ω 2 RC 1 2 RC 3 4 RC 5 6 RC 7 8 RC 9 1 RC ω J-1 c RC RC ω J RC RC Andreas Groth, ENS, Paris Natural disasters (12) on a dynamic economy PIK seminar 12 / 36

26 Reconstruction of synchronization cluster ω 1 c Chain of Rössler oscillators 1 coupled and detuned oscillators Reconstructed components RCs x x x x x x x x x x ω 2 RC 1 2 RC 3 4 RC 5 6 RC 7 8 RC 9 1 RC ω J-1 c RC RC ω J RC RC Andreas Groth, ENS, Paris Natural disasters (12) on a dynamic economy PIK seminar 12 / 36

27 Reconstruction of synchronization cluster ω 1 c Chain of Rössler oscillators 1 coupled and detuned oscillators Reconstructed components RCs x x x x x x x x x x ω 2 RC 1 2 RC 3 4 RC 5 6 RC 7 8 RC 9 1 RC ω J-1 c RC RC ω J RC RC Andreas Groth, ENS, Paris Natural disasters (12) on a dynamic economy PIK seminar 12 / 36

28 Reconstruction of synchronization cluster ω 1 c Chain of Rössler oscillators 1 coupled and detuned oscillators Reconstructed components RCs x x x x x x x x x x ω 2 RC 1 2 RC 3 4 RC 5 6 RC 7 8 RC 9 1 RC ω J-1 c RC RC ω J RC RC Andreas Groth, ENS, Paris Natural disasters (12) on a dynamic economy PIK seminar 12 / 36

29 Reconstruction of synchronization cluster ω 1 c Chain of Rössler oscillators 1 coupled and detuned oscillators Reconstructed components RCs x x x x x x x x x x ω 2 RC 1 2 RC 3 4 RC 5 6 RC 7 8 RC 9 1 RC ω J-1 c RC RC ω J RC RC Andreas Groth, ENS, Paris Natural disasters (12) on a dynamic economy PIK seminar 12 / 36

30 Reconstruction of synchronization cluster ω 1 c Chain of Rössler oscillators 1 coupled and detuned oscillators Mean observed frequency 1.15 ω Modified variance.3.2 ω J (Groth&Ghil, PRE 211) ω J c Cluster strength * Coupling strength c (Vejmelka&Paluš, Chaos 21) Andreas Groth, ENS, Paris Natural disasters (13) on a dynamic economy PIK seminar 13 / 36

31 Reconstruction of synchronization cluster ω 1 Chain of Rössler oscillators + high observational noise (SNR=1) 1 coupled and detuned oscillators c ω Modified variance.3.2 ω J-1.1 (Groth&Ghil, PRE 211) c Cluster strength * ω J Coupling strength c (Vejmelka&Paluš, Chaos 21) Andreas Groth, ENS, Paris Natural disasters (14) on a dynamic economy PIK seminar 14 / 36

32 Regular behavior vs. stochastic fluctuations Question: Deterministic oscillations or stochastic fluctuations? e 1 T=inf e 1 e 2 T=15.1 e 2 e 3 T=14.5 e 3 e 4 T=7.5 e 4 e 5 T=7.5 e 5 e 6 T=9.3 e 6 e 7 T=9.2 e 7 e 8 T=29.3 e 8 e 9 T=26.3 e 9 e 1 T=21.2 e 1 e 11 T=19.8 e 11 e 12 T=6.8 e 12 e 13 T=6.8 e 13 e 14 T=2.8 e 14 e 15 T=2.8 e 15 e 16 T=62.3 e Frequency Andreas Groth, ENS, Paris Natural disasters (15) on a dynamic economy PIK seminar 15 / 36

33 Regular behavior vs. stochastic fluctuations Question: Deterministic oscillations or stochastic fluctuations? e 1 T=inf e 1 e 2 T=15.1 e 2 e 3 T=14.5 e 3 e 4 T=7.5 e 4 e 5 T=7.5 e 5 e 6 T=9.3 e 6 e 7 T=9.2 e 7 e 8 T=29.3 e 8 e 9 T=26.3 e 9 e 1 T=21.2 e 1 e 11 T=19.8 e 11 e 12 T=6.8 e 12 e 13 T=6.8 e 13 e 14 T=2.8 e 14 e 15 T=2.8 e 15 e 16 T=62.3 e Frequency Andreas Groth, ENS, Paris Natural disasters (15) on a dynamic economy PIK seminar 15 / 36

