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Hu, C. (2002). Advanced tourism demand forecasting: Artificial neural network and Box-Jenkins modeling. Unpublished Doctoral dissertation, Purdue University, West Lafayette, IN.
ABSTRACT
Hu, Clark, Ph.D. Purdue University, December 2002. Advanced Tourism Demand Forecasting: Artificial Neural Network and Box-Jenkins Modeling. Major Professors: Stephen J. Hiemstra and Joseph A. Ismail.
The global tourism industry has witnessed a significant growth in the past few decades. Many researchers have used different forecasting methods to predict future tourism demand. This study represented a major improvement over previous similar tourism forecasting studies. The author provided a detailed but practical treatment of the Box-Jenkins modeling and two kinds of artificial neural network (backpropagation network and radial basis function network) modeling on tourism demand forecasting across thirty time series (ten origin-destination pairs by three data frequencies). He also gave in-depth discussions on the implementation of the complicated Box-Jenkins methodology as well as the ANN modeling techniques in the context of international tourism demand forecasting. Major literature related to the Box-Jenkins and ANN methods in tourism demand forecasting/modeling in recent years was reviewed. More than 60 tourism demand forecasting models were evaluated. Point forecasts along with their 90% prediction intervals through the final Box-Jenkins and naοve models were generated.
It was found that the more sophisticated Box-Jenkins modeling was more accurate than the simple naοve no-change method to forecast the seasonal international tourism demand in the study. For non-seasonal international tourism demand such as annual time series of tourist arrival data, the naοve no-change method might be a better choice given short available annual series. The author also found that the Box-Jenkins modeling produced a significantly smaller MAPE errors than ANN modeling did and that both BPNN (backpropagation neural network) and RBFNN (radial basis function neural network) modeling techniques performed at the same level based on formal statistical procedures and more sophisticated measures on forecasting performance.
The author also investigated data frequency issues with forecasting techniques. The results of this study suggested that quarterly tourism demand data might be more suitable (likely to perform better) for the ANN modeling when BPNN and RBFNN techniques were considered. Finally, unlike many previous studies in tourism demand forecasting that only used simple ranking comparisons, this study invented an overall performance index (OPI) to assess forecasting techniques overall performance. Both the new performance measure and formal statistical test procedures made the results of comparing different forecasting techniques more robust and convincing.
TABLE OF CONTENTS
LIST OF TABLES ---- x
LIST OF FIGURES ---- xii
ABSTRACT ---- xviii
CHAPTER ONE INTRODUCTION ---- 1
1.1 International Tourism Demand and Forecasting ---- 1
1.2 Development of Tourism Demand Forecasting ---- 4
1.2.1 Tourism Demand Studies ---- 4
1.2.2 Classification and Development in Forecasting Techniques ---- 6
1.3 Advancing Quantitative Techniques for Tourism Demand Forecasting ---- 8
1.4 Problem Statement ---- 10
1.5 Research Objectives and Questions ---- 13
1.6 Organization of the Dissertation ---- 14
CHAPTER TWO LITERATURE REVIEW ---- 16
2.1 Basic Concepts of Tourism Demand ---- 16
2.2 The Worldwide Tourism Demand ---- 18
2.2.1 International tourist/visitor arrivals ---- 20
2.2.2 International tourism receipts ---- 25
2.3 Forecasting Strategy and Horizons ---- 30
2.4 Overview of Forecasting Methods ---- 34
2.4.1 Major Quantitative Forecasting Methods ---- 37
2.4.1.1 Non-casual/Univariate/Time Series Methods ---- 37
2.4.1.1a Naοve No-change Models ---- 37
2.4.1.1b Moving Average (MA) Models ---- 38
2.4.1.1c Autoregressive (AR) Models ---- 41
2.4.1.1d Exponential Smoothing Models ---- 42
