Innovative Trend Methodologies in Science and Engineering (eBook)

Prof. Zekâi Şen obtained his B.Sc. and M.Sc. degrees from Technical University of İstanbul, Civil Engineering Faculty, Department of Reinforced Concrete in 1971. His further post-graduate studies were carried out at the University of London, Imperial College of Science and Technology. He was granted Diploma of Imperial College (D.I.C) and M.Sc. in Engineering Hydrology in 1972 and Ph. D. in stochastic hydrology in 1974. He worked in different countries such as England, Norway, Saudi Arabia and Turkey. He worked in different faculties as the head of department. His main interests are hydrology, water resources, hydrogeology, hydrometeorology, hydraulics, science philosophy and history. He has published numerous (Science Citation Indexed) SCI scientific papers in different internationally top journals on various topics in addition to numerous publications in international conferences, symposiums and technical reports as well as edited proceedings and books. Under his supervision many students from different countries (Turkey, Saudi Arabia, Yemen, Jordan, Libya, and Pakistan) have obtained Ph. D. degrees in different energy aspects and water science topics. He holds several national and international scientific prizes and the most recent one is given as a team work due to his contribution to "Nobel Peace Prize" through his works in IPCC form 2002-2007 concerning Climate Change. He is currently working at the Technical University of Istanbul, Civil Engineering Faculty. He is also the president of Turkish Water Foundation.

Preface 6
Contents 8
1 Introduction 13
Abstract 13
1.1 General 13
1.2 Trend Definition and Analysis 15
1.2.1 Conceptual and Visual Trends 16
1.2.2 Mathematical Trend 19
1.2.3 Statistical Trend 21
1.3 Trend in Some Disciplines 23
1.3.1 Atmospheric Sciences 24
1.3.2 Environmental Sciences 24
1.3.3 Earth Sciences 24
1.3.4 Engineering 25
1.3.5 Global Warming 25
1.3.6 Climate Change 26
1.3.7 Social Sciences 26
1.3.7.1 Economy 27
1.3.7.2 Business 27
1.3.7.3 Health 28
1.4 Pros and Cons of Trend Analysis 29
1.5 Future Research Directions 29
1.6 Purpose of This Book 30
References 31
2 Uncertainty and Time Series 33
Abstract 33
2.1 General 33
2.2 Random and Randomness 36
2.3 Empirical Frequency and Distribution Function 37
2.3.1 Empirical Frequency and Trend 40
2.4 Theoretical Probability Distribution Function (Pdf) 42
2.5 Statistical Modeling 44
2.5.1 Deterministic-Uncertain Model 46
2.5.2 Probabilistic-Statistical Model 47
2.5.3 Transitional Probability Model 48
2.6 Stochastic Models 49
2.6.1 Homogeneity (Consistency) 50
2.6.2 Stationarity 51
2.6.3 Periodicity (Seasonality) 52
2.6.3.1 Known Period Case 55
2.7 Time Series Truncation 57
2.7.1 Statistical Truncations 59
2.8 Data Smoothing 61
2.8.1 Moving Averages 62
2.8.2 Difference Smoothing 62
2.9 Jump (Shift) 64
2.10 Correlation Coefficients 65
2.10.1 Pearson Correlation Coefficient 66
2.10.2 Kendall Correlation Coefficient 70
2.10.3 Spearman Correlation Coefficient 71
2.11 Persistence/Nonrandomness 73
2.11.1 Short-Memory (Correlation) Components 73
2.11.2 Long-Memory (Persistence) Component 74
2.11.2.1 Rescaled Range and Hurst Phenomenon 75
References 77
3 Statistical Trend Tests 79
Abstract 79
3.1 General 79
3.2 Nonparametric Tests 80
3.2.1 Data Ordering (Ranks) 81
3.3 Statistical Tests 82
3.3.1 Wald–Wolfowitz 82
3.3.2 Sign Test 82
3.3.3 Sign Difference Test 83
3.3.4 Run Test 84
3.3.5 Mann–Whitney (MW) Test 85
3.3.6 Kruskal–Wallis (KW) Test 91
3.3.7 Nonparametric Correlation Coefficient 95
3.3.8 Spearman’s Rho Test of Trend 96
3.3.9 Turning Point Test 97
3.3.10 Mann–Kendall (MK) Test 98
3.3.10.1 Mann–Kendall Trend Search 101
3.3.10.2 Sen Slope Estimator 102
3.3.10.3 Spearman’s Tau 103
3.3.10.4 Regression Trend 103
3.3.11 Two-Sample Wilcoxon Test 104
3.3.11.1 Signed-Wilcoxon Test 105
3.3.11.2 Wilcoxon Signed Rank Test 105
3.3.12 von Neuman Test 106
3.3.13 Cumulative Departures Test 107
3.3.13.1 Cumulative Deviations 107
3.3.14 Bayesian Test 109
3.3.15 Relative Error Test 110
3.3.16 t Test 111
