Forecasting with Exponential Smoothing: The State Space Approach

Front Cover
Springer Science & Business Media, Jun 19, 2008 - Mathematics - 362 pages
0 Reviews

Exponential smoothing methods have been around since the 1950s, and are still the most popular forecasting methods used in business and industry. However, a modeling framework incorporating stochastic models, likelihood calculation, prediction intervals and procedures for model selection, was not developed until recently. This book brings together all of the important new results on the state space framework for exponential smoothing. It will be of interest to people wanting to apply the methods in their own area of interest as well as for researchers wanting to take the ideas in new directions. Part 1 provides an introduction to exponential smoothing and the underlying models. The essential details are given in Part 2, which also provide links to the most important papers in the literature. More advanced topics are covered in Part 3, including the mathematical properties of the models and extensions of the models for specific problems. Applications to particular domains are discussed in Part 4.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Basic Concepts
3
12 Forecasting Methods and Models
4
13 History of Exponential Smoothing
5
14 State Space Models
6
Getting Started
9
22 Classification of Exponential Smoothing Methods
11
23 Point Forecasts for the BestKnown Methods
12
24 Point Forecasts for All Methods
17
121 Innovations State Space Models with a Random Seed Vector
180
122 Estimation
182
123 Information Filter
185
124 Prediction
193
125 Model Selection
194
126 Smoothing Time Series
195
127 Kalman Filter
197
128 Exercises
200

26 Initialization and Estimation
23
27 Assessing Forecast Accuracy
25
28 Model Selection
27
29 Exercises
28
Essentials
30
Linear Innovations State Space Models
33
32 Innovations and OneStepAhead Forecasts
35
33 Model Properties
36
34 Basic Special Cases
38
35 Variations on the Common Models
47
36 Exercises
51
Nonlinear and Heteroscedastic Innovations State Space Models
52
42 Basic Special Cases
56
43 Nonlinear Seasonal Models
61
44 Variations on the Common Models
64
45 Exercises
66
Estimation of Innovations State Space Models
67
52 A Heuristic Approach to Estimation
71
53 Exercises
73
Prediction Distributions and Intervals
75
61 Simulated Prediction Distributions and Intervals
77
Linear Homoscedastic State Space Models
80
Linear Heteroscedastic State Space Models
83
65 Prediction Intervals
88
66 LeadTime Demand Forecasts for Linear Homoscedastic Models
90
67 Exercises
94
Derivations Derivation of Results for Class 1
95
Selection of Models
105
72 Choosing a Model Selection Procedure
108
73 Implications for Model Selection Procedures
116
74 Exercises
117
Model Selection Algorithms The Linear Empirical Information Criterion
118
Further Topics
120
Normalizing Seasonal Components
121
81 Normalizing Additive Seasonal Components
124
82 Normalizing Multiplicative Seasonal Components
128
Canadian Gas Production
131
84 Exercises
134
Derivations for Additive Seasonality
135
Models with Regressor Variables
137
91 The Linear Innovations Model with Regressors
138
92 Some Examples
139
93 Diagnostics for Regression Models
143
94 Exercises
147
Some Properties of Linear Models
149
102 Stability and the Parameter Space
152
103 Conclusions
161
Reduced Forms and Relationships with ARIMA Models
163
111 ARIMA Models
164
112 Reduced Forms for Two Simple Cases
168
113 Reduced Form for the General Linear Innovations Model
170
114 Stationarity and Invertibility
171
115 ARIMA Models in Innovations State Space Form
173
116 Cyclical Models
176
Linear Innovations State Space Models with Random Seed States
178
Triangularization of Stochastic Equations
203
Conventional State Space Models
209
131 State Space Models
210
132 Estimation
212
133 Reduced Forms
215
134 Comparison of State Space Models
219
135 Smoothing and Filtering
223
136 Exercises
226
Maximizing the Size of the Parameter Space
227
Time Series with Multiple Seasonal Patterns
229
141 Exponential Smoothing for Seasonal Data
231
142 Multiple Seasonal Processes
234
143 An Application to Utility Data
240
144 Analysis of Traffic Data
246
145 Exercises
250
Alternative Forms FirstOrder Form of the Model
251
Nonlinear Models for Positive Data
255
151 Problems with the Gaussian Model
256
152 Multiplicative Error Models
260
153 Distributional Results
263
154 Implications for Statistical Inference
266
155 Empirical Comparisons
270
156 An Appraisal
274
157 Exercises
275
Models for Count Data
277
161 Models for Nonstationary Count Time Series
278
162 Crostons Method
281
Car Parts
283
164 Exercises
286
Vector Exponential Smoothing
287
171 The Vector Exponential Smoothing Framework
288
172 Local Trend Models
290
174 Other Multivariate Models
293
Exchange Rates
296
176 Forecasting Experiment
299
Applications
301
Inventory Control Applications
302
181 Forecasting Demand Using Sales Data
304
182 Inventory Systems
308
183 Exercises
315
Conditional Heteroscedasticity and Applications in Finance
317
191 The BlackScholes Model
318
192 Autoregressive Conditional Heteroscedastic Models
319
193 Forecasting
322
194 Exercises
324
Economic Applications The BeveridgeNelson Decomposition
325
201 The BeveridgeNelson Decomposition
328
202 State Space Form and Applications
330
203 Extensions of the BeveridgeNelson Decomposition to Nonlinear Processes
334
204 Conclusion
336
References
338
Author Index
349
Data Index
352
Subject Index
353
Copyright

Common terms and phrases

Popular passages

Page 7 - The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity.

Bibliographic information