2.4.1.2 Box-Jenkins Methodology ARIMA and SARIMA Models ---- 44
2.4.1.2a ARMA (AutoRegressive Moving Average) Process ---- 45
2.4.1.2b ARIMA and SARIMA Models ---- 46
2.4.1.2c General Non-seasonal ARIMA Models ---- 48
2.4.1.2d General Seasonal ARIMA (SARIMA) Models ---- 49
2.4.1.2e Autocorrelation Analysis ---- 50
2.4.1.2f Identify ARIMA/SARIMA Models ---- 52
2.4.1.2g Model Estimation and Selection ---- 56
2.4.1.2h Model Diagnosis ---- 59
2.4.1.3 Casual/Behavioral/Econometric/Multivariate Methods ---- 63
2.4.1.3a Regression Models ---- 63
2.4.1.3b Structural Econometric Models ---- 66
2.4.1.3c Spatial Models ---- 67
2.4.1.4 Other Related Quantitative Methods ---- 70
2.4.2 Major Artificial Intelligence Forecasting Methods ---- 72
2.4.2.1 Artificial Neural Networks (ANNs) ---- 75
2.4.2.2 Fuzzy Logic Systems ---- 75
2.4.2.3 Genetic Algorithms (GAs) ---- 76
2.4.2.4 Rule-Based Expert Systems (ESs) ---- 77
2.5 Accuracy Measures for Quantitative Forecasting Methods ---- 78
2.5.1 Error Magnitude Measures ---- 78
2.5.1.1 Mean Absolute Percentage Error (MAPE) ---- 78
2.5.1.2 Mean Squared Error (MSE) ---- 79
2.5.1.3 Theils U (Theils Inequality Coefficient) ---- 80
2.5.2 Turning Points (or Trend Change) Accuracy ---- 81
2.5.3 Directional (Change) Accuracy (DCA) ---- 84
2.6 Review of Tourism Demand Studies ---- 86
2.6.1 Determinants That Affect Tourism Demand ---- 86
2.6.1.1 Business/Economic Cycles (Origin Country) ---- 87
2.6.1.2 Climates or Natural Disasters (Destination Country) ---- 88
2.6.1.3 Costs of Travel/Transportation (between Origin and Destination Countries) ---- 88
2.6.1.4 Employment (Origin Country) ---- 89
2.6.1.5 Exchange Rates (between Origin and Destination Countries) ---- 89
2.6.1.6 Income (Origin Country) ---- 89
2.6.1.7 International Trade (between Origin and Destination Countries) ---- 90
2.6.1.8 Lagged Dependent Variables/Trend and Fashion (Origin Country) ---- 90
2.6.1.9 Leisure Time (Origin Country) ---- 91
2.6.1.10 Neighborhood Effect (Destination Country) ---- 92
2.6.1.11 Population (Origin and/or Destination Country) ---- 93
2.6.1.12 Relative/Tourism Price (Destination Country) ---- 93
2.6.1.13 Seasonality (Origin and Destination Countries) ---- 94
2.6.1.14 Special Event (Origin and Destination Countries) ---- 95
2.6.1.15 Substitution Effect/Prices (Origin and Destination Countries) ---- 96
2.6.1.16 Supply-side Factors (Destination Country) ---- 98
2.6.1.17 Tourism Marketing Variables (Destination Country) ---- 98
2.6.1.18 Other Qualitative Effects (Origin and Destination Countries) ---- 99
2.6.2 Reviews on Tourism Demand Forecasting Studies ---- 102
2.6.2.1 Tourism Forecasting/Demand Research in Recent Years ---- 102
2.6.2.2 Time Series Forecasting by Box-Jenkins Methodology ---- 115
2.7 Artificial Neural Networks (ANNs) ---- 124
2.7.1 Background of Artificial Neural Networks ---- 125
2.7.2 Supervised Neural Network Models ---- 130
2.7.3 Unsupervised Neural Network Models ---- 131
2.7.4 Artificial Neural Network Applications in Business ---- 133
2.7.5 Designing a Neural Network Forecasting Model ---- 136
2.7.5.1 Step 1: Variable Selection ---- 137
2.7.5.2 Step 2: Data Collection and Audit ---- 138
2.7.5.3 Step 3: Data Preprocessing ---- 138
2.7.5.4 Step 4: Data Partition ---- 139
2.7.5.5 Step 5: Neural Network Topology/Architectures ---- 141
2.7.5.5a Number of Hidden Layers ---- 141
2.7.5.5b Number of Hidden Neurons ---- 141
2.7.5.5c Number of Input and Output Neurons ---- 143
2.7.5.5d Selection of Transfer Functions ---- 145
2.7.5.6 Step 6: Selection of Evaluation Criteria ---- 145
2.7.5.7 Step 7: Neural Network Training and Optimization ---- 146
2.7.5.7a The Number of Training Iterations ---- 146
2.7.5.7b Stopping to Avoid Overtraining ---- 147
2.7.5.7c Training Styles ---- 147
2.7.5.7d Training Algorithm (Backpropagation) ---- 148
2.7.5.7e Learning Rate and Momentum Term ---- 149
2.7.5.8 Step 8: Neural Network Implementation and Maintenance ---- 151
2.8 The Use of ANN Modeling in Tourism Studies ---- 153
2.8.1 Rationales of Applying ANNs In Tourism Forecasting ---- 154
2.8.2 Literature Review of ANNs in Tourism/Hospitality Studies ---- 156
