Statistical Methods for Forecasting

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Format: Nonspecific Binding
Pub. Date: 2009-09-25
Publisher(s): Wiley Professional Development (P&T)
List Price: $182.66

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Summary

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "This book, it must be said, lives up to the words on its advertising cover: 'Bridging the gap between introductory, descriptive approaches and highly advanced theoretical treatises, it provides a practical, intermediate level discussion of a variety of forecasting tools, and explains how they relate to one another, both in theory and practice.' It does just that!" -Journal of the Royal Statistical Society "A well-written work that deals with statistical methods and models that can be used to produce short-term forecasts, this book has wide-ranging applications. It could be used in the context of a study of regression, forecasting, and time series analysis by PhD students; or to support a concentration in quantitative methods for MBA students; or as a work in applied statistics for advanced undergraduates." -Choice Statistical Methods for Forecasting is a comprehensive, readable treatment of statistical methods and models used to produce short-term forecasts. The interconnections between the forecasting models and methods are thoroughly explained, and the gap between theory and practice is successfully bridged. Special topics are discussed, such as transfer function modeling; Kalman filtering; state space models; Bayesian forecasting; and methods for forecast evaluation, comparison, and control. The book provides time series, autocorrelation, and partial autocorrelation plots, as well as examples and exercises using real data. Statistical Methods for Forecasting serves as an outstanding textbook for advanced undergraduate and graduate courses in statistics, business, engineering, and the social sciences, as well as a working reference for professionals in business, industry, and government.

Author Biography

About the authors Bovas Abraham is Associate Professor in the Department of Statistics and Actuarial Science, at the University of Waterloo, Ontario, Canada. He is a member of the American Statistical Association, the American Society for Duality Control, the Canadian Statistical Association and a Fellow of the Royal Statistical Society. Dr. Abraham received his Ph.D. in statistics from the University of Wisconsin, Madison. Johannes Ledolter is an Associate Professor in bath the Deportment of Statistics and Actuarial Science, and the Department of Management Sciences at the University of Iowa. He is a member of the American Statistical Association and a Fellow of the Royal Statistical Society. Dr. Ledolter is also coauthor of Forecasting Using Leading Indicators. He received his Ph.D. in statistics from the University of Wisconsin, Madison.

