Intro
Preface
Contents
1 Time Series Concepts and Python
1.1 The Concept of Time Series
1.1.1 What Is Time Series
1.1.2 Brief History of Time Series Analysis
1.1.3 Objectives of Time Series Analysis
1.2 The Programming Language Python
1.2.1 Introduction and Installing
1.2.2 Demonstrations
1.2.3 Python Extension Packages and Some Usages
1.3 Time Series Moment Functions and Stationarity
1.3.1 Moment Functions
1.3.2 Stationarity and Ergodicity
1.3.3 Sample Autocorrelation Function
1.3.4 White Noise and Random Walk

1.4 Time Series Data Visualization
Problems
2 Exploratory Time Series Data Analysis
2.1 Partial Autocorrelation Functions
2.1.1 Definition of PACF
2.1.2 Sample PACF and PACF Plot
2.2 White Noise Test
2.3 Simple Time Series Compositions
2.4 Time Series Decomposition and Smoothing
2.4.1 Deterministic Components and Decomposition Models
2.4.2 Decomposition and Smoothing Methods
2.4.3 Example
Problems
3 Stationary Time Series Models
3.1 Backshift Operator, Differencing, and Stationarity Test
3.1.1 Backshift Operator
3.1.2 Differencing and Stationarity

3.1.3 KPSS Stationarity Test
3.2 Moving Average Models
3.2.1 Definition of Moving Average Models
3.2.2 Properties of MA Models
3.2.3 Invertibility
3.3 Autoregressive Models
3.3.1 Definition of Autoregressive Models
3.3.2 Durbin-Levinson Recursion Algorithm
3.3.3 Properties of Autoregressive Models
3.3.4 Stationarity and Causality of AR Models
3.4 Autoregressive Moving Average Models
3.4.1 Definitions
3.4.2 Properties of ARMA Models
Problems
4 ARMA and ARIMA Modeling and Forecasting
4.1 Model Building Problems
4.2 Estimation Methods

4.2.1 The Innovations Algorithm
4.2.2 Method of Moments
4.2.3 Method of Conditional Least Squares
4.2.4 Method of Maximum Likelihood
4.3 Order Determination
4.4 Diagnosis of Models
4.5 Forecasting
4.6 Examples
Problems
5 Nonstationary Time Series Models
5.1 The Box-Jenkins Method
5.1.1 Seasonal Differencing
5.1.2 SARIMA Models
5.2 SARIMA Model Building
5.2.1 General Idea
5.2.2 Case Studies
5.3 REGARMA Models
Problems
6 Financial Time Series and Related Models
6.1 Stylized Facts of Financial Time Series
6.1.1 Examples of Return Series

6.1.2 Stylized Facts of Financial Time Series
6.2 GARCH Models
6.2.1 ARCH Models
6.2.2 GARCH Models
6.2.3 Estimation and Testing
6.2.4 Examples
6.3 Other Extensions
6.3.1 EGARCH Models
6.3.2 TGARCH Models
6.3.3 An Example
Problems
7 Multivariate Time Series Analysis
7.1 Basic Concepts
7.1.1 Covariance and Correlation Matrix Functions
7.1.2 Stationarity and Vector White Noise
7.1.3 Sample Covariance and Correlation Matrices
7.1.4 Multivariate Portmanteau Test
7.2 VARMA Models
7.2.1 Definitions
7.2.2 Properties