2.9 Comparisons between Conventional and ANN Forecasting Models ---- 161
CHAPTER THREE METHODOLOGY ---- 164
3.1 Research Data ---- 164
3.1.1 Variables Selection ---- 164
3.1.2 Decision on Country Selection ---- 165
3.1.3 Data Sources and Collection ---- 168
3.1.4 Data Structure and Availability ---- 168
3.2 Preliminary Descriptive Analysis ---- 172
3.2.1 Basic Descriptive Statistics ---- 172
3.2.2 Pearsons Correlation Analysis ---- 172
3.2.3 Growth Rate Analysis ---- 172
3.2.4 Graphical Analysis (Data Pattern Inspection) ---- 173
3.2.5 Unit Root Test (Seasonal Augmented Dickey-Fuller Test) ---- 174
3.3 Box-Jenkins Approach ---- 176
3.3.1 Phase I (Visual Inspection, Data Preparation, and Model Identification) ---- 177
3.3.2 Phase II (Model Estimation and Diagnostic Checking) ---- 181
3.3.3 Phase III (Model Evaluation and Forecasting) ---- 183
3.3.4 Decision Rules for Selecting the Best Final Model ---- 183
3.3.5 Producing Prediction Intervals (or Interval Forecasts) ---- 187
3.4 Artificial Neural Network Approach ---- 189
3.4.1 Supervised Network Architecture (Model Designs) ---- 192
3.4.1.1 Back-propagation Neural Network (BPNN) ---- 192
3.4.1.2 Radial Basis Function Neural Network (RBFNN) ---- 196
3.4.1.2 Radial Basis Function Neural Network (RBFNN) ---- 196
3.4.2 Concerns on time series data ---- 199
3.4.3 Data Preprocessing and Partitioning ---- 200
3.4.4 Determination of Transfer Functions ---- 200
3.5 Comparison methods for Forecasting Techniques ---- 201
CHAPTER FOUR RESULTS ---- 203
4.1 Results of Preliminary Analysis ---- 203
4.1.1 Basic Descriptive Statistics ---- 203
4.1.1.1 USA Arrivals ---- 205
4.1.1.2 World Arrivals ---- 205
4.1.2 Pearsons Correlation Analysis ---- 211
4.1.2.1 Between USA and World Series ---- 211
4.1.1.2 Arrival Series among Five Destination Countries ---- 212
4.1.3 Growth Rate Analysis ---- 221
4.1.3.1 Growth of USA Arrivals ---- 221
4.1.3.2 Growth of World Arrivals ---- 223
4.1.4 Graphical Analysis: Exploring Data Patterns by Visual Inspections ---- 223
4.1.4.1 Patterns in Monthly Time Series ---- 223
4.1.4.2 Patterns in Quarterly Time Series ---- 224
4.1.4.3 Patterns in Annual Time Series ---- 224
4.1.5 Augmented Dickey-Fuller Test Results ---- 226
4.2 Results of Box-Jenkins Modeling ---- 228
4.2.1 SARIMA Models for Monthly Series ---- 229
4.2.1.1 USA-Australia Series ---- 229
4.2.1.2 USA-Germany Series ---- 232
4.2.1.3 USA-Italy Series ---- 235
4.2.1.4 USA-Japan Series ---- 237
4.2.1.5 USA-Spain Series ---- 239
4.2.1.6 World-Australia Series ---- 244
4.2.1.7 World-Germany Series ---- 247
4.2.1.8 World-Italy Series ---- 250
4.2.1.9 World-Japan Series ---- 253
4.2.1.10 World-Spain Series ---- 256
4.2.2 SARIMA Models for Quarterly Series ---- 259
4.2.2.1 USA-Australia Series ---- 259
4.2.2.2 USA-Germany Series ---- 261
4.2.2.3 USA-Italy Series ---- 263
4.2.2.4 USA-Japan Series ---- 265
4.2.2.5 USA-Spain Series ---- 267
4.2.2.6 World-Australia Series ---- 269
4.2.2.7 World-Germany Series ---- 271
4.2.2.8 World-Italy Series ---- 273
4.2.2.9 World-Japan Series ---- 275
4.2.2.10 World-Spain Series ---- 277
4.2.3 ARIMA Models for Annual Series ---- 279
4.2.3.1 USA-Australia Series ---- 280
4.2.3.2 USA-Germany Series ---- 283
4.2.3.3 USA-Italy Series ---- 284
4.2.3.4 USA-Japan Series ---- 285
4.2.3.5 USA-Spain Series ---- 287
4.2.3.6 World-Australia Series ---- 288
4.2.3.7 World-Germany Series ---- 291
4.2.3.8 World-Italy Series ---- 292
4.2.3.9 World-Japan Series ---- 293
4.2.3.10 World-Spain Series ---- 294
4.2.4 Turning-Point Forecasting Power (TPFP) ---- 296
4.3 Results of Artificial Neural Network Modeling ---- 298
4.3.1 ANN Modeling on Monthly Time Series ---- 299
4.3.2 ANN Modeling on Quarterly Time Series ---- 319
VOLUME II
CHAPTER FIVE SUMMARY OF FINDINGS ---- 339
5.1 Forecasting Performance of Box-Jenkins Modeling ---- 339
5.2 Forecasting Performance of Two ANN Techniques ---- 356
5.3 Performance Comparisons among Different Forecasting Methods ---- 362
5.3.1 Box-Jenkins vs. Naοve No-Change Models ---- 362
5.3.2 Box-Jenkins vs. Artificial Neural Network Modeling ---- 363
