http://www.complexeconomics.org/

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?????????

• ??
• ??????????? ????
• ???????????? ?????
• http//www.complexeconomics.org/
• pchen_at_nsd.pku.edu.cn
• ????????? ??
• 2013?11?21?

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?????????

• ???????? (Auguste Comte, 1798-1857 ) social
  physics ?????????(1856)?
• ?????????????????,????????(?????)????????(2012
  ???????),??? Ilya Prigogine ??,??????????(1987
  )???????????????(1989,?? 2004)
• ????????????H. Eugene Stanley (1995)?power law
  ?????????????? econophysics,???????,??????????

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?????????????????

• ?????????????(Daniel Bernoulli
  1700-1782)gambling and utility function(1738)
• John von Neumann (1903-1957 ) game theory,
  growth model
• Ilya Prigogine (1917-2003) Brussletor gt BZ
  reactiongt dissipative structure, chemical
  reaction and population dynamics,
  self-organization(1971, 1977), complex systems
  (1987)
• Hermann Haken (1927- ) synergetics (1973),
  adiabatic approximation, laser gt Hamiltonian
  system
• Wolfgan Weidlich (1931- ) Ising model for
  public opinion, social dynamics
• Santa Fe Institute (SFI, 1984-), Philip Anderson
  (spin glass model), Murray Gell-mann (complex
  adaptive system), edge of chaos, artificial
  life,automata system,interacting agents

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?????????

• ????(???,???,???,??,???,????)?????????????????
• (1)????????????????????
• (2)??????????????????????????
• (3)????????????,???????????-????-?????
• ??????????????????

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???????????????????-??????

• ???????????????????
• ??????????????????????
•  
• ??????????????? - - FD vs. HP (von Neumann)
  filter
• ????????? Louis Bachelier (1900) ?Brownian motion
  ?? Schumpeter?????
• ????????????(???????)
•  

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?????????????????vs. ??(???)??

• ???????????
• ???,???,? wavelets
• Wigner transform, Gabor wavelet, and logistic
  wavelet
• ???? (business cycles) ????????????????
• Frisch model of noise driven harmonic cycles
  (1933), Harmonically bounded Brownian motion
  (Unlenbeck Orstein 1930, Unlenbeck Wang ???
  1945)

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??????????
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Math Representation in Frequency Domain

• Fourier spectrum E(f) for color cycle and white
  noise

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Spectrum E(f) of Harmonic Wave, White Noise, and
Color Noise (Chaos)

• Wave Noise

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Stationary (Discrete Fourier Transform)
vs.Non-Stationary (Joint-Time-Frequency
Analysis)Time Series Analysis ???,???(1994)
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SP500 Stock Price Index FSPCOM with log-linear
(LL) and HP growth trends
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Detrended cycles with varying lengths
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Different images of auto-correlations
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Uncertainty Principle in Signal Processing
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Gabor (Gaussian) Wavelet with Minimum Uncertainty
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Gabor Space (1946) in discrete time-frequency
space

• Minimum uncertainty in time-frequency space
• Un-orthogonal base function

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The Coherent State (Gaussian Packet, Gabor
Wavelet)The Uncertainty Principle in Quantum
Mechanics Information Theory
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Separating noise and signal in Gabor space

• Time section in Gabor space (signal peak is far
  above the noise level)
• Time-dependent band filter in time-frequency space

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Separating signals and noise in Gabor
(time-frequency) space
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Phase portraits of HP cyclesWhite noise vs.
color chaos
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Stock Price Indexes (Standard Poor
500)correlation dimension of color chaos in
2.5variance of color chaos 69
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Structural instability of linear dynamical models
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Structural Stability (Resilience) and Regime
Switch in Nonlinear Dynamics
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Linear Demand-Supply Curves gt Unique Equilibrium
???????????????
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??????????????

• ????????????????
• ??????
• Frisch ?????????(1933)
• Friedman ?????Lucas ????????????(RBC)??Bernank
  e ???????
• ?????????????????????(???)??

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??????? ???? ????????????????
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Noise-Driven Cycles( Frisch 1933)vs. Harmonic
Brownian Motion(Unlenbeck Orstein, 1930)

• Wang ??? Unlenbeck (1945)
• Frisch model for American business cycles,which
  would be damped in 5-20 years(Chen 1999,2004)!

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Frisch modelPerpetual Motion Machine of Second
Type?

• Frisch was not the FIRST G.E.Uhlenbeck and L.S.
  Ornstein, "On the Theory of Brownian Motion,"
  Physical Review, 36(3), 823-841 (1930).
• Frischs Informal conference paper R. Frisch,
  Propagation Problems and Impulse Problems in
  Dynamic Economics, in Economic Essays in Honour
  of Gustav Cassel, George Allen Unwin, London
  (1933).
• Frisch's promised paper, "Changing harmonics
  studied from the point of view of linear
  operators and erratic shocks," was advertised
  three times under the category "papers to appear
  in early issues" in Econometrica, including Issue
  No. 2, 3, and 4 of Volume I (April, July, and
  October 1933) but never appeared in Econometrica
  since 1934.
• Frisch never mentioned a word about his
  prize-winning model in his Nobel speech in 1969
  (Frisch 1981).

