Time Series Analysis and Forecasting by Example (eBook)

The late Søren Bisgaard, PhD, was professor of technology management at the University of Massachusetts Amherst. Throughout his esteemed career, Dr. Bisgaard made significant research contributions in the areas of experimental design, operations management, time series analysis, and Lean Six Sigma. A Fellow of the American Statistical Association and the American Society for Quality, he was also one of the cofounders of the European Network for Business and Industrial Statistics (ESBIS) in 1999. Dr. Bisgaard was awarded many honors for his achievements in the field of statistics, including the Brumbaugh Award (1988, 1996, and 2008), the Shewhart Medal (2002), the William G. Hunter Award (2002), and the George Box Award (2004). Murat Kulahci, PhD, is Associate Professor of Statistics in the Department of Informatics and Mathematical Modeling at the Technical University of Denmark. He has authored or coauthored over forty journal articles in the areas of time series analysis, design of experiments, and statistical process control and monitoring. Dr. Kulahci is coauthor of Introduction to Time Series Analysis and Forecasting (Wiley).

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 Tools21

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

2.8 Bad Graphics 38

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) Models83

4.4 Forecasting using ARIMA Models 91

4.5 Example 2: Concentration Measurements from a ChemicalProcess 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 Models166

6.6 Comparing Impulse Response Functions for Competing Models169

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 aSpreadsheet 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. Addition Topics 263

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

"It is a suitable text for courses on time series analysis
at the (upper) undergraduate and graduate level. It can also serve
as a guide for practitioners and researchers who carry out time
series analysis in engineering, business and
economics." (Zentralblatt MATH, 2012)
"Time Series Analysis and Forecasting by Example is well
recommended as a great introductory book for students transitioning
from general statistics to time series as well as a good source
book for intermediate level time series model builders." (Book
Pleasures, 2012)

"They set out to provide an introduction that is easy to
understand and use, and that draws heavily from examples to
demonstrate the principles and techniques." (Book News, 1 October
2011)