5.3.3 Backpropagation NN vs. Radial Basis Function NN modeling ---- 366
5.4 Performance Comparisons by Different Data Frequencies ---- 367
5.4.1 Data Frequencies and the Box-Jenkins Modeling ---- 368
5.4.2 Data Frequencies and the ANN Modeling ---- 368
5.4.3 Data Frequencies and the BPNN and RBFNN Modeling ---- 369
CHAPTER SIX CONCLUSIONS & RECOMMENDATIONS ---- 371
6.1 Major Contributions of This Study ---- 371
6.2 Concluding Remarks ---- 373
6.3 Limitations of the Study ---- 377
6.4 Recommendations for Future Research ---- 378
BIBLIOGRAPHY ---- 381
APPENDICES
Appendix A: A Synopsis of Travel & Tourism Satellite Accounting (TSA) System ---- 433
Appendix B: Bivariate scatterplots (USA vs. World series) for all 5 destinations ---- 439
Appendix C: Growth rate time plots of all data series ---- 447
Appendix D: Time Series Plots for All 30 Data Series ---- 455
Appendix E: An example of SPSS syntax script for SARIMA modeling ---- 470
Appendix F: Computer output example of a SARIMA model ---- 474
Appendix G: Plots of 90% Prediction Intervals (P.I.s) ---- 476
VITA ---- 486
LIST OF TABLES
Table 1. Regional demand profile (by international tourist arrivals), 1990~2000. ---- 24
Table 2. Regional demand profile (by international tourist receipts), 1990~2000. ---- 28
Table 3. Requirements and characteristics of tourism forecasting methods. ---- 36
Table 4. General guidance of expected ACF and PACF patterns. ---- 54
Table 5. Contingency table for calculating DCA (directional change accuracy). ---- 86
Table 6. Contingency table for testing directional accuracy. ---- 86
Table 7. A summary table of tourism forecasting research in the recent years. ---- 103
Table 8. Common procedure in designing a BPNN forecasting model. ---- 137
Table 9. General guidelines for deciding the number of hidden neurons. ---- 142
Table 10. Data structure matrix Unidirectional inbound tourism (arrivals). ---- 170
Table 11. Available inbound tourism data for five destinations in the study. ---- 171
Table 12. Decision rules for selecting final forecasting models. ---- 186
Table 13. Summary of basic descriptive statistics (All series). ---- 204
Table 14. Pearson's correlations between USA and World series. ---- 214
Table 15. Pearson's correlation matrix (Monthly data: From USA). ---- 215
Table 16. Pearson's correlation matrix (Monthly data: From World). ---- 216
Table 17. Pearson's correlation matrix (Quarterly data: From USA). ---- 217
Table 18. Pearson's correlation matrix (Quarterly data: From World). ---- 218
Table 19. Pearson's correlation matrix (Annual data: From USA). ---- 219
Table 20. Pearson's correlation matrix (Annual data: From World). ---- 220
Table 21. Annual growth rate (%) of each data series. ---- 222
Table 22. Summary of visualized data patterns in time series. ---- 225
Table 23. Results of Seasonal ADF tests for unit roots. ---- 227
Table 24. Monthly USA-Australia ex ante forecasts. ---- 231
Table 25. Monthly USA-Germany ex ante forecasts. ---- 234
Table 26. Monthly USA-Italy ex ante forecasts. ---- 236
Table 27. Monthly USA-Japan ex ante forecasts. ---- 239
Table 28. Monthly USA-Spain ex ante forecasts. ---- 242
Table 29. Monthly World-Australia ex ante forecasts. ---- 246
Table 30. Monthly World-Germany ex ante forecasts. ---- 249
Table 31. Monthly World-Italy ex ante forecasts. ---- 252
Table 32. Monthly World-Japan ex ante forecasts. ---- 255
Table 33. Monthly World-Spain ex ante forecasts. ---- 258
Table 34. Quarterly USA-Australia ex ante forecasts. ---- 261
Table 35. Quarterly USA-Germany ex ante forecasts. ---- 263
Table 36. Quarterly USA-Italy ex ante forecasts. ---- 265
Table 37. Quarterly USA-Japan ex ante forecasts. ---- 267
Table 38. Quarterly USA-Spain ex ante forecasts. ---- 269
Table 39. Quarterly World-Australia ex ante forecasts. ---- 271
Table 40. Quarterly World-Germany ex ante forecasts. ---- 273
Table 41. Quarterly World-Italy ex ante forecasts. ---- 275
Table 42. Quarterly World-Japan ex ante forecasts. ---- 277
Table 43. Quarterly World-Spain ex ante forecasts. ---- 279