34 Monte Carlo SSA Significance test against null hypothesis; e.g. AR(1) Surrogate data: x S embedding X S Covariance matrix: C S = X S X S Projection: Λ AS = E C S E and compare with Λ = E C E (Allen&Smith, J. Climate 1996) Andreas Groth, ENS, Paris Natural disasters (16) on a dynamic economy PIK seminar 16 / 36

35 Monte Carlo SSA e 1 e 2 e 4 e 12 e 14 e 15 Significance test against null hypothesis; e.g. AR(1) Surrogate data: x S embedding X S Covariance matrix: C S = X S X S Projection: Λ AS = E C S E and compare with Λ = E C E (Allen&Smith, J. Climate 1996) e 3 Eigenvalue λ k e 5 e 6 e 7 e 8 e 9 e 1 e 11.1 e Order k e Andreas Groth, ENS, Paris Natural disasters (16) on a dynamic economy PIK seminar 16 / 36

36 Monte Carlo SSA e 1 e 2 e 12 e 14 e 15 Significance test against null hypothesis; e.g. AR(1) Surrogate data: x S embedding X S Covariance matrix: C S = X S X S Projection: Λ AS = E C S E and compare with Λ = E C E (Allen&Smith, J. Climate 1996) Eigenvalue λ k Matching problem on short multivariate data e 3 e 4 e 5 e 6 e 7 e 8 e 9 e 1 e 11.1 e Order k e Andreas Groth, ENS, Paris Natural disasters (16) on a dynamic economy PIK seminar 16 / 36

37 Monte Carlo SSA New Significance test against null hypothesis; e.g. AR(1) Surrogate data: x S embedding X S Andreas Groth, ENS, Paris Natural disasters (17) on a dynamic economy PIK seminar 17 / 36

38 Monte Carlo SSA New Significance test against null hypothesis; e.g. AR(1) Surrogate data: x S embedding X S Covariance matrix: C S = X S X S Andreas Groth, ENS, Paris Natural disasters (17) on a dynamic economy PIK seminar 17 / 36

39 Monte Carlo SSA New Significance test against null hypothesis; e.g. AR(1) Surrogate data: x S embedding X S Covariance matrix: C S = X S X S SSA: Λ S = E S C SE S compare with Λ = E CE Andreas Groth, ENS, Paris Natural disasters (17) on a dynamic economy PIK seminar 17 / 36

40 Monte Carlo SSA New Significance test against null hypothesis; e.g. AR(1) Surrogate data: x S embedding X S Covariance matrix: C S = X S X S SSA: Λ S = E S C SE S compare with Λ = E CE Rotation: Find rotation T that best matches E S Σ S T with EΣ (eigenvectors scaled by singular values Σ = Λ 1/2 ) Andreas Groth, ENS, Paris Natural disasters (17) on a dynamic economy PIK seminar 17 / 36

41 Monte Carlo SSA New Significance test against null hypothesis; e.g. AR(1) Surrogate data: x S embedding X S Covariance matrix: C S = X S X S SSA: Λ S = E S C SE S compare with Λ = E CE Rotation: Find rotation T that best matches E S Σ S T with EΣ (eigenvectors scaled by singular values Σ = Λ 1/2 ) Solution provides Procrustes rotation T = UV Andreas Groth, ENS, Paris Natural disasters (17) on a dynamic economy PIK seminar 17 / 36

42 Monte Carlo SSA New Significance test against null hypothesis; e.g. AR(1) Surrogate data: x S embedding X S Covariance matrix: C S = X S X S SSA: Λ S = E S C SE S compare with Λ = E CE Rotation: Find rotation T that best matches E S Σ S T with EΣ (eigenvectors scaled by singular values Σ = Λ 1/2 ) Solution provides Procrustes rotation T = UV with singular value decomposition (E S Σ S ) EΣ = USV Andreas Groth, ENS, Paris Natural disasters (17) on a dynamic economy PIK seminar 17 / 36

43 Monte Carlo SSA New Significance test against null hypothesis; e.g. AR(1) Surrogate data: x S embedding X S Covariance matrix: C S = X S X S SSA: Λ S = E S C SE S compare with Λ = E CE Rotation: Find rotation T that best matches E S Σ S T with EΣ (eigenvectors scaled by singular values Σ = Λ 1/2 ) Solution provides Procrustes rotation T = UV with singular value decomposition (E S Σ S ) EΣ = USV Compare: data Λ with surrogate Λ GG = T Λ S T Andreas Groth, ENS, Paris Natural disasters (17) on a dynamic economy PIK seminar 17 / 36

