0. Intro & Reference

학부 시절 수강한 금융시계열분석 과목의 경험을 되살리고, 여러 교재들을 참고하여 다시 내용을 정리하고자 한다. 우수하지도 나쁘지도 않은 성적이었기에(A0였나 A-였나) 내용이 기억이 잘 나지 않지만.

 

주교재는 Ruey S. Tsay - Analysis of Financial Time Series(2010, 3ed.)였고, 요로코롬 생겼다.

 

현재 국내 서점에서는 7만 5천원에(...) 만나볼 수 있다. 내가 수강했을 당시에는 중고나라를 뒤적거렸던 기억이...

 

초판은 2003년에 발매되었다. 특히 빠르게 변하는 금융시장에서 2003년이면(심지어 글로벌 금융위기 이전) outdated 되었다고 느껴지지만, 그래도 현재 금융이론의 기반이 되는 다양한 이론들을 포함한다.

 

목차는 아래와 같다. 

목차

Financial Time Series and Their Characteristics

Asset Returns

Distributional Properties of Returns

Processes Considered

Linear time series

Stationarity

Autocorrelation

Linear time series

Simple AR models

Simple MA models

Simple ARMA Models

Unit-Root Nonstationarity

Seasonal Models

Regression with Correlated Errors

Consistent Covariance Matrix Estimation

Long-Memory Models

Volatility models

Characteristics of Volatility

Structure of a Model

Model Building

Testing for ARCH Effect

The ARCH Model

The GARCH Model

The Integrated GARCH Model

The GARCH-M Model

The Exponential GARCH Model

The Threshold GARCH Model

The CHARMA Model

Random Coefficient Autoregressive Models

The Stochastic Volatility Model

The Long-Memory Stochastic Volatility Model

Application

Alternative Approaches

Kurtosis of GARCH Models

Nonlinear Models and Their Applications

Nonlinear Models

Modeling

Forecasting

Application

High-Frequency Data Analysis and Market Microstructure

Nonsynchronous Trading

Bid-Ask Spread

Empirical Characteristics of Transactions Data

Models for Price Changes

Duration Models

Nonlinear Duration Models

Bivariate Models for Price Change and Duration

Application

Continuous-Time Models and Their Applications

Options

Some Continuous-Time Stochastic Processes

Ito's Lemma

Distributions of Price and Return

Black-Scholes Equation

Black-Scholes Pricing Formulas

An Extension of Ito's Lemma

Stochastic Integral

Jump Diffusion Models

Estimation of Continuous-Time Models

Extreme Values, Quantiles, and Value at Risk

Value at Risk

RiskMetrics

An Econometric Approach to VaR Calculation

Quantile Estimation

Extreme Value Theory

Extreme Value Approach to VaR

A New Approach to VaR

The Extremal Index

Multivariate Time Series Analysis and Its Applications

Weak Stationarity and Cross-Correlation Matrices

Vector Autoregressive Models

Vector Moving-Average Models

Vector ARMA Models

Unit-Root Nonstationarity and Cointegration

Cointegrated VAR Models

Threshold Cointegration and Arbitrage

Pairs Trading

Principal Component Analysis and Factor Models

A Factor Model

Macroeconometric Factor Models

Fundamental Factor Models

Principal Component Analysis

Statistical Factor Analysis

Asymptotic Principal Component Analysis

Multivariate Volatility Models and Their Applications

Exponentially Weighted Estimate

Some Multivariate GARCH Models

Reparameterization

GARCH Models for Bivariate Returns

Higher Dimensional Volatility Models

Factor-Volatility Models

Application

Multivariate t Distribution

State-Space Models and Kalman Filter

Local Trend Model

Linear State-Space Models

Model Transformation

Kalman Filter and Smoothing

Missing Values

Forecasting

Application

Markov Chain Monte Carlo Methods with Applications

Markov Chain Simulation

Gibbs Sampling

Bayesian Inference

Alternative Algorithm

Linear Regression With Time Series Errors

Missing Values and Outliers

Stochastic Volatility Models

A New Approach to SV Estimation

Markov Switching Models

Forecasting

Other Applications

 

학부에서는 EGARCH Model까지 배운 것으로 기억하는데, 이 내용들은 당연히 다루고 이후에도 중요한 이토의 보조정리(Ito's lemma), 블랙숄즈 방정식(Black-Scholes Equation), VaR(Value at Risk), 벡터자기회귀(VAR), 공적분(Cointegration) 등을 다루어볼 예정이다. (cf. VaR과 VAR은 전혀 다른 개념이다.) 대부분의 notation은 위 교재를 따르며, 그렇지 않을 경우 따로 표기한다.

 

부교재

Helmut Lütkepohl - New Introduction To Multiple Time Series Analysis(2006)

Box, Jenkins, Reinsel, Ljung - Time Series Analysis Forecasting and Control(2015)