Table 44. Annual USA-Destination ex ante forecasts. ---- 282
Table 45. Annual World-Destination ex ante forecasts. ---- 290
Table 46. Model identification of Box-Jenkins models (Preliminary). ---- 342
Table 47. Model identification - Final forecasting models. ---- 343
Table 48. In-sample model evaluation of monthly SARIMA models. ---- 344
Table 49. In-sample model evaluation of quarterly SARIMA models. ---- 345
Table 50. In-sample model evaluation of annual ARIMA models (1). ---- 346
Table 51. In-sample model evaluation of annual ARIMA models (2). ---- 347
Table 52. Out-of-sample model evaluation of monthly SARIMA models. ---- 348
Table 53. Out-of-sample model evaluation of quarterly SARIMA models. ---- 349
Table 54. In-sample model evaluation Turning point forecasting power (TPFP). ---- 354
Table 55. Out-of-sample Turning point forecasting power (SARIMA models only). ---- 355
Table 56. Architectures of all BP (backpropagation) neural network models. ---- 358
Table 57. Architectures of all RBF (Radial basis function) neural network models. ---- 359
Table 58. Monthly time series Ex post evaluations of all ANN models. ---- 360
Table 59. Quarterly time series Ex post evaluations of all ANN models. ---- 361
Table 60. Box-Jenkins vs. ANN Modeling (winning counts). ---- 364
Table 61. Box-Jenkins vs. ANN modeling (Overall performance indices). ---- 365
Table 62. Box-Jenkins vs. ANN modeling (ANOVA). ---- 365
Table 63. Box-Jenkins vs. BPNN/RBFNN modeling (ANOVA). ---- 365
Table 64. BPNN vs. RBFNN modeling (Overall performance indices). ---- 366
Table 65. BPNN vs. RBFNN modeling (ANOVA). ---- 367
Table 66. Data frequencies and the Box-Jenkins technique. ---- 368
Table 67. Data frequencies and the ANN technique. ---- 369
Table 68. Data frequencies and the BPNN technique. ---- 369
Table 69. Data frequencies and the RBFNN technique. ---- 370
LIST OF FIGURES
Figure 1. Total number of international tourist arrivals (Worldwide), 1970~2000. ---- 23
Figure 2. International tourism receipts (Worldwide), 1990~2000. ---- 26
Figure 3. World tourism growth for the past five decades, 1950~2000. ---- 29
Figure 4. Time horizon of ex post and ex ante forecasts. ---- 32
Figure 5. One-step vs. h-step ahead forecast. ---- 34
Figure 6. Schematic representation of Box-Jenkins methodology. ---- 62
Figure 7. Strength of intelligent systems by five key features. ---- 74
Figure 8. Graphical representation of tourism demand determinants. ---- 101
Figure 9. An illustration of the biological neuron. ---- 126
Figure 10. An illustration of the artificial neuron. ---- 126
Figure 11. Historical development of the ANN research. ---- 129
Figure 12. The supervised learning paradigm. ---- 132
Figure 13. The unsupervised learning paradigm. ---- 132
Figure 14. Data partition approaches for ANN forecasting models. ---- 140
Figure 15. An example of univariate ANN forecasting model ---- 144
Figure 16. An example of multivariate ANN forecasting model. ---- 144
Figure 17. Training strategy: Learning rate and momentum. ---- 152
Figure 18. Conventional vs. ANN forecasting process. ---- 163
Figure 19. Geographical illustration of 6 countries studied. ---- 167
Figure 20. The flowchart of ARIMA modeling in the study. ---- 178
Figure 21. Model identification in seasonal ARIMA modeling. ---- 180
Figure 22. An illustration of a BPNN(4-7-1) forecasting model. ---- 191
Figure 23. Topology of the BPNN forecasting model in the study. ---- 195
Figure 24. Topology of the RBFNN forecasting model in the study. ---- 195
Figure 25. Means and medians of monthly USA arrivals. ---- 207
Figure 26. Means and medians of quarterly USA arrivals. ---- 207
Figure 27. Means and medians of annual USA arrivals. ---- 208
Figure 28. Means and medians of monthly World arrivals. ---- 208
Figure 29. Means and median of quarterly World arrivals. ---- 209
Figure 30. Means and medians of annual World arrivals. ---- 209
Figure 31. USA market for all five destination countries from 1966 to 1999. ---- 210
Figure 32. Forecasts of the monthly USA-AUS model: SARIMA(2,0,0)(1,1,0)12. ---- 230