44 Monte Carlo SSA New Significance test against null hypothesis; e.g. AR(1) Surrogate data: x S embedding X S Covariance matrix: C S = X S X S SSA: Λ S = E S C SE S compare with Λ = E CE Rotation: Find rotation T that best matches E S Σ S T with EΣ (eigenvectors scaled by singular values Σ = Λ 1/2 ) Solution provides Procrustes rotation T = UV with singular value decomposition (E S Σ S ) EΣ = USV Compare: data Λ with surrogate Λ GG = T Λ S T Note: classical test Λ AS = E C S E = E E S Λ S E S E T Λ S T Andreas Groth, ENS, Paris Natural disasters (17) on a dynamic economy PIK seminar 17 / 36

45 Monte Carlo SSA New e 12 e e 1.5 Classical significance test e 2 e 3 e 4.4 e 5 e 6 Eigenvalue λ k.3.2 e 7 e 8 e 9 e 1 e 11.1 e Order k e 15 e Andreas Groth, ENS, Paris Natural disasters (18) on a dynamic economy PIK seminar 18 / 36

46 Monte Carlo SSA New e 12 e 14 e e 1.5 Classical significance test New significance test e 2 e 3 e 4 e 5 Eigenvalue λ k T = 7.7 T = 6.9 T = 2.8 T = 2.3 e 6 e 7 e 8 e 9 e 1 e 11.1 e Order k Discriminant power substantially improved e Andreas Groth, ENS, Paris Natural disasters (18) on a dynamic economy PIK seminar 18 / 36

47 Monte Carlo SSA Discriminant power # FP # TP SNR=1/4; AR(1) observational noise N = 25 M = D Number of true positives (TP), false positives (FP) classical SSA test ( ), new SSA test ( ) Andreas Groth, ENS, Paris Natural disasters (19) on a dynamic economy PIK seminar 19 / 36

48 Outline 1 Singular spectrum analysis 2 Macroeconomic activity business cycles 3 International business cycles 4 Oscillatory climate modes 5 Conclusions and discussion Andreas Groth, ENS, Paris Natural disasters (2) on a dynamic economy PIK seminar 2 / 36

49 U.S. business cycles 12 (a) Real GDP in million U.S. Dollar (b) Trend deviations Around a longterm trend we observe short-terms fluctuations Short-term fluctuations are referred to as business cyles Year U.S. macroeconomic data from the Bureau of Economic Analysis (BEA); detrended with Hodrick-Prescott filter (λ = 16) Andreas Groth, ENS, Paris Natural disasters (21) on a dynamic economy PIK seminar 21 / 36

50 U.S. business cycles Vertical lines Recession dates provided by the National Bureau of Economic Research (NBER) Andreas Groth, ENS, Paris Natural disasters (22) on a dynamic economy PIK seminar 22 / 36

51 U.S. business cycles Recession U.S. National Bureau of Economic Research (NBER) provides the following definition: [... ] significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales. Consider comovements as well as lead/lag structure Vertical lines Recession dates provided by the National Bureau of Economic Research (NBER) Andreas Groth, ENS, Paris Natural disasters (22) on a dynamic economy PIK seminar 22 / 36

52 U.S. business cycles Two competing business cycle theories Exogenous Exogenous (real) shocks yield to fluctuations of a system in equilibrium Real business cycle theory Endogenous Intrinsic dynamics and instability yields non-equilibrium (cyclical) behavior Endogenous business cycle theory Vertical lines Recession dates provided by the National Bureau of Economic Research (NBER) Andreas Groth, ENS, Paris Natural disasters (22) on a dynamic economy PIK seminar 22 / 36

53 U.S. business cycles - Non-equilibrium dynamical model (NEDyM) Production Investment flexibility Γ inv.5 Employment rate a.u. Real wage Price Investment Time in years Production losses (% GDP) α inv Production cycle Time lag (years) Production losses Production (arbitrary units) Time lag (years) Neoclassical model with adjustment delays (Hallegatte et al., 28; Hallegatte&Ghil, 28) Andreas Groth, ENS, Paris Natural disasters (23) on a dynamic economy PIK seminar 23 / 36

54 Endogenous dynamics vs. stochastic fluctuations Problem Time series are short with high stochasticity Only a single realization is available GDP Andreas Groth, ENS, Paris Natural disasters (24) on a dynamic economy PIK seminar 24 / 36

