Introduction to
Economic Physics
•
Ping Chen
• Ilya Prigogine Center for Studies in Statistical Mechanics & Complex Systems
University of Texas at Austin and
• China Center for Economic research Peking University
History of Economic Physics
• Bernoulli (1700) – St.Petersburrg Paradox: nonlinear utility function
• Bachelier (1900) – stochastic model of bond prices
• Samuelson (1939) – multiplier-accelerator model
• Von Neumann (1948) – expected utility function & game theory
• Osborne (1959) – Brownian motion of
stock price changes
• Mandelbrot(1963) – Levy distribution of
cotton price changes
Sources of Economic Complexity
Non-Stationarity (Copernicus Problem?)Long/Short Run
Open System (No Conservation Law):
Dissipative System (Bio)/ Hamiltonian (Micro)
Dynamical Competition/Static Optimization
Nonlinearity (Non-Integrable System):
Non-Parametric/Parametric Regression in Econometrics
Many Variables: Statistical Mechanics/Representative (One-Body)
Noisy Data: Chaos/Noise, Endogenous/Exogenous
Rapid Changes: Evolutionary/Stationary
Players & Observers: Interactive/Independent
Linear Demand & Supply Curve >
Unique Stable Equilibrium >
Nonlinear Demand & Supply >
Deterministic
and
Stochastic
(
Probabilistic
) Representation:
Basis of Life in
Quantum Biology
:
Meta-Stable State
Ilya Prigogine
:
Order
Out of
Chaos
(1984)
Equilibrium order
in
closed system
vs.
How to analyze
non-stationary
&
noisy
economic time series?
•
Copernicus problem
in macro & financial
economics > find a
proper observation
referenc
e >
•
Decompose into
Trend
+
Cycles
•
Investment decision > proper time window
•
Short > random noise (equilibrium illusion)
•
Medium > trend + persistent cycles
Trend-Cycle Decomposition for FSPCOM
(S&P 500) Monthly Index
1 9 5 0 1 9 5 5 1 9 6 0 1 9 6 5 1 9 7 0 1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 2 . 5
3 3 . 5 4 4 . 5 5 5 . 5 6 6 . 5
FD Series, HP and LL Cycles
1 9 5 0 1 9 5 5 1 9 6 0 1 9 6 5 1 9 7 0 1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0 -0 . 4
-0 . 2 0 0 . 2 0 . 4 0 . 6
Auto-Correlations of FDs, HPc, and LLc
0 2 0 4 0 6 0 8 0 1 0 0 -1
-0 . 5 0 0 . 5 1
Detrending Statistics for FSPCOM
(S&P 500) Monthly
Detrending Mean STD Variance T0 (month) Pdc (year)
---
FD 0.061 0.0338 0.0011 1.94 0.6
HP 0.000 0.0752 0.0057 8.94 3.0
LL 0.000 0.2456 0.0603 85.6 28.5
An Information Illusion of
“The Efficient Market”
The FD (First Differencing) Filter
FD[F(t)] = F(t+1)-F(t)
A Sine signal with unitary energy:
Frequency Response Function
•
Frequency Response Function =
•
Average Energy =
R(f)= 2 2
|
)
sin(
|
1
|
)
(
|
X
t
f
A Whitening Filter in
Econometrics and Econophysics
0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5
Time-Frequency Range in
Empirical Analysis
•
Sampling Time Unit
D
t
•
Time Length TL=Pmax
•
Pmin=2
D
t
t
f
D
0
.
5
max
Time Scale in Economic Analysis
• High frequency data (1-10min)
– (Santa Fe approach and econophysics)
– Analyzing trading psychology (Intra-day)?
• Daily & Weekly data
– – Technical analysis of speculative traders
– (Days – Weeks)
• Monthly & quarterly data
– – Economic analysis
Stationary (Fourier Transform) versus
The Coherent State (Gaussian Packet, Gabor Wavelet)
The Uncertainty Principle in
Quantum Mechanics & Information Theory
Separating Signals with Noise
0 0.05 0.1 0.15 0.2 0.25 0.3 |C (n ,m )|1 3 5 7 9
n
Time Section of Gabor Distribution for F SPCOMln
C(n,m)
H=0
H=0.5
H=1
Time-Dependent Band-Pass Filter
5 10 15
5 10 15 20 25
M ask for FSPCOM (H=0.5)
m
Mountain (Deterministic Cycles) and
VAR(Sg)/VAR(S0) = 69%; Ccgo = 0.847
70 % of Signal Energy Is Deterministic Chaos
30% of Signal Energy Is White Noise
-4 -2 0 2 4
1945 1955 1965
S
(t
)
1975 1985 1995
t
FSPCOM Original & Filtered Cycles (H=0.5)
So
Correlation Dimension
of
Filtered HPc
=
2.5
Cross-Correlation =
0.94
-1 -0.5 0 0.5 1 0 A C (I )
20 40 60 80 100
I
FSPCOMln Original & Filtered HP Cycles
HPCg
HPCo
Natural Experiments and
Economic Diagnosis
• External Shock of Oil Price Shock
• Endogenous Instability of Stock Market Crash 1 9 6 5 1 9 7 0 1 9 7 5 1 9 8 0 1 9 8 5 1 9 9 0
0 5 1 0 1 5 2 0
Unlimited (Malthus-Exponential) and
Limited (Verhelst-Logistic) Growth
0 5 1 0 1 5 2 0
0 5 1 0 1 5 2 0 2 5 3 0
Why Over Investment and Excess Capacity?
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 0
Logistic Growth in
US Automobile Industry
1 9 0 0 1 9 1 0 1 9 2 0 1 9 3 0 1 9 4 0 1 9 5 0 1 9 6 0 1 9 7 0 0