Figure 33. Forecasts of the monthly USA-GER model: SARIMA(1,0,1)(1,1,1)12. ---- 233
Figure 34. Forecasts of the monthly USA-ITA model: SARIMA(1,0,1)(1,1,0)12. ---- 237
Figure 35. Forecasts of the monthly USA-JAP model: SARIMA(2,0,0)(0,1,1)12. ---- 238
Figure 36. Forecasts of the monthly USA-SPA model: SI(1)12. ---- 243
Figure 37. Forecasts of the monthly USA-SPA model: SARIMA(1,0,1)(0,1,0)12. ---- 243
Figure 38. Forecasts of the monthly WLD-AUS model: SARIMA(2,0,0)(2,1,0)12. ---- 247
Figure 39. Forecasts of the monthly WLD-GER model: SARIMA(1,0,1)(1,1,0)12. ---- 250
Figure 40. Forecasts of the monthly WLD-ITA model: SARIMA(2,0,0)(2,1,0)12. ---- 253
Figure 41. Forecasts of the monthly WLD-JAP model: SARIMA(2,0,0)(2,1,0)12. ---- 256
Figure 42. Forecasts of the monthly WLD-SPA model: SARIMA(2,0,0)(2,1,0)12. ---- 259
Figure 43. Forecasts of the quarterly USA-AUS model: SARIMA(1,0,0)(0,1,0)4. ---- 260
Figure 44. Forecasts of the quarterly USA-GER model: SARIMA(1,0,0)(1,1,1)4. ---- 262
Figure 45. Forecasts of the quarterly USA-ITA model: SARIMA(1,0,1)(0,1,1)4. ---- 264
Figure 46. Forecasts of the quarterly USA-JAP model: SARIMA(0,0,2)(0,1,1)4. ---- 266
Figure 47. Forecasts of the quarterly USA-SPA model: SARIMA(0,0,2)(1,1,0)4. ---- 268
Figure 48. Forecasts of the quarterly WLD-AUS model: SARIMA(1,0,0)(2,1,0)4. ---- 271
Figure 49. Forecasts of the quarterly WLD-GER model: SARIMA(2,0,0)(1,1,0)4. ---- 273
Figure 50. Forecasts of the quarterly WLD-ITA model: SARIMA(0,0,1)(0,1,1)4. ---- 275
Figure 51. Forecasts of the quarterly WLD-JAP model: SARIMA(1,0,0)(2,1,0)4. ---- 277
Figure 52. Forecasts of the quarterly WLD-SPA model: SARIMA(1,0,0)(0,1,0)4. ---- 279
Figure 53. Forecasts of the annual USA-AUS models. ---- 281
Figure 54. Forecasts of the annual USA-GER models. ---- 284
Figure 55. Forecasts of the annual USA-ITA models. ---- 285
Figure 56. Forecasts of the annual USA-JAP models. ---- 286
Figure 57. Forecasts of the annual USA-SPA models. ---- 288
Figure 58. Forecasts of the annual WLD-AUS models. ---- 289
Figure 59. Forecasts of the annual WLD-GER models. ---- 292
Figure 60. Forecasts of the annual WLD-ITA models. ---- 293
Figure 61. Forecasts of the annual WLD-JAP models. ---- 294
Figure 62. Forecasts of the annual WLD-SPA models. ---- 296
Figure 63. MUA series by BPNN Testing. ---- 299
Figure 64. MUA series by BPNN Training & validation ---- 299
Figure 65. MUA series by RBFNN Testing. ---- 300
Figure 66. MUA series by RBFNN Training & validation ---- 300
Figure 67. MUG series by BPNN Testing. ---- 301
Figure 68. MUG series by BPNN Training & validation. ---- 301
Figure 69. MUG series by RBFNN Testing. ---- 302
Figure 70. MUG series by RBFNN Training & validation. ---- 302
Figure 71. MUI series by BPNN Testing. ---- 303
Figure 72. MUI series by BPNN Training & validation. ---- 303
Figure 73. MUI series by RBFNN Testing. ---- 304
Figure 74. MUI series by RBFNN Training & validation. ---- 304
Figure 75. MUJ series by BPNN Testing. ---- 305
Figure 76. MUJ series by BPNN Training & validation. ---- 305
Figure 77. MUJ series by RBFNN Testing. ---- 306
Figure 78. MUJ series by RBFNN Training & validation. ---- 306
Figure 79. MUS series by BPNN Testing. ---- 307
Figure 80. MUS series by BPNN Training & validation. ---- 307
Figure 81. MUS series by RBFNN Testing. ---- 308
Figure 82. MUS series by RBFNN Training & validation. ---- 308
Figure 83. MWA series by BPNN Testing. ---- 309
Figure 84. MWA series by BPNN Training & validation. ---- 309
Figure 85. MWA series by RBFNN Testing. ---- 310
Figure 86. MWA series by RBFNN Training & validation. ---- 310
Figure 87. MWG series by BPNN Testing. ---- 311
Figure 88. MWG series by BPNN Training & validation. ---- 311
Figure 89. MWG series by RBFNN Testing. ---- 312
Figure 90. MWG series by RBFNN Training & validation. ---- 312
Figure 91. MWI series by BPNN Testing. ---- 313
Figure 92. MWI series by BPNN Training & validation. ---- 313
Figure 93. MWI series by RBFNN Testing. ---- 314
Figure 94. MWI series by RBFNN Training & validation. ---- 314
Figure 95. MWJ series by BPNN Testing. ---- 315
