Intro
Preface
Contents
1 Introduction
1.1 What Is Time Series Analysis?
1.2 Two Approaches in Time Series Analysis
1.3 Use of R
1.3.1 Library in R and External Software
1.3.2 Code and Data in This Book
1.4 Notation in This Book
References
2 Fundamentals of Probability and Statistics
2.1 Probability
2.2 Mean and Variance
2.3 Normal Distribution
2.4 Relation Among Multiple Random Variables
2.5 Stochastic Process
2.6 Covariance and Correlation
2.7 Stationary and Nonstationary Processes

2.8 Maximum Likelihood Estimation and Bayesian Estimation
References
3 Fundamentals of Handling Time Series Data with R
3.1 Object for Handling Time Series
3.2 Handling of Time Information
Reference
4 Quick Tour of Time Series Analysis
4.1 Confirmation of the Purpose and Data Collection
4.2 Preliminary Examination of Data
4.2.1 Plot with Horizontal Axis as Time
4.2.2 Histogram and Five-Number Summary
4.2.3 Autocorrelation Coefficient
4.2.4 Frequency Spectrum
4.3 Model Definition
4.4 Specification of Parameter Values

4.5 Execution of Filtering, Prediction, and Smoothing
4.6 Diagnostic Checking for the Results
4.7 Guideline When Applying the State-Space Model
References
5 State-Space Model
5.1 Stochastic Model
5.2 Definition of State-Space Model
5.2.1 Representation by Graphical Model
5.2.2 Representation by Probability Distribution
5.2.3 Representation by Equation
5.2.4 Joint Distribution of State-Space Model
5.3 Features of State-Space Model
5.4 Classification of State-Space Models
References
6 State Estimation in the State-Space Model

6.1 State Estimation Through the Posterior Distribution
6.2 How to Obtain the State Sequentially
6.2.1 A Simple Example
6.2.2 Conceptual Diagram of Recursion
6.2.3 Formulation of Filtering Distribution
6.2.4 Formulation of Predictive Distribution
6.2.5 Formulation of the Smoothing Distribution
6.3 Likelihood and Model Selection in the State-Space Model
6.4 Treatment of Parameters in the State-Space Model
6.4.1 When Parameters are Not Regarded as Random Variables
6.4.2 When Parameters are Regarded as Random Variables
References

7 Batch Solution for Linear Gaussian State-Space Model
7.1 Wiener Filter
7.1.1 Wiener Smoothing
7.2 Example: AR(1) Model Case
References
8 Sequential Solution for Linear Gaussian State-Space Model
8.1 Kalman Filter
8.1.1 Kalman Filtering
8.1.2 Kalman Prediction
8.1.3 Kalman Smoothing
8.2 Example: Local-level Model Case
8.2.1 Confirmation of the Purpose and Data Collection
8.2.2 Preliminary Examination of Data
8.2.3 Model Definition
8.2.4 Specification of Parameter Values
8.2.5 Execution of Filtering, Prediction, and Smoothing