55 Endogenous dynamics vs. stochastic fluctuations Problem Time series are short with high stochasticity Only a single realization is available GDP Random walk Andreas Groth, ENS, Paris Natural disasters (24) on a dynamic economy PIK seminar 24 / 36

56 Endogenous dynamics vs. stochastic fluctuations SSA of GDP alone M-SSA of multiple aggregates (Groth, Ghil, Hallegatte & Dumas, FEEM working paper ; JBCMA in revision) Andreas Groth, ENS, Paris Natural disasters (25) on a dynamic economy PIK seminar 25 / 36

57 Endogenous dynamics vs. stochastic fluctuations SSA of GDP alone M-SSA of multiple aggregates (Groth, Ghil, Hallegatte & Dumas, FEEM working paper ; JBCMA in revision) Andreas Groth, ENS, Paris Natural disasters (25) on a dynamic economy PIK seminar 25 / 36

58 Endogenous dynamics vs. stochastic fluctuations SSA of GDP alone M-SSA of multiple aggregates Business cycles are a multivariate phenomenon not limited to GDP variations, but involves all aspects of the economy in particular reflected in the comovements M-SSA greatly helps to extract regular behavior (Groth, Ghil, Hallegatte & Dumas, FEEM working paper ; JBCMA in revision) Andreas Groth, ENS, Paris Natural disasters (25) on a dynamic economy PIK seminar 25 / 36

59 Reconstruction of phase-dependent fluctuations.2 Reconstruction (a) GDP and reconstruction with M SSA RCs (b) Local variance fraction of M SSA PCs (c) Local variance fraction of M SSA PCs (d) Local variance fraction of PCA PCs Andreas Groth, ENS, Paris Natural disasters (26) on a dynamic economy PIK seminar 26 / 36

60 Reconstruction of phase-dependent fluctuations.2 Reconstruction (a) GDP and reconstruction with M SSA RCs (b) Local variance fraction of M SSA PCs 1 2 (c) Local variance fraction of M SSA PCs 3 15 (d) Local variance fraction of PCA PCs 1 2 Phase-dependent volatility Recession phase dominated by five-year mode Expansion phase exhibits more complex dynamics, with other modes coming into play In agreement with NEDyM-model predictions Groth, Dumas, Ghil and Hallegatte (213), Impacts of natural disasters on a dynamic economy, in Extreme Events : Observations, Modeling, and Economics, AGU book Andreas series, Groth, inens, press Paris Natural disasters (26) on a dynamic economy PIK seminar 26 / 36

61 Outline 1 Singular spectrum analysis 2 Macroeconomic activity business cycles 3 International business cycles 4 Oscillatory climate modes 5 Conclusions and discussion Andreas Groth, ENS, Paris Natural disasters (27) on a dynamic economy PIK seminar 27 / 36

62 International business cycles... not only a U.S. phenomenon Participation index (relative) x x x x x RCs 1 2 RCs 1 2 United States τ =. yr United Kingdom τ =. yr Portugal τ = 1. yr Netherlands τ = 1. yr Italy τ = 1. yr 2 2 x 11 France τ =. yr 2 x x China τ = 1. yr Canada τ =. yr Andreas Groth, ENS, Paris Natural disasters (28) on a dynamic economy PIK seminar 28 / 36

63 International business cycles Different clusters Participation index (relative) x x x x x RCs 3 4 United States τ =. yr United Kingdom τ = 1. yr Portugal τ = 1. yr Netherlands τ =. yr Italy τ = 2. yr 2 2 x 11 France τ =. yr 2 x x China τ =. yr Canada τ = 1. yr Andreas Groth, ENS, Paris Natural disasters (29) on a dynamic economy PIK seminar 29 / 36

64 International business cycles Cluster linked to China Relative participation index x x x x x RCs 5 6 RCs 5 6 United States τ =. yr United Kingdom τ =. yr Portugal τ = 2. yr Netherlands τ = 1. yr Italy τ = 1. yr 2 2 x 11 France τ = 2. yr 2 x x China τ = 2. yr Canada τ =. yr Andreas Groth, ENS, Paris Natural disasters (3) on a dynamic economy PIK seminar 3 / 36