Figure 96. MWJ series by BPNN Training & validation. ---- 315
Figure 97. MWJ series by RBFNN Testing. ---- 316
Figure 98. MWJ series by RBFNN Training & validation. ---- 316
Figure 99. MWS series by BPNN Testing. ---- 317
Figure 100. MWS series by BPNN Training & validation. ---- 317
Figure 101. MWS series by RBFNN Testing. ---- 318
Figure 102. MWS series by RBFNN Training & validation. ---- 318
Figure 103. QUA series by BPNN Testing. ---- 319
Figure 104. QUA series by BPNN Training & validation. ---- 319
Figure 105. QUA series by RBFNN Testing. ---- 320
Figure 106. QUA series by RBFNN Training & validation. ---- 320
Figure 107. QUG series by BPNN Testing. ---- 321
Figure 108. QUG series by BPNN Training & validation. ---- 321
Figure 109. QUG series by RBFNN Testing. ---- 322
Figure 110. QUG series by RBFNN Training & validation. ---- 322
Figure 111. QUI series by BPNN Testing. ---- 323
Figure 112. QUI series by BPNN Training & validation. ---- 323
Figure 113. QUI series by RBFNN Testing. ---- 324
Figure 114. QUI series by RBFNN Training & validation. ---- 324
Figure 115. QUJ series by BPNN Testing. ---- 325
Figure 116. QUJ series by BPNN Training & validation. ---- 325
Figure 117. QUJ series by RBFNN Testing. ---- 326
Figure 118. QUJ series by RBFNN Training & validation. ---- 326
Figure 119. QUS series by BPNN Testing. ---- 327
Figure 120. QUS series by BPNN Training & validation. ---- 327
Figure 121. QUS series by RBFNN Testing. ---- 328
Figure 122. QUS series by RBFNN Training & validation. ---- 328
Figure 123. QWA series by BPNN Testing. ---- 329
Figure 124. QWA series by BPNN Training & validation. ---- 329
Figure 125. QWA series by RBFNN Testing. ---- 330
Figure 126. QWA series by RBFNN Training & validation. ---- 330
Figure 127. QWG series by BPNN Testing. ---- 331
Figure 128. QWG series by BPNN Training & validation. ---- 331
Figure 129. QWG series by RBFNN Testing. ---- 332
Figure 130. QWG series by RBFNN Training & validation. ---- 332
Figure 131. QWI series by BPNN Testing. ---- 333
Figure 132. QWI series by BPNN Training & validation. ---- 333
Figure 133. QWI series by RBFNN Testing. ---- 334
Figure 134. QWI series by RBFNN Training & validation. ---- 334
Figure 135. QWJ series by BPNN Testing. ---- 335
Figure 136. QWJ series by BPNN Training & validation. ---- 335
Figure 137. QWJ series by RBFNN Testing. ---- 336
Figure 138. QWJ series by RBFNN Training & validation. ---- 336
Figure 139. QWS series by BPNN Testing. ---- 337
Figure 140. QWS series by BPNN Training & validation. ---- 337
Figure 141. QWS series by RBFNN Testing. ---- 338
Figure 142. QWS series by RBFNN Training & validation. ---- 338
Figure 143. Illustration of two concepts in TSA system. ---- 437
Figure 144. Structure of the TSA system. ---- 438
Figure 145. Bivariate scatterplot of monthly Australia series. ---- 439
Figure 146. Bivariate scatterplot of monthly Germany series. ---- 439
Figure 147. Bivariate scatterplot of monthly Italy series. ---- 440
Figure 148. Bivariate scatterplot of monthly Japan series. ---- 440
Figure 149. Bivariate scatterplot of monthly Spain series. ---- 441
Figure 150. Bivariate scatterplot of quarterly Australia series. ---- 441
Figure 151. Bivariate scatterplot of quarterly Germany series. ---- 442
Figure 152. Bivariate scatterplot of quarterly Italy series. ---- 442
Figure 153. Bivariate scatterplot of quarterly Japan series. ---- 443
Figure 154. Bivariate scatterplot of quarterly Spain series. ---- 443
Figure 155. Bivariate scatterplot of annual Australia series. ---- 444
Figure 156. Bivariate scatterplot of annual Germany series. ---- 444
Figure 157. Bivariate scatterplot of annual Italy series. ---- 445
Figure 158. Bivariate scatterplot of annual Japan series. ---- 445
Figure 159. Bivariate scatterplot of annual Spain series. ---- 446
Figure 160. Growth rates: Monthly arrivals to Australia. ---- 447
Figure 161. Growth rates: Monthly arrivals to Germany. ---- 447
Figure 162. Growth rates: Monthly arrivals to Italy. ---- 448
Figure 163. Growth rates: Monthly arrivals to Japan. ---- 448
