Lecture Note of Econophyscs

Jinshan Wu

Sept, 2002

Abstract:

Econophysics means to apply physics into economical phenomena. Its objects include stock price, exchange rate, size of firms, income and wealth, economy growth and technology development, and production chain. It aims to reveal the stylized facts or universal statistical properties, including distribution, autocorrelation, and fluctuation etc, and to analyze the mechanism behind by incorporating idea, concepts and technics from Physics. In this note, the author summarized recent development of Econophysics in data analysis and modelling, and presented some required knowledge from Math and Physics as theoretical foundation.

Introduction
Theoretical Foundation
- Probability Theory and Stochastic Process
  - Guassian Distribution and Lévy Distribution Central Limit Theorem
  - Statistics for Extreme Value and Fisher-Tippett Limit Theorem
  - Introduction to Random Matrix Theory
  - Basic Stochastic Processes and Time Series Models
- Statistical Physics--Framework, Technics and Models
  - $\Gamma$ Space, Distribution Function and Master Equation -- Shown by Ising Model
  - Aggregation and Annihilation Reaction and Rate Equation
  - Fokker-Planck Equation for Distribution Function
  - Phase Transition, Critical Phenomena, Scaling Laws and Renormalization Group Theory -- Shown by Ising Model and Percolation
Data Analysis
- Before Statistical Analysis
- Stock Price and Exchange Rate
  - For high and low frequency data of stock price
  - For Bid-Ask and order book data
- Size of Firms
- Wealth and income
- Networks for Economy systems
  - Trade web
  - Production chain
Reference Models
- Spin System and Critical Phenomena
- Self-Organized Criticality (SOC)
- Cellular Automata
- Aggregation--Annihilation Reaction
- Time Series Models in Econometrics
Why is it Econophysics?
Power Law
- Phenomenon Emergent from Different Systems
- Mechanism, really?
Resource online
Acknowledgment
Bibliography

This note was used by Jinshan Wu in his lecture of Econophysics in Beijing Normal University during Fall 2002.

经济物理学讲义

吴金闪

九月, 2002

摘要：

所谓经济物理学（Econophysics）是指用物理学的方法对经济现象所进行的研究。其对象是股票价格与汇率，企业销售规模，以及收入与财富分布等数据。研究其典型统计性质，包括分布形式，时间关联性，发掘数据的一些普适性特征与标度行为，并且借鉴统计物理学的方法与模型，研究其普适特征的形成机制。本文从理论基础、数据分析和模型三个方面对经济物理学的部分研究进行了总结整理。

引言
理论基础
- 概率论与随机过程
  - 高斯分布与Lévy分布中心极限定理
  - 极值统计学与Fisher-Tippett极限定理
  - 随机矩阵理论简介
  - 随机过程的基本概念与时间序列模型
- 统计物理学--框架、方法与模型
  - $\Gamma$ 空间，分布函数与Master方程--以Ising模型为例
  - 集聚消灭反应及其平均场方程
  - 分布函数演化的Fokker-Planck方程
  - 相变，临界现象，标度律与重整化群--以Ising模型与渗流模型为例
数据分析
- 统计分析的前提
- 股票价格与汇率的变化
  - 高频与低频时间序列纪录
  - 交易与报价数据
- 企业规模及增长率
- 个人财富，货币持有量，股票持有量
- 经济现象的网络分析
  - 贸易网络
  - 产业链
- 模型
  - 自旋模型与临界现象
  - 自组织临界性
  - 元胞自动机
  - 集聚-消灭反应
  - 计量模型与其他随机过程模型
- 为什么是经济物理学
- 幂律（Power Law）--现象与机理？
  - 各种各样的幂律分布
  - 机理--一个有待解决的问题
- 相关网络资源
- 致谢
- 参考文献
本讲义为吴金闪于2002年秋季在北京师范大学开设经济物理学课程所用。