# Time Series Analysis and Forecasting by Example

## Books

An intuition-based approach enables you to master time series analysis with ease

Time Series Analysis and Forecasting by Example provides the fundamental techniques in time series analysis using various examples. By introducing necessary theory through examples that showcase the discussed topics, the authors successfully help readers develop an intuitive understanding of seemingly complicated time series models and their implications.

The book presents methodologies for time series analysis in a simplified, example-based approach. Using graphics, the authors discuss each presented example in detail and explain the relevant theory while also focusing on the interpretation of results in data analysis. Following a discussion of why autocorrelation is often observed when data is collected in time, subsequent chapters explore related topics, including:

• Graphical tools in time series analysis
• Procedures for developing stationary, non-stationary, and seasonal models
• How to choose the best time series model
• Constant term and cancellation of terms in ARIMA models
• Forecasting using transfer function-noise models

The final chapter is dedicated to key topics such as spurious relationships, autocorrelation in regression, and multiple time series. Throughout the book, real-world examples illustrate step-by-step procedures and instructions using statistical software packages such as SAS®, JMP, Minitab, SCA, and R. A related Web site features PowerPoint slides to accompany each chapter as well as the book's data sets.

With its extensive use of graphics and examples to explain key concepts, Time Series Analysis and Forecasting by Example is an excellent book for courses on time series analysis at the upper-undergraduate and graduate levels. it also serves as a valuable resource for practitioners and researchers who carry out data and time series analysis in the fields of engineering, business, and economics.

Preface xi

1. Time Series Data: Examples and Basic Concepts 1

1.1 Introduction 1

1.2 Examples of Time Series Data 1

1.3 Understanding Autocorrelation 10

1.4 The World Decomposition 12

1.5 The Impulse Response Function 14

1.6 Superposition Principle 15

1.7 Parsimonious Models 18

Exercises 19

2. Visualizing Time Series Data Structures: Graphical Tools 21

2.1 Introduction 21

2.2 Graphical Analysis of Time Series 22

2.3 Graph Terminology 23

2.4 Graphical Perception 24

2.5 Principles of Graph Construction 28

2.6 Aspect Ratio 30

2.7 Time Series Plots 34

Exercises 46

3. Stationary Models 47

3.1 Basics of Stationary Time Series Models 47

3.2 Autoregressive Moving Average (ARMA) Models 54

3.3 Stationary and Invertibility of ARMA Models 62

3.4 Checking for Stationary using Variogram 66

3.5 Transformation of Data 69

Exercises 73

4. Nonstationary Models 79

4.1 Introduction 79

4.2 Detecting Nonstationarity 79

4.3 Antoregressive Integrated Moving Average (ARIMA) Models 83

4.4 Forecasting using ARIMA Models 91

4.5 Example 2: Concentration Measurements from a Chemical Process 93

4.6 The EWMA Forecast 103

Exercises 104

5. Seasonal Models 111

5.1 Seasonal Data 111

5.2 Seasonal ARIMA Models 116

5.3 Forecasting using Seasonal ARIMA Models 124

5.4 Example 2: Company X’s Sales Data 126

Exercises 152

6. Time Series Model Selection 155

6.1 Introduction 155

6.2 Finding the “BEST” Model 155

6.3 Example: Internet Users Data 156

6.4 Model Selection Criteria 163

6.5 Impulse Response Function to Study the Differences in Models 166

6.6 Comparing Impulse Response Functions for Competing Models 169

6.7 ARIMA Models as Rational Approximations 170

6.8 AR Versus Arma Controversy 171

6.9 Final Thoughts on Model Selection 173

Appendix 6.1: How to Compute Impulse Response Functions with a Spreadsheet 173

Exercises 174

7. Additional Issues in ARIMA Models 177

7.1 Introduction 177

7.2 Linear Difference Equations 177

7.3 Eventual Forecast Function 183

7.4 Deterministic Trend Models 187

7.5 Yet Another Argument for Differencing 189

7.6 Constant Term in ARIMA Models 190

7.7 Cancellation of Terms in ARIMA Models 191

7.8 Stochastic Trend: Unit Root Nonstationary Processes 194

7.9 Overdifferencing and Underdifferencing 195

7.10 Missing Values in Time Series Data 197

Exercises 201

8. Transfer Function Models 203

8.1 Introduction 203

8.2 Studying Input-Output Relationships 203

8.3 Example 1: The Box-Jenkins’ Gas Furnace 204

8.4 Spurious Cross Correlations 207

8.5 Prewhitening 207

8.6 Identification of the Transfer Function 213

8.7 Modeling the Noise 215

8.8 The General Methodology for Transfer Function Models 222

8.9 Forecasting Using Transfer Function-Noise Models 224

8.10 Intervention Analysis 238

Exercises 261

9.1 Spurious Relationships 263

9.2 Autocorrelation in Regression 271

9.3 Process Regime Changes 278

9.4 Analysis of Multiple Time Series 285

9.5 Structural Analysis of Multiple Time Series 296

Exercises 310

Appendix A. Datasets Used in the Examples 311

Appendix B. Datasets Used in the Exercises 327

Bibliography 361

Index 365

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