Figure 164. Growth rates: Monthly arrivals to Spain. ---- 449
Figure 165. Growth rates: Quarterly arrivals to Australia. ---- 449
Figure 166. Growth rates: Quarterly arrivals to Germany. ---- 450
Figure 167. Growth rates: Quarterly arrivals to Italy. ---- 450
Figure 168. Growth rates: Quarterly arrivals to Japan. ---- 451
Figure 169. Growth rates: Quarterly arrivals to Spain. ---- 451
Figure 170. Growth rates: Annual arrivals to Australia. ---- 452
Figure 171. Growth rates: Annual arrivals to Germany. ---- 452
Figure 172. Growth rates: Annual arrivals to Italy. ---- 453
Figure 173. Growth rates: Annual arrivals to Japan. ---- 453
Figure 174. Growth rates: Annual arrivals to Spain. ---- 454
Figure 175. Monthly arrivals from USA to Australia. ---- 455
Figure 176. Monthly arrivals from World to Australia. ---- 455
Figure 177. Monthly arrivals from USA to Germany. ---- 456
Figure 178. Monthly arrivals from World to Germany. ---- 456
Figure 179. Monthly arrivals from USA to Italy. ---- 457
Figure 180. Monthly arrivals from World to Italy. ---- 457
Figure 181. Monthly arrivals from USA to Japan. ---- 458
Figure 182. Monthly arrivals from World to Japan. ---- 458
Figure 183. Monthly arrivals from USA to Spain. ---- 459
Figure 184. Monthly arrivals from World to Spain. ---- 459
Figure 185. Quarterly arrivals from USA to Australia. ---- 460
Figure 186. Quarterly arrivals from World to Australia. ---- 460
Figure 187. Quarterly arrivals from USA to Germany. ---- 461
Figure 188. Quarterly arrivals from World to Germany. ---- 461
Figure 189. Quarterly arrivals from USA to Italy. ---- 462
Figure 190. Quarterly arrivals from World to Italy. ---- 462
Figure 191. Quarterly arrivals from USA to Japan. ---- 463
Figure 192. Quarterly arrivals from World to Japan. ---- 463
Figure 193. Quarterly arrivals from USA to Spain. ---- 464
Figure 194. Quarterly arrivals from World to Spain. ---- 464
Figure 195. Annual arrivals from USA to Australia. ---- 465
Figure 196. Annual arrivals from World to Australia. ---- 465
Figure 197. Annual arrivals from USA to Germany. ---- 466
Figure 198. Annual arrivals from World to Germany. ---- 466
Figure 199. Annual arrivals from USA to Italy. ---- 467
Figure 200. Annual arrivals from World to Italy. ---- 467
Figure 201. Annual arrivals from USA to Japan. ---- 468
Figure 202. Annual arrivals from World to Japan. ---- 468
Figure 203. Annual arrivals from USA to Spain. ---- 469
Figure 204. Annual arrivals from World to Spain. ---- 469
Figure 205. Residual ACF plot of the monthly USA-GER SARIMA model. ---- 475
Figure 206. Residual PACF plot of the monthly USA-GER SARIMA model. ---- 475
Figure 207. 90% P.I. S/ARIMA model for USAAUS monthly series. ---- 476
Figure 208. 90% P.I. SARIMA model for USAGER monthly series. ---- 476
Figure 209. 90% P.I. SARIMA model for USAITA monthly series. ---- 477
Figure 210. 90% P.I. SARIMA model for USAJAP monthly series. ---- 477
Figure 211. 90% P.I. SARIMA model for USASPA monthly series. ---- 478
Figure 212. 90% P.I. SARIMA model for WLDAUS monthly series. ---- 478
Figure 213. 90% P.I. SARIMA model for WLDGER monthly series. ---- 479
Figure 214. 90% P.I. SARIMA model for WLDITA monthly series. ---- 479
Figure 215. 90% P.I. SARIMA model for WLDJAP monthly series. ---- 480
Figure 216. 90% P.I. SARIMA model for WLDSPA monthly series. ---- 480
Figure 217. 90% P.I. SARIMA model for USAAUS quarterly series. ---- 481
Figure 218. 90% P.I. SARIMA model for USAGER quarterly series. ---- 481
Figure 219. 90% P.I. SARIMA model for USAITA quarterly series. ---- 482
Figure 220. 90% P.I. SARIMA model for USAJAP quarterly series. ---- 482
Figure 221. 90% P.I. SARIMA model for USASPA quarterly series. ---- 483
Figure 222. 90% P.I. SARIMA model for WLDAUS quarterly series. ---- 483
Figure 223. 90% P.I. SARIMA model for WLDGER quarterly series. ---- 484
Figure 224. 90% P.I. SARIMA model for WLDITA quarterly series. ---- 484
Figure 225. 90% P.I. SARIMA model for WLDJAP quarterly series. ---- 485
Figure 226. 90% P.I. SARIMA model for WLDSPA quarterly series. ---- 485
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