Forecasting with Exponential Smoothing: The State Space Approach

Springer Science & Business Media, Jun 19, 2008 - Mathematics - 362 pages

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.

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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

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