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Introduction to Time Series Analysis and Forecasting

Douglas C. Montgomery, Cheryl L. Jennings, and Murat Kulahci
John Wiley
Publication Date: 
Number of Pages: 
Wiley Series in Probability and Statistics
[Reviewed by
Ita Cirovic Donev
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When it comes to time series analysis one really is not shorthanded with respect to the list of books that every serious library should hold. So we should naturally ask what is the contribution and goal of this book. After all, many classes on time series analysis have already adopted a text that is more of a reference than a course textbook.

The main emphasis of the book is to teach practitioners and students in fields other than mathematics the importance and use of time series models and forecasting methods. Important topics are covered, such as the description and analysis of time series data, regression analysis, smoothing techniques, ARIMA models, transfer functions, and other models.

While reading the book everything seemed in place until I started reading the last chapter on the survey of other methods. I was expecting to find a separate chapter on ARCH and GARCH models, especially given that the book is mainly intended for practitioners. This last chapter is written as if there was not time left so the authors just gathered some thoughts.

The main body of the book gives simple presentations of the mathematics accompanied with very detailed narrative. The book is packed with illustrations and output from the statistical software MINITAB and SAS. Illustrations are provided for almost every notion mentioned, which is really useful when explaining the autocorrelation function and ARIMA models, smoothing techniques, etc. Computations are shown in detail, not avoiding the trivialities.

The theory is not explained via theorems or definitions; rather, the results are just stated and followed. The ARIMA chapter is rather good: it enables the reader to grasp quickly and easily the structure of the model. There are a lot of examples, computational and applied, which are presented in great detail. The discussions in examples are worth half the chapter itself.

Exercises are provided at the end of each chapter. They range from simple ones which are formed of small questions (directly testing the knowledge one should have acquired from reading the chapter) to applied small projects that involve usage of computer program in order to analyze the data provided.

Overall, the book is great for readers who need to apply the methods and models presented but have little background in mathematics and statistics. It would be a good side reference book for students of economics, finance, business, life sciences and similar fields. It will provide them with the adequate introduction to time series analysis and forecasting, enough to enable to go to the library or a bookstore and get another book that will be a bit more complex so that they can relate the methods to the real world problems we encounter in various fields.

Ita Cirovic Donev holds a Masters degree in statistics from Rice University. Her main research areas are in mathematical finance; more precisely, statistical methods for credit and market risk. Apart from the academic work she does statistical consulting work for financial institutions in the area of risk management.

1. Introduction to Forecasting.

1.1 The Nature and uses of Forecasts.

1.2 Some Examples of Time Series.

1.3 The Forecasting Process.

1.4 Resources for Forecasting.

2. Statistics Background for Forecasting.

2.1 Introduction.

2.2 Graphical Displays.

2.3 Numerical Description of Time Series Data.

2.4 Use of Data Transformations and Adjustments.

2.5 General Approach to Time Series Analysis and Forecasting.

2.6 Evaluating and Monitoring Forecasting Model Performance.

3. Regression Analysis and Forecasting.

3.1 Introduction.

3.2 Least Squares Estimation in Linear Regression Models.

3.3 Statistical Inference in Linear Regression.

3.4 Prediction of New Observations.

3.5 Model Adequacy Checking.

3.6 Variable Selection Methods in Regression.

3.7 Generalized and Weighted Least Squares.

3.8 Regression Models for General Time Series Data.

4. Exponential Smoothing Methods.

4.1 Introduction.

4.2 First-Order Exponential Smoothing.

4.3 Modeling Time series Data.

4.4 Second-Order Exponential Smoothing.

4.5 Higher-Order Exponential Smoothing.

4.6 Forecasting.

4.7 Exponential Smoothing for Seasonal Data.

4.8 Exponential Smoothers and ARIMA Models.

5. Autoregressive Integrated Moving Average (ARIMA) Models.

5.1 Introduction.

5.2 Linear Models for Stationary Time Series.

5.3 Finite Order Moving Average (MA) Processes.

5.4 Finite Order Autoregressive Processes.

5.5 Mixed Autoregressive-Moving Average (ARMA) Processes.

5.6 Non-stationary Processes.

5.7 Time Series Model Building .

5.8 Forecasting ARIMA Processes .

5.9 Seasonal Processes.

5.10 Final Comments.

6. Transfer Function and Intervention Models.

6.1 Introduction.

6.2 Transfer Function Models.

6.3 Transfer Function-Noise Models.

6.4 Cross Correlation Function.

6.5 Model Specification.

6.6 Forecasting with Transfer Function-Noise Models.

6.7 Intervention Analysis.

7. Survey of Other Forecasting Methods.

7.1 Multivariate Time Series Models and Forecasting.

7.2 State Space Models.

7.3 ARCH and GARCH Models.

7.4 Direct Forecasting of Percentiles.

7.5 Combining Forecasts to Improve Prediction Performance.

7.6 Aggregation and Disaggregation of Forecasts.

7.7 Neural Networks and Forecasting.

7.8 Some Comments on Practical Implementation and use of Statistical Forecasting Techniques.



Appendix A Statistical Tables.

Table A.1 Cumulative Normal Distribution.

Table A.2 Percentage Points of the Chi-Square Distribution.

Table A.3 Percentage Points of the t Distribution.

Table A.4 Percentage Points of the F Distribution.

Table A.5 Critical Values of the Durbin-Watson Statistic.

Appendix B Data Sets for Exercises.

Table B.1 Market Yield on U.S. Treasury Securities at 10-year Constant Maturity.

Table B.2 Pharmaceutical Product Sales.

Table B.3 Chemical Process Viscosity.

Table B.4 U.S Production of Blue and Gorgonzola Cheeses.

Table B.5 U.S. Beverage Manufacturer Product Shipments, Unadjusted.

Table B.6 Global Mean Surface Air Temperature Anomaly and Global CO22 Concentration.

Table B.7 Whole Foods Market Stock Price, Daily Closing Adjusted for Splits.

Table B.8 Unemployment Rate - Full-Time Labor Force, Not Seasonally Adjusted.

Table B.9 International Sunspot Numbers.

Table B.10 United Kingdom Airline Miles Flown.

Table B.11 Champagne Sales.

Table B.12 Chemical Process Yield, with Operating Temperature (Uncontrolled).

Table B.13 U.S. Production of Ice Cream and Frozen Yogurt.

Table B.14 Atmospheric CO2 Concentrations at Mauna Loa Observatory.

Table B.15 U.S. National Violent Crime Rate.

Table B.16 U.S. Gross Domestic Product.

Table B.17 U.S. Total Energy Consumption.

Table B.18 U.S. Coal Production.

Table B.19 Arizona Drowning Rate, Children 1-4 Years Old.

Table B.20 U.S. Internal Revenue Tax Refunds.