|
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) |
|
|
5 | (1) |
|
|
5 | (3) |
|
2 THE REGRESSION MODEL AND ITS APPLICATION IN FORECASTING |
|
|
8 | (71) |
|
|
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) |
|
|
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) |
|
|
31 | (2) |
|
|
33 | (8) |
|
2.8 Model Selection Techniques |
|
|
41 | (4) |
|
|
45 | (4) |
|
|
49 | (3) |
|
2.11 General Principles of Statistical Model Building |
|
|
52 | (8) |
|
2.11.1 Model Specification |
|
|
53 | (1) |
|
|
54 | (1) |
|
2.11.3 Diagnostic Checking |
|
|
54 | (1) |
|
|
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) |
|
|
81 | (4) |
|
|
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) |
|
|
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) |
|
|
96 | (2) |
|
|
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) |
|
|
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) |
|
|
127 | (2) |
|
3.8.3 Estimation of the Variance |
|
|
129 | (3) |
|
3.8.4 An Alternative Variance Estimate |
|
|
132 | (1) |
|
|
133 | (2) |
|
4 REGRESSION AND EXPONENTIAL SMOOTHING METHODS TO FORECAST SEASONAL TIME SERIES |
|
|
135 | (57) |
|
|
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) |
|
|
173 | (9) |
|
4.5.1 Regression Approach |
|
|
174 | (1) |
|
|
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) |
|
|
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) |
|
|
238 | (10) |
|
|
240 | (6) |
|
|
246 | (1) |
|
|
247 | (1) |
|
|
248 | (2) |
|
|
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) |
|
|
261 | (2) |
|
5.7.1 An Improved Approximation of the Standard Error |
|
|
262 | (1) |
|
|
263 | (1) |
|
|
263 | (10) |
|
|
264 | (3) |
|
|
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) |
|
|
293 | (6) |
|
6.4.1 Model Specification |
|
|
293 | (6) |
|
|
299 | (1) |
|
6.4.3 Diagnostic Checking |
|
|
299 | (1) |
|
6.5 Regression and Seasonal ARIMA Models |
|
|
299 | (3) |
|
|
302 | (4) |
|
|
306 | (11) |
|
|
306 | (2) |
|
|
308 | (2) |
|
|
310 | (1) |
|
|
310 | (3) |
|
6.7.5 Demand for Repair Parts |
|
|
313 | (4) |
|
6.8 Seasonal Adjustment Using Seasonal ARIMA Models |
|
|
317 | (2) |
|
|
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) |
|
|
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) |
|
|
336 | (43) |
|
8.1 Transfer Function Analysis |
|
|
336 | (19) |
|
8.1.1 Construction of Transfer Function-Noise Models |
|
|
338 | (6) |
|
|
344 | (4) |
|
|
348 | (1) |
|
|
348 | (7) |
|
8.2 Intervention Analysis and Outliers |
|
|
355 | (4) |
|
8.2.1 Intervention Analysis |
|
|
355 | (1) |
|
|
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) |
|
|
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) |
|
|
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 | |