Table of Contents

1 INTRODUCTION AND SUMMARY
1(7)
1.1 Importance of Good Forecasts
1(1)
1.2 Classification of Forecast Methods
2(1)
1.3 Conceptual Framework of a Forecast System
3(1)
1.4 Choice of a Particular Forecast Model
4(1)
1.5 Forecast Criteria
5(1)
1.6 Outline of the Book
5(3)
2 THE REGRESSION MODEL AND ITS APPLICATION IN FORECASTING
8(71)
2.1 The Regression Model
9(3)
2.1.1 Linear and Nonlinear Models
10(2)
2.2 Prediction from Regression Models with Known Coefficients
12(1)
2.3 Least Squares Estimates of Unknown Coefficients
13(7)
2.3.1 Some Examples
13(3)
2.3.2 Estimation in the General Linear Regression Model
16(4)
2.4 Properties of Least Squares Estimators
20(5)
2.5 Confidence Intervals and Hypothesis Testing
25(5)
2.5.1 Confidence Intervals
25(1)
2.5.2 Hypothesis Tests for Individual Coefficients
26(1)
2.5.3 A Simultaneous Test for Regression Coefficients
26(1)
2.5.4 General Hypothesis Tests: The Extra Sum of Squares Principle
27(2)
2.5.5 Partial and Sequential F Tests
29(1)
2.6 Prediction from Regression Models with Estimated Coefficients
30(3)
2.6.1 Examples
31(2)
2.7 Examples
33(8)
2.8 Model Selection Techniques
41(4)
2.9 Multicollinearity
45(4)
2.10 Indicator Variables
49(3)
2.11 General Principles of Statistical Model Building
52(8)
2.11.1 Model Specification
53(1)
2.11.2 Model Estimation
54(1)
2.11.3 Diagnostic Checking
54(1)
2.11.4 Lack of Fit Tests
56(2)
2.11.5 Nonconstant Variance and Variance-Stabilizing Transformations
58(2)
2.12 Serial Correlation among the Errors
60(14)
2.12.1 Serial Correlation in a Time Series
61(2)
2.12.2 Detection of Serial Correlation among the Errors in the Regression Model
63(3)
2.12.3 Regression Models with Correlated Errors
66(8)
2.13 Weighted Least Squares
74(3)
Appendix 2 Summary of Distribution Theory Results
77(2)
3 REGRESSION AND EXPONENTIAL SMOOTHING METHODS TO FORECAST NONSEASONAL TIME SERIES
79(56)
3.1 Forecasting a Single Time Series
79(2)
3.2 Constant Mean Model
81(4)
3.2.1 Updating Forecasts
82(1)
3.2.2 Checking the Adequacy of the Model
83(2)
3.3 Locally Constant Mean Model and Simple Exponential Smoothing
85(10)
3.3.1 Updating Forecasts
86(1)
3.3.2 Actual Implementation of Simple Exponential Smoothing
87(2)
3.3.3 Additional Comments and Example
89(6)
3.4 Regression Models with Time as Independent Variable
95(6)
3.4.1 Examples
96(2)
3.4.2 Forecasts
98(2)
3.4.3 Updating Parameter Estimates and Forecasts
100(1)
3.5 Discounted Least Squares and General Exponential Smoothing
101(3)
3.5.1 Updating Parameter Estimates and Forecasts
102(2)
3.6 Locally Constant Linear Trend Model and Double Exponential Smoothing
104(16)
3.6.1 Updating Coefficient Estimates
107(1)
3.6.2 Another Interpretation of Double Exponential Smoothing
107(1)
3.6.3 Actual Implementation of Double Exponential Smoothing
108(2)
3.6.4 Examples
110(10)
3.7 Locally Quadratic Trend Model and Triple Exponential Smoothing
120(5)
3.7.1 Implementation of Triple Exponential Smoothing
123(1)
3.7.2 Extension to the General Polynomial Model and Higher Order Exponential Smoothing
124(1)
3.8 Prediction Intervals for Future Values
125(8)
3.8.1 Prediction Intervals for Sums of Future Observations
127(1)
3.8.2 Examples
127(2)
3.8.3 Estimation of the Variance
129(3)
3.8.4 An Alternative Variance Estimate
132(1)
3.9 Further Comments
133(2)
4 REGRESSION AND EXPONENTIAL SMOOTHING METHODS TO FORECAST SEASONAL TIME SERIES
135(57)
4.1 Seasonal Series
135(4)
4.2 Globally Constant Seasonal Models
139(16)
4.2.1 Modeling the Seasonality with Seasonal Indicators
140(9)
4.2.2 Modeling the Seasonality with Trigonometric Functions
149(6)
4.3 Locally Constant Seasonal Models
155(12)
4.3.1 Locally Constant Seasonal Models Using Seasonal Indicators
158(6)
4.3.2 Locally Constant Seasonal Models Using Trigonometric Functions
164(3)
4.4 Winters' Seasonal Forecast Procedures
167(6)
4.4.1 Winters' Additive Seasonal Forecast Procedure
167(3)
4.4.2 Winters' Multiplicative Seasonal Forecast Procedure
170(3)
4.5 Seasonal Adjustment
173(9)
4.5.1 Regression Approach
174(1)
