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Introduction to Time Series Analysis and Forecasting

Introduction to Time Series Analysis and Forecasting

Douglas C. Montgomery, Cheryl L. Jennings, Murat Kulahci

ISBN: 978-1-118-21150-2

Sep 2011

472 pages

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An accessible introduction to the most current thinking in and practicality of forecasting techniques in the context of time-oriented data.

Analyzing time-oriented data and forecasting are among the most important problems that analysts face across many fields, ranging from finance and economics to production operations and the natural sciences. As a result, there is a widespread need for large groups of people in a variety of fields to understand the basic concepts of time series analysis and forecasting. Introduction to Time Series Analysis and Forecasting presents the time series analysis branch of applied statistics as the underlying methodology for developing practical forecasts, and it also bridges the gap between theory and practice by equipping readers with the tools needed to analyze time-oriented data and construct useful, short- to medium-term, statistically based forecasts.

Seven easy-to-follow chapters provide intuitive explanations and in-depth coverage of key forecasting topics, including:

  • Regression-based methods, heuristic smoothing methods, and general time series models

  • Basic statistical tools used in analyzing time series data

  • Metrics for evaluating forecast errors and methods for evaluating and tracking forecasting performance over time

  • Cross-section and time series regression data, least squares and maximum likelihood model fitting, model adequacy checking, prediction intervals, and weighted and generalized least squares

  • Exponential smoothing techniques for time series with polynomial components and seasonal data

  • Forecasting and prediction interval construction with a discussion on transfer function models as well as intervention modeling and analysis

  • Multivariate time series problems, ARCH and GARCH models, and combinations of forecasts

The ARIMA model approach with a discussion on how to identify and fit these models for non-seasonal and seasonal time series

The intricate role of computer software in successful time series analysis is acknowledged with the use of Minitab, JMP, and SAS software applications, which illustrate how the methods are imple-mented in practice. An extensive FTP site is available for readers to obtain data sets, Microsoft Office PowerPoint slides, and selected answers to problems in the book. Requiring only a basic working knowledge of statistics and complete with exercises at the end of each chapter as well as examples from a wide array of fields, Introduction to Time Series Analysis and Forecasting is an ideal text for forecasting and time series courses at the advanced undergraduate and beginning graduate levels. The book also serves as an indispensable reference for practitioners in business, economics, engineering, statistics, mathematics, and the social, environmental, and life sciences.

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Preface ix

1. Introduction to Forecasting 1

1.1 The Nature and Uses of Forecasts, 1

1.2 Some Examples of Time Series, 5

1.3 The Forecasting Process, 12

1.4 Resources for Forecasting, 14

2. Statistics Background for Forecasting 18

2.1 Introduction, 18

2.2 Graphical Displays, 19

2.3 Numerical Description of Time Series Data, 25

2.4 Use of Data Transformations and Adjustments, 34

2.5 General Approach to Time Series Modeling and Forecasting, 46

2.6 Evaluating and Monitoring Forecasting Model Performance, 49

3. Regression Analysis and Forecasting 73

3.1 Introduction, 73

3.2 Least Squares Estimation in Linear Regression Models, 75

3.3 Statistical Inference in Linear Regression, 84

3.4 Prediction of New Observations, 96

3.5 Model Adequacy Checking, 98

3.6 Variable Selection Methods in Regression, 106

3.7 Generalized and Weighted Least Squares, 111

3.8 Regression Models for General Time Series Data, 133

4. Exponential Smoothing Methods 171

4.1 Introduction, 171

4.2 First-Order Exponential Smoothing, 176

4.3 Modeling Time Series Data, 180

4.4 Second-Order Exponential Smoothing, 183

4.5 Higher-Order Exponential Smoothing, 193

4.6 Forecasting, 193

4.7 Exponential Smoothing for Seasonal Data, 210

4.8 Exponential Smoothers and ARIMA Models, 217

5. Autoregressive Integrated Moving Average (ARIMA) Models 231

5.1 Introduction, 231

5.2 Linear Models for Stationary Time Series, 231

5.3 Finite Order Moving Average (MA) Processes, 235

5.4 Finite Order Autoregressive Processes, 239

5.5 Mixed Autoregressive–Moving Average (ARMA) Processes, 253

5.6 Nonstationary Processes, 256

5.7 Time Series Model Building, 265

5.8 Forecasting ARIMA Processes, 275

5.9 Seasonal Processes, 282

5.10 Final Comments, 286

6. Transfer Functions and Intervention Models 299

6.1 Introduction, 299

6.2 Transfer Function Models, 300

6.3 Transfer Function–Noise Models, 307

6.4 Cross Correlation Function, 307

6.5 Model Specification, 309

6.6 Forecasting with Transfer Function–Noise Models, 322

6.7 Intervention Analysis, 330

7. Survey of Other Forecasting Methods 343

7.1 Multivariate Time Series Models and Forecasting, 343

7.2 State Space Models, 350

7.3 ARCH and GARCH Models, 355

7.4 Direct Forecasting of Percentiles, 359

7.5 Combining Forecasts to Improve Prediction Performance, 365

7.6 Aggregation and Disaggregation of Forecasts, 369

7.7 Neural Networks and Forecasting, 372

7.8 Some Comments on Practical Implementation and Use of Statistical Forecasting Procedures, 375

Appendix A. Statistical Tables 387

Appendix B. Data Sets for Exercises 407

Bibliography 437

Index 443

"This would be an appropriate source for use in a first course in time series analysis. It might also be useful as a reference for researchers who want to apply time series analysis to their data sets." (CHOICE, October 2008)

"The result is a book that can be used with a wide variety of audiences, with different interests and technical backgrounds, whose common interests are understanding how to analyze time-oriented data and constructing good short-term statistically based forecasts." (Mathematical Reviews, 2008m)

"The book is great for readers who need to apply the methods and models presented but have little background in mathematics and statistics." (MAA Reviews,  July 2008)

  • The book is complete with over 300 exercises; 125 computer-drawn illustrations; and 50 programming algorithms.
  • An extensive ftp site is available that includes data sets, Power Point slides, and selected answers to problems in the book.
  • A detailed student solutions manual is available.