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Modeling Malaysian Road Accidents: the Structural Time Series Approach MODELING MALAYSIAN ROAD ACCIDENTS: THE STRUCTURAL TIME SERIES APPROACH NOOR WAHIDA BINTI MD JUNUS UNIVERSITI SAINS MALAYSIA 2018 MODELING MALAYSIAN ROAD ACCIDENTS: THE STRUCTURAL TIME SERIES APPROACH by NOOR WAHIDA BINTI MD JUNUS Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy January 2018 ACKNOWLEDGEMENT First and foremost praise to Allah the Almighty who give knowledge, strength and determination to finally finish my thesis even though the journey was so hard. This success cannot be achieved without the guidance and assistance from others. Therefore I would like to express my sincere gratitude to my supervisor Assoc. Prof. Dr. Mohd Tahir Ismail for the continuous support of my Ph.D study and related research, for his patience, motivation, and immense knowledge. Besides, I would like to thank my co-supervisor Dr. Zainudin Arsad for his insightful comments and encouragement, but also for the hard question which incented me to widen my research from various perspectives. A very special gratitude goes out to Ministry of Higher Education as well as Sultan Idris Education University for helping and providing the funding of my study. This special gratitude also goes to Institute of Postgraduate Study and School of Mathematical Sciences that supported several conference fees along my study period. Finally I am grateful to my family members especially my mother who have provided me through moral and emotional support in my life. Last but by no means least, to all my friends especially everyone in School of Mathematical Sciences postgraduate lab, it was great sharing laboratory with all of you during last four years. Thanks for all your encouragement. ii TABLE OF CONTENTS ACKNOWLEDGEMENT ii TABLE OF CONTENTS iii LIST OF TABLES viii LIST OF FIGURES xi LIST OF SYMBOLS AND ABBREVIATIONS xiii ABSTRAK xxi ABSTRACT xxiii CHAPTER 1- INTRODUCTION 1.1 Background of the Study 1 1.2 Motivation and Problem Statements 4 1.3 Objective 5 1.4 Contribution of the Study 7 1.5 Scope of data 8 1.5.1 Road Accidents 9 1.5.2 Climate Related Variables 10 1.5.3 Economic Related Variables 13 1.5.4 Seasonal Related Variables 14 1.5.5 Road Safety Related Variables 17 1.6 Limitation of the Study 18 1.7 Summary and Thesis Organization 19 CHAPTER 2 - LITERATURE REVIEW 2.1 Structural Time Series 21 2.2 Advantages of Structural Time Series 23 iii 2.3 Application of the Structural Time Series Model 24 2.3.1 Economics 24 2.3.2 Meteorology, Ecology and Agriculture 26 2.3.3 Other Disciplines 27 2.4 Common Techniques of Road Safety Modeling 28 2.5 Structural Time Series in Road Safety 43 2.6 Comparison of Road Accidents Models between This Study with Previous Studies 47 2.7 Summary 49 CHAPTER 3 - METHODOLOGY 3.1 Properties of Data 50 3.1.1 Descriptive Statistics 50 3.1.2 Time Series Plot 52 3.1.3 Correlation analysis 52 3.1.4 Unit Root Test 53 3.2 Regression Analysis 55 3.2.1 Time Series Regression 55 3.2.2 Parameter Estimation and Hypothesis Testing 56 3.2.3 Diagnostics Checking 59 3.3 Box and Jenkins Analysis 62 3.3.1 Box and Jenkins ARIMA Model 63 3.3.2 Box and Jenkins Model Identification 66 3.3.3 Box and Jenkins Model Estimation and Validation 70 3.4 Structural Time Series 72 3.4.1 Trend Model 73 iv 3.4.2 Seasonal Model 74 3.4.3 Incorporating Explanatory and Intervention Variable 76 3.4.4 State Space Form 77 3.4.5 Kalman Filter Estimation 79 3.5 Evaluation of Structural Time Series Model 82 3.5.1 Model Diagnostic 82 3.5.2 Goodness-of-fit of Structural Time Series 84 3.6 Application on Road Accidents 85 3.7 Summary 87 CHAPTER 4 - PRELIMINARY STUDY 4.1 Descriptive Statistics 89 4.1.1 Road Accidents Series 89 4.1.2 Climate Related Variable 90 4.1.3 Economic Related Variables 92 4.2 Time Series Plot 93 4.2.1 Road Accident Series 93 4.2.2 Climate Related Variables 97 4.2.3 Economic Related Variables 108 4.3 Correlation Analysis 110 4.3.1 Correlation Analysis for Regions 111 4.3.2 Correlation Analysis for Individual State 112 4.3.3 Unit Root Test 113 4.4 Time Series Regression 114 4.4.1 Time Series Regression with Seasonal Dummies 115 4.4.2 Incorporating Explanatory Variables 119 v 4.5 Box and Jenkins SARIMA 130 4.5.1 Estimating SARIMA Model for Regional Road Accidents 131 4.5.2 Estimating SARIMA Model for Individual States Road Accidents 132 4.6 Summary 134 CHAPTER 5 - MODELING UNIVARIATE ROAD ACCIDENTS MODEL 5.1 Model Estimation 135 5.1.1 Estimating Road Accident Model for Northern Region 136 5.1.2 Estimating Road Accident Model for Other Regions 137 5.2 Understanding Estimated Regional Road Accidents Model. 