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Equilibrium Illusion through First-Differencing
(High Frequency Noise Amplifier Whitening
Filter) in Econometric Analysis????????????????
???

• Frequency response for the FD filter
• X(t) FDS(t)S(t1)-S(t)

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????????

• ?????????????
• ??,??,???????????????????(Lotka-Volterra ??)
• ???????? ???????????????(????)??????(??????????
  ?)
• ??????-??(?????)-?????

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??????????????(????)?????????

• Principle of Large Numbers
• ?????????????????? (resilience) ?
• ???????????????????
• relative deviation (RD) ?birth and death process
•  

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Principle of Large Numbers for Positive Variables

• SNX1X2 . . . . . . XN
• Observed relative deviation of US real GDP is 20
  times larger than Lucas model(Chen 2002)!

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Relative Deviation (RD) and the Implied Number
(N) from Empirical Observation

• Relative deviation
• Implied number

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Large Numbers in US Economy
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Weak microfoundations in labor and producer
market

• The observed implied numbers predicted by the
  Lucas model is 400 500 times smaller (RD is 20
  times larger ) than in US real economy.
• Possible microfoundations
• in financial markets and industrial organization
• not in labor or producer market
• Implication gt
• Three layer structure (micro, meso, macro)
• rather than two layer structure (micro, macro)
• in economies

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Implications from the Failure of Lucas Model of
Microfoundations

• Roots of persistent business cycles
• Financial intermediates and industrial
  organization
• From two layer model (micro-macro) gt
• Three layer model (micro-meso-macro)
• Nature of macro fluctuations gt social movements

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Stable RD in US Macro Indexesobserved under HP
filter
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RD Behavior for Stochastic Models

• Random walk is damping over time
• Brownian motion is exploding over time
• Only the Birth-death process is stable in time,
  which is a statistical model of endogenous
  fluctuations

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Economic diagnosis
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?????????????????????

• ?????????
• Fat tail distribution (Levy, fractal Brownian
  motion, power law),
• regime switch between calm and turbulent market
• ???,????????,??????????
•  

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Linear (BS) Empirical (SP 500) Transition
Probability in Birth-Death Process from SP data
(Tang Chen 2010)
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Higher Moment Deviations (System Risk) during
Crisis (4-5th Moments are 1000 times larger than
2nd Moment gt Failure of Portforlio
Diversification)
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Source of Financial InstabilityNonlinear Trend
Higher Moments in Birth-Death Process

• Option pricing model based on nonlinear
  birth-death process
• Stability condition
• Under stability finite first second moment
  Ito construct arbitrage portfolio
  Black-Scholes model

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Corrections of Option Pricing Model for
Interacting Trend Diffusion

• No such thing as risk-free interest rate gt only
  exist moving trend in interest rate
• Multiple frequency co-exist in financial market gt
  interacting between market trend group players
  gt complex dynamics

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??????,??????,????????

• ?????, Wallerstein paradox, ?????????
• Lotka-Volterra model with culture factor
• Logistic wavelets ?????????
• ????????trade-off ???????????
• ?????????????????????????????

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Metabolic Growth (Life Cycles)
???????????????????
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Physics Foundation of Biology

• Schrödinger (1948) What is life? (Quantum
  biology)
• Large molecule, meta-stable state, non-periodic
  structure, information as negative entropy
• Prigogine (1972) Thermodynamics of evolution
• Dissipative structure with matter flow, energy
  flow, and information flow in open system
• Constructive role of positive feedback (catalytic
  reaction)
• Self-organization (order out of chaos)

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????????????Haken vs. Prigogine

• Haken synergetics ???
• Laser Hamiltonian system
• Adiabetic approximation gt take out slow variables
  (language)
• Prigogine dissipative systems no potential
  function slef-organization ???
• Chemical reaction population dynamics
  nonlinear evolutionary dynamics nonlinear
  economic dynamics

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???????????

• ??????????????
• ????????????
• ?????????? ???????,
• ???????????????? ????????,GDP ???????

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References

• ??, ????, ????, ????????, ??????? (2004).
• Chen, Ping. Economic Complexity and Equilibrium
  Illusion, Routledge, London (2010).

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Readings in Complexity Science

• Wienner, N. Cybernetics or Control and
  Communication in the Animal and the Machine, MIT
  Press, MA Cambridge (1948).
• Schrödinger, E. What is Life? Cambridge
  University Press, Cambridge (1948).
• Prigogine, I. From Being to Becoming Time and
  Complexity in the Physical Sciences, Freeman, San
  Francisco (1980).
• May, R. M., Stability and Complexity in Model
  Ecosystem, Princeton University Press, Princeton
  (1974).