65 International business cycles Reconstruction with leading modes x United States 2 x 1 1 United Kingdom 2 2 x 1 9 Portugal 2 2 x 1 9 Netherlands 5 5 x Italy 2 2 x 11 France 2 x China x 1 1 Canada Local variance fraction PCs 1 2 PCs 3 4 PCs Andreas Groth, ENS, Paris Natural disasters (31) on a dynamic economy PIK seminar 31 / 36

66 International business cycles Presence of genuinely oscillatory albeit not purely periodic modes, which are pervasive in many aggregates and countries Presence of endogenous business cycle dynamics changes and complicates the response to exogenous shocks and the dynamics of reconstruction Overall cost of a natural disaster might depend on the preexisting economic situation There is no isolated, closed country or region Andreas Groth, ENS, Paris Natural disasters (32) on a dynamic economy PIK seminar 32 / 36

67 Outline 1 Singular spectrum analysis 2 Macroeconomic activity business cycles 3 International business cycles 4 Oscillatory climate modes 5 Conclusions and discussion Andreas Groth, ENS, Paris Natural disasters (33) on a dynamic economy PIK seminar 33 / 36

68 Oscillatory climate modes - Interannual oscillations SOI NAO Core monsoon NAO (a) (a) Power.2.1 Power.2.1 RC 1 2 RC 3 4 RC Frequency (cycles/year) (b).1.1 (c).1.1 (d).1 7.8yr τ = 3.8yr ε =.2 5.8yr τ = 1.9yr ε =.6 3.6yr τ =.5yr ε = Frequency (cycles/year) (b) 7.7yr τ = 3.3yr ε = (c).1 SOI NAO Andreas Groth, ENS, Paris Year Natural disasters (34) on a dynamic economy PIK seminar 34 / 36 RC 1 2 RC yr τ =.1yr ε =.9 Core NAO Year (Feliks, Groth, Ghil, Robertson, submitted)

69 Conclusions and discussion Implications on climate impact assessment and research What is a disaster? Cost of a disaster? Baseline scenario in the absence of disaster vs. actual trajectory with disaster impact (Hallegatte&Przyluski, The economics of natural disasters, 21) Multitude of different shocks that are not isolated in time; permanently forced system Fluctuation-Dissipation system in near equilibrium reacts in the same way to internal and external shocks Coexistance of economic and climate dynamic complicates the problem and needs much better understanding (of interactions) SSA appears to be a powerful tool in identifying mechanisms that operate in various frequency bands and spatial configurations Andreas Groth, ENS, Paris Natural disasters (35) on a dynamic economy PIK seminar 35 / 36

70 References Related work: Groth & Ghil (211): Multivariate singular spectrum analysis and the road to phase synchronisation, Physical Review E, 84, 3626 Groth, Ghil, Hallegatte & Dumas (212): The role of oscillatory modes in the U.S. business cycle, FEEM working paper, ; JBCMA, in revision Groth, Dumas, Ghil & Hallegatte (213): Impacts of natural disasters on a dynamic economy, in Extreme Events : Observations, Modeling, and Economics, AGU book Dumas, Ghil, Groth & Hallegatte (212): Dynamic coupling of the climate and macroeconomic systems, Math. & Sci. hum. / Mathematics and Social Sciences Feliks, Groth, Ghil & Robertson: Oscillatory Climate Modes in the Indian Monsoon, North Atlantic and Tropical Pacific, Journal of Climate, submitted SSA review: Ghil et al. (22): Advanced spectral methods for climatic time series, Reviews of Geophysics, 4(1), Allen & Smith (1996): Monte Carlo SSA: Detecting irregular oscillations in the Presence of Colored Noise. Journal of Climate, 1996, 9, Broomhead & King (1986a): Extracting qualitative dynamics from experimental data, Physica D, 2(2-3), Broomhead & King (1986b): On the qualitative analysis of experimental dynamical systems, in Nonlinear Phenomena and Chaos, ed. by S. Sarkar, pp Adam Hilger, Bristol, England. Ghil & Vautard (1991): Interdecadal oscillations and the warming trend in global temperature time series, Nature, 35(6316), Plaut & Vautard (1994): Spells of Low-Frequency Oscillations and Weather Regimes in the Northern Hemisphere, Journal of the Atmospheric Sciences, 51(2), Vautard & Ghil (1989): Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series, Physica D, 35(3), Vautard, Yiou & Ghil (1992): Singular-spectrum analysis: A toolkit for short, noisy chaotic signals, Physica D, 58, Andreas Groth, ENS, Paris Natural disasters (36) on a dynamic economy PIK seminar 36 / 36