141 5.2.1 Trend Pattern of Regional Road Accidents 141 5.2.2 Seasonal Pattern for Regional Road Accidents 145 5.3 Estimating Road Accidents Model for Individual State Level 148 5.3.1 Northern State Road Accidents Pattern 150 5.3.2 Road Accidents Pattern for Other States 155 5.4 Special Features of Seasonal Road Accidents Pattern 166 5.5 Prediction and Forecasting Performance of the Structural Time Series 167 5.6 Summary 174 CHAPTER 6 - INCORPORATING EXPLANATORY AND INTERVENTION VARIABLE OF ROAD ACCIDENTS MODEL 6.1 Estimating and Understanding Regional Road Accidents Model 176 6.1.1 Error Estimate 178 6.1.2 Estimation of Trend and Seasonal Component 181 6.1.3 Estimation of Explanatory Variables 187 6.1.4 Observing Outliers and Structural Breaks 188 vi 6.2 Estimating and Understanding Individual State Road Accidents Model 191 6.2.1 Error Estimate 193 6.2.1 States Level Road Accidents Pattern with Explanatory Variables 197 6.2.2 Estimation of Explanatory Variables 210 6.2.3 Observing Possible Outliers and Structural Breaks 213 6.3 Prediction Performance of STS with Explanatory Variables 214 6.4 Summary 222 CHAPTER 7 - CONCLUSION AND RECOMMENDATION 7.1 Concluding Remarks 224 7.2 Implications of the Study 227 7.3 Suggestion for Future Research 229 REFERENCES 230 APPENDICES LIST OF PUBLICATIONS vii LIST OF TABLES Page Table 1.1: List of Variables and unit of measurements 9 Table 1.2: Aggregated regions and their corresponding states 10 Table 1.3: Location of stations that record climate related variables 12 Table 1.4: Computation of Aggregation Samples 12 Table 1.5: An example of BLKG coding 16 Table 1.6: An example of SAFE coding 18 Table 2.1: Recent studies on application of structural time series 27 Table 2.2: Recent methods/ models used in road safety study 38 Table 2.3: Recent studies on the application of structural time series on 45 road safety Table 2.4: Comparisons between model used in this thesis with 49 previous models Table 3.1: Value range of coefficient of correlation 53 Table 3.2: Durbin-Watson test decision 60 Table 3.3: Model identification 69 Table 3.4: Structural time series specification model (trend+seasonal) 75 Table 4.1: Descriptive statistics of road accidents series 90 Table 4.2: Descriptive statistics of climate related variables 91 Table 4.3: Descriptive statistics of the monthly economic related 93 variables Table 4.4: Correlation coefficient between number of road accident for 111 each region with selected dependent variables Table 4.5: Correlation coefficient between the number of road accidents 113 and selected dependent variables for each state viii Table 4.6: Estimated regional road accidents model 116 Table 4.7: Road accidents model for individual states 117 Table 4.8: Durbin-Watson test of autocorrelation 119 Table 4.9: Variance of inflation factor for regions 120 Table 4.10: Variance of inflation factor for individual states 120 Table 4.11: List of possible outlier observations 121 Table 4.12: Estimated regional road accidents model by incorporating 123 explanatory variables Table 4.13: Estimated individual states’ road accidents model by 127 incorporating explanatory variables Table 4.14: Estimated regional road accidents model based on Box and 131 Jenkins SARIMA models Table 4.15: Estimated road accidents model for individual states based 132 on Box and Jenkins SARIMA models Table 5.1: Estimated results and performance criteria of STS model for 137 northern region road accidents Table 5.2: Estimated results and performance criteria of STS model for 138 central region road accidents Table 5.3: Estimated results and performance criteria of STS model for 139 east coast region road accidents Table 5.4: Estimated results and performance criteria of STS model for 140 southern region road accidents Table 5.5: Estimated results and performance criteria of STS model for 140 Borneo region road accidents Table 5.6: Final estimation results according to regions 142 Table 5.7: Best road accident model specification for each individual 149 state Table 5.8: Final estimation result of northern state road accident model 151 Table 5.9: Final estimation result of central and southern state road 155 accident model ix Table 5.10: Final estimation results of east coast and Borneo states road 161 accident models Table 5.11: Special feature of seasonality of road accidents pattern 166 Table 5.12: Error values for prediction road accidents models 173 Table 5.13: Error values for forecasting road accidents models 174 Table 6.1: Estimation of regional road accidents after adding 178 explanatory variables Table 6.2: Final road accidents model estimates with explanatory 182 variables Table 6.3: Estimation of state level road accidents with explanatory 192 variables Table 6.4: Final estimate of road accidents model with the explanatory 195 variables Table 6.5: Error values for prediction road accidents models with 221 explanatory variables x LIST OF FIGURES Page Figure 1.1: 16 An illustration of process determining g1 and g2 Figure 3.1: Box and Jenkins methodology 67 Figure 3.2: Box and Jenkins model identification process 69 Figure 3.3: Step by step procedure of designing of road accidents 86 modeling Figure 4.1: Monthly time series plot of road accidents for all regions.
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