4.5.2 Smoothing Approach
174(5)
4.5.3 Seasonal Adjustment Procedures
179(3)
Appendix 4 Computer Programs for Seasonal Exponential Smoothing
182(10)
EXPSIND. General Exponential Smoothing with Seasonal Indicators
182(3)
EXPHARM. General Exponential Smoothing with Trigonometric Forecast Functions
185(3)
WINTERS1. Winters' Additive Forecast Procedure
188(2)
WINTERS2. Winters' Multiplicative Forecast Procedure
190(2)
5 STOCHASTIC TIME SERIES MODELS
192(89)
5.1 Stochastic Processes
192(5)
5.1.1 Stationary Stochastic Processes
194(3)
5.2 Stochastic Difference Equation Models
197(28)
5.2.1 Autoregressive Processes
199(10)
5.2.2 Partial Autocorrelations
209(4)
5.2.3 Moving Average Processes
213(6)
5.2.4 Autoregressive Moving Average (ARMA) Processes
219(6)
5.3 Nonstationary Processes
225(13)
5.3.1 Nonstationarity, Differencing, and Transformations
225(6)
5.3.2 Autoregressive Integrated Moving Average (ARIMA) Models
231(6)
5.3.3 Regression and ARIMA Models
237(1)
5.4 Forecasting
238(10)
5.4.1 Examples
240(6)
5.4.2 Prediction Limits
246(1)
5.4.3 Forecast Updating
247(1)
5.5 Model Specification
248(2)
5.6 Model Estimation
250(11)
5.6.1 Maximum Likelihood Estimates
250(3)
5.6.2 Unconditional Least Squares Estimates
253(4)
5.6.3 Conditional Least Squares Estimates
257(1)
5.6.4 Nonlinear Estimation
258(3)
5.7 Model Checking
261(2)
5.7.1 An Improved Approximation of the Standard Error
262(1)
5.7.2 Portmanteau Test
263(1)
5.8 Examples
263(10)
5.8.1 Yield Data
264(3)
5.8.2 Growth Rates
267(3)
5.8.3 Demand for Repair Parts
270(3)
Appendix 5 Exact Likelihood Functions for Three Special Models
273(8)
I. Exact Likelihood Function for an ARMA(1, 1) Process
273(5)
II. Exact Likelihood Function for an AR(1) Process
278(1)
III. Exact Likelihood Function for an MA(1) Process
279(2)
6 SEASONAL AUTOREGRESSIVE INTEGRATED MOVING AVERAGE MODELS
281(41)
6.1 Multiplicative Seasonal Models
283(2)
6.2 Autocorrelation and Partial Autocorrelation Functions of Multiplicative Seasonal Models
285(6)
6.2.1 Autocorrelation Function
286(5)
6.2.2 Partial Autocorrelation Function
291(1)
6.3 Nonmultiplicative Models
291(2)
6.4 Model Building
293(6)
6.4.1 Model Specification
293(6)
6.4.2 Model Estimation
299(1)
6.4.3 Diagnostic Checking
299(1)
6.5 Regression and Seasonal ARIMA Models
299(3)
6.6 Forecasting
302(4)
6.7 Examples
306(11)
6.7.1 Electricity Usage
306(2)
6.7.2 Gas Usage
308(2)
6.7.3 Housing Starts
310(1)
6.7.4 Car Sales
310(3)
6.7.5 Demand for Repair Parts
313(4)
6.8 Seasonal Adjustment Using Seasonal ARIMA Models
317(2)
6.8.1 X-11-ARIMA
317(1)
6.8.2 Signal Extraction or Model-Based Seasonal Adjustment Methods
318(1)
Appendix 6 Autocorrelations of the Multiplicative (O, d, 1)(1, D, 1)(12) Model
319(3)
7 RELATIONSHIPS BETWEEN FORECASTS FROM GENERAL EXPONENTIAL SMOOTHING AND FORECASTS FROM ARIMA TIME SERIES MODELS
322(14)
7.1 Preliminaries
322(5)
7.1.1 General Exponential Smoothing
322(1)
7.1.2 ARIMA Time Series Models
323(4)
7.2 Relationships and Equivalence Results
327(3)
7.2.1 Illustrative Examples
329(1)
7.3 Interpretation of the Results
330(1)
Appendix 7 Proof of the Equivalence Theorem
331(5)
8 SPECIAL TOPICS
336(43)
8.1 Transfer Function Analysis
336(19)
8.1.1 Construction of Transfer Function-Noise Models
338(6)
8.1.2 Forecasting
344(4)
8.1.3 Related Models
348(1)
8.1.4 Example
348(7)
8.2 Intervention Analysis and Outliers
355(4)
8.2.1 Intervention Analysis
355(1)
8.2.2 Outliers
356(3)
8.3 The State Space Forecasting Approach, Kalman Filtering, and Related Topics
359(9)
8.3.1 Recursive Estimation and Kalman Filtering
361(2)
8.3.2 Bayesian Forecasting
363(1)
8.3.3 Models with Time-Varying Coefficients
364(4)
8.4 Adaptive Filtering
368(2)
8.5 Forecast Evaluation, Comparison, and Control
370(9)
8.5.1 Forecast Evaluation
372(1)
8.5.2 Forecast Comparison
373(1)
8.5.3 Forecast Control
374(3)
8.5.4 Adaptive Exponential Smoothing
377(2)
REFERENCES 379(7)
EXERCISES 386(32)
DATA APPENDIX 418(8)
TABLE APPENDIX 426(9)
AUTHOR INDEX 435(2)
SUBJECT INDEX 437

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