3.3.17 Cramer Test 114
3.3.18 F Test 115
3.3.19 Truncation Test 118
3.3.20 Deviations Test 119
3.3.21 Subtraction Test 119
3.3.22 ?en Autorun Test 120
3.3.23 Seasonal Kendall Test 123
3.4 Unit Root Model Trend Determination 124
3.4.1 Integration and Dickey–Fuller (DF) Test 125
3.4.2 The Kwiatkowski, Phillips, Schmidt, and Shin Test 126
3.4.3 Critical Values of the KPSS Test 129
3.4.4 Empirical Power of the KPSS 130
3.4.5 Example: Comparison of the DF and KPSS Tests for Several Macro-Economic Time Series 133
3.4.5.1 Test of Stationarity Around Mean 133
3.4.5.2 Test of Stationarity Around a Linear Trend 136
3.5 Parametric Tests 136
3.5.1 Regression Analysis 138
3.5.2 Regression Line Assumptions 139
3.5.3 Goodness of Fit (R2) for Regression 140
3.5.4 Cumulative Sum (CUSUM) Method 141
References 142
4 Temporal Trend Analysis 145
Abstract 145
4.1 General 145
4.2 Visual Inspection 147
4.3 Monotonic Trend Analysis 149
4.4 Scatter Diagrams and Regression Model 150
4.5 Linear Regression Model 153
4.5.1 Statistical Procedure 154
4.6 Unrestricted Regression Model 157
4.6.1 Application 159
4.7 Partial Regression Method (PRM) 160
4.8 Cluster Regression and Markov Chain 163
4.8.1 Cluster Regression Model 164
4.8.2 Application and Discussion 165
4.9 Trend Over-whitening Procedures 171
4.9.1 Over-whitening (OW) Process 172
4.9.2 Simulation 176
4.9.3 Application 177
References 185
5 Innovative Trend Analyses 187
Abstract 187
5.1 General 187
5.2 Probability Distribution-Statistical Parameter Trend Implications 189
5.3 Innovative Trend Identification Methodologies 194
5.3.1 Application 196
5.4 Innovative Trend Simulation 198
5.4.1 Fundamental Methodology 200
5.4.1.1 Simulation Methodology 201
5.4.1.2 Dependent Process Simulation Results 204
5.5 Innovative Trend Significance Test 211
5.5.1 Deterministic Basis 212
5.5.2 Stochastic Basis 214
5.5.2.1 Normally Distributed Stochastic Time Series 214
5.5.2.2 Gamma Distributed Stochastic Time Series 215
5.5.3 Statistical Innovative Trend Test 216
5.5.4 Application 217
5.6 Crossing Trend Analysis Methodology 222
5.6.1 Rational Concept 224
5.6.2 Theoretical Background 224
5.6.3 Monte Carlo Simulations 227
5.6.4 Application 227
References 237
6 Spatial Trend Analysis 239
Abstract 239
6.1 General 239
6.2 Numerical Solution 242
6.3 Spatial Data Analysis 244
6.4 Homogeneity and Isotropy 247
6.5 Spatial Trend Surfaces 250
6.5.1 Horizontal Plane 252
6.5.2 Horizontal Planes 253
6.5.3 Inclined Trend Plane 253
6.5.4 Inclined Trend Planes 254
6.5.5 Curved Trend Surface 255
6.5.6 Random Surface 255
6.6 Spatial Dependence Function (SDF) 257
6.6.1 Spatial Correlation Parameter Calculation 259
6.7 Double Mass Curve Test 262
6.8 Trend Surface Analysis 266
6.8.1 Planer Trend Regression Analysis 266
6.8.2 Polynomial Trend Regression Analysis 269
6.8.3 Kriging Methodology 274
6.8.3.1 Simple Kriging (SK) 277
Methodology 277
6.9 Triple Diagram Model (TDM) 283
6.9.1 Parallel-Triple Model 284
6.9.2 Serial-Triple Model 288
References 292
7 Trend Variability Detection 293
Abstract 293
7.1 General 293
7.2 Variability Measures 295
7.2.1 Range 295
7.2.2 Standard Deviation 296
7.2.3 The Interquartile Range (IQR) 298
7.2.4 Investment Variability 299
7.3 Trend and Variability Detection by Innovative Methodology 300
7.3.1 Methodology 301
7.3.2 Simulation Study 304
7.3.3 Applications 306
7.4 Trend Significance Limits 309
7.5 Trend and Variability Analyses by Innovative and Classical Methodologies 316
7.5.1 ?en Innovative Trend Analysis 317
7.6 Application and Interpretations 318
7.6.1 Probability Distribution Functions (pdf) 320
7.6.2 Different Trends 321
7.7 Trend and Variability 323
7.8 Innovative Trend Template and Significance Limits 326
References 329
8 Partial Trend Detection 332
Abstract 332
8.1 General 332
8.2 Qualitative Partial Trend Methodology 335
8.3 Previous Works 337
8.4 Innovative Piecewise Trend Analysis 341
8.5 Innovative Trend Template 346
8.6 Stochastic Simulation Approach 348
8.7 Data and the Study Area 352
8.7.1 Partial Trend Groups 352
8.7.2 Partial Trend Lines 353
References 356
Index 358