This textbook presents methods and techniques for time series analysis and forecasting and shows how to use Python to implement them and solve data science problems. It covers not only common statistical approaches and time series models, including ARMA, SARIMA, VAR, GARCH and state space and Markov switching models for (non)stationary, multivariate and financial time series, but also modern machine learning procedures and challenges for time series forecasting. Providing an organic combination of the principles of time series analysis and Python programming, it enables the reader to study methods and techniques and practice writing and running Python code at the same time. Its data-driven approach to analyzing and modeling time series data helps new learners to visualize and interpret both the raw data and its computed results. Primarily intended for students of statistics, economics and data science with an undergraduate knowledge of probability and statistics, the book will equally appeal to industry professionals in the fields of artificial intelligence and data science, and anyone interested in using Python to solve time series problems.
Author(s): Changquan Huang, Alla Petukhina
Series: Statistics and Computing
Publisher: Springer
Year: 2022
Language: English
Pages: 376
City: Cham
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
7.3 VAR Model Building and Analysis
7.3.1 VAR(1) Representation of VARMA Processes
7.3.2 VAR Model Building Steps
7.3.3 Granger Causality
7.3.4 Impulse Response Analysis
7.4 Examples
Problems
8 State Space Models and Markov Switching Models
8.1 State Space Models and Representations
8.1.1 State Space Models
8.1.2 State Space Representations of Time Series
8.2 Kalman Recursions
8.3 Local-Level Model and SARIMAX Models
8.3.1 Local-Level Model
8.3.2 SARIMAX Models
8.4 Markov Switching Models
8.4.1 Definitions
8.4.2 Examples
Problems
9 Nonstationarity and Cointegrations
9.1 Stochastic Trend and Stochastic Seasonality
9.1.1 Deterministic Trend and Stochastic Trend
9.1.2 Deterministic Seasonality and Stochastic Seasonality
9.2 Brownian Motions and Simulation
9.2.1 Probability Space
9.2.2 Brownian Motions
9.3 Stationarity, Nonstationarity, and Unit Root Tests
9.3.1 Trend Stationarity and Difference Stationarity
9.3.2 Unit Root Tests
9.3.3 Stationarity Tests
9.4 Cointegrations and Granger's Representation Theorem
9.4.1 Spurious Regressions and I(d) Processes
9.4.2 Cointegrations
9.4.3 Granger's Representation Theorem
9.4.4 Estimation of Vector Error Correction Models
9.4.5 Real Case of Spurious Regression and Noncointegration
Problems
10 Modern Machine Learning Methods for Time Series Analysis
10.1 Introduction
10.1.1 Brief History of Artificial Intelligence
10.1.2 AI in Time Series Analysis
10.2 Artificial Neural Networks
10.2.1 Artificial Neural Network Developments
10.2.2 Neural Network Models
10.3 Deep Learning and Backpropagation Algorithms
10.3.1 What Is Deep Learning?
10.3.2 Gradient Descent and Backpropagation Algorithms
10.4 Time Series Forecasting and TensorFlow
10.4.1 Time Series Forecasting
10.4.2 TensorFlow and Keras
10.5 Implementation and Example
10.5.1 Implementation Steps
10.5.2 An Example
10.6 Concluding Remarks
Problems
References
Index
