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Table of Contents
Preface; Contents; 1 Introduction; Abstract; 1.1 General; 1.2 Trend Definition and Analysis; 1.2.1 Conceptual and Visual Trends; 1.2.2 Mathematical Trend; 1.2.3 Statistical Trend; 1.3 Trend in Some Disciplines; 1.3.1 Atmospheric Sciences; 1.3.2 Environmental Sciences; 1.3.3 Earth Sciences; 1.3.4 Engineering; 1.3.5 Global Warming; 1.3.6 Climate Change; 1.3.7 Social Sciences; 1.3.7.1 Economy; 1.3.7.2 Business; 1.3.7.3 Health; 1.4 Pros and Cons of Trend Analysis; 1.5 Future Research Directions; 1.6 Purpose of This Book; References; 2 Uncertainty and Time Series; Abstract; 2.1 General
2.2 Random and Randomness2.3 Empirical Frequency and Distribution Function; 2.3.1 Empirical Frequency and Trend; 2.4 Theoretical Probability Distribution Function (Pdf); 2.5 Statistical Modeling; 2.5.1 Deterministic-Uncertain Model; 2.5.2 Probabilistic-Statistical Model; 2.5.3 Transitional Probability Model; 2.6 Stochastic Models; 2.6.1 Homogeneity (Consistency); 2.6.2 Stationarity; 2.6.3 Periodicity (Seasonality); 2.6.3.1 Known Period Case; 2.7 Time Series Truncation; 2.7.1 Statistical Truncations; 2.8 Data Smoothing; 2.8.1 Moving Averages; 2.8.2 Difference Smoothing; 2.9 Jump (Shift)
2.10 Correlation Coefficients2.10.1 Pearson Correlation Coefficient; 2.10.2 Kendall Correlation Coefficient; 2.10.3 Spearman Correlation Coefficient; 2.11 Persistence/Nonrandomness; 2.11.1 Short-Memory (Correlation) Components; 2.11.2 Long-Memory (Persistence) Component; 2.11.2.1 Rescaled Range and Hurst Phenomenon; References; 3 Statistical Trend Tests; Abstract; 3.1 General; 3.2 Nonparametric Tests; 3.2.1 Data Ordering (Ranks); 3.3 Statistical Tests; 3.3.1 Wald-Wolfowitz; 3.3.2 Sign Test; 3.3.3 Sign Difference Test; 3.3.4 Run Test; 3.3.5 Mann-Whitney (MW) Test
3.3.6 Kruskal-Wallis (KW) Test3.3.7 Nonparametric Correlation Coefficient; 3.3.8 Spearman's Rho Test of Trend; 3.3.9 Turning Point Test; 3.3.10 Mann-Kendall (MK) Test; 3.3.10.1 Mann-Kendall Trend Search; 3.3.10.2 Sen Slope Estimator; 3.3.10.3 Spearman's Tau; 3.3.10.4 Regression Trend; 3.3.11 Two-Sample Wilcoxon Test; 3.3.11.1 Signed-Wilcoxon Test; 3.3.11.2 Wilcoxon Signed Rank Test; 3.3.12 von Neuman Test; 3.3.13 Cumulative Departures Test; 3.3.13.1 Cumulative Deviations; 3.3.14 Bayesian Test; 3.3.15 Relative Error Test; 3.3.16 t Test; 3.3.17 Cramer Test; 3.3.18 F Test; 3.3.19 Truncation Test
3.3.20 Deviations Test3.3.21 Subtraction Test; 3.3.22 Şen Autorun Test; 3.3.23 Seasonal Kendall Test; 3.4 Unit Root Model Trend Determination; 3.4.1 Integration and Dickey-Fuller (DF) Test; 3.4.2 The Kwiatkowski, Phillips, Schmidt, and Shin Test; 3.4.3 Critical Values of the KPSS Test; 3.4.4 Empirical Power of the KPSS; 3.4.5 Example: Comparison of the DF and KPSS Tests for Several Macro-Economic Time Series; 3.4.5.1 Test of Stationarity Around Mean; 3.4.5.2 Test of Stationarity Around a Linear Trend; 3.5 Parametric Tests; 3.5.1 Regression Analysis; 3.5.2 Regression Line Assumptions
2.2 Random and Randomness2.3 Empirical Frequency and Distribution Function; 2.3.1 Empirical Frequency and Trend; 2.4 Theoretical Probability Distribution Function (Pdf); 2.5 Statistical Modeling; 2.5.1 Deterministic-Uncertain Model; 2.5.2 Probabilistic-Statistical Model; 2.5.3 Transitional Probability Model; 2.6 Stochastic Models; 2.6.1 Homogeneity (Consistency); 2.6.2 Stationarity; 2.6.3 Periodicity (Seasonality); 2.6.3.1 Known Period Case; 2.7 Time Series Truncation; 2.7.1 Statistical Truncations; 2.8 Data Smoothing; 2.8.1 Moving Averages; 2.8.2 Difference Smoothing; 2.9 Jump (Shift)
2.10 Correlation Coefficients2.10.1 Pearson Correlation Coefficient; 2.10.2 Kendall Correlation Coefficient; 2.10.3 Spearman Correlation Coefficient; 2.11 Persistence/Nonrandomness; 2.11.1 Short-Memory (Correlation) Components; 2.11.2 Long-Memory (Persistence) Component; 2.11.2.1 Rescaled Range and Hurst Phenomenon; References; 3 Statistical Trend Tests; Abstract; 3.1 General; 3.2 Nonparametric Tests; 3.2.1 Data Ordering (Ranks); 3.3 Statistical Tests; 3.3.1 Wald-Wolfowitz; 3.3.2 Sign Test; 3.3.3 Sign Difference Test; 3.3.4 Run Test; 3.3.5 Mann-Whitney (MW) Test
3.3.6 Kruskal-Wallis (KW) Test3.3.7 Nonparametric Correlation Coefficient; 3.3.8 Spearman's Rho Test of Trend; 3.3.9 Turning Point Test; 3.3.10 Mann-Kendall (MK) Test; 3.3.10.1 Mann-Kendall Trend Search; 3.3.10.2 Sen Slope Estimator; 3.3.10.3 Spearman's Tau; 3.3.10.4 Regression Trend; 3.3.11 Two-Sample Wilcoxon Test; 3.3.11.1 Signed-Wilcoxon Test; 3.3.11.2 Wilcoxon Signed Rank Test; 3.3.12 von Neuman Test; 3.3.13 Cumulative Departures Test; 3.3.13.1 Cumulative Deviations; 3.3.14 Bayesian Test; 3.3.15 Relative Error Test; 3.3.16 t Test; 3.3.17 Cramer Test; 3.3.18 F Test; 3.3.19 Truncation Test
3.3.20 Deviations Test3.3.21 Subtraction Test; 3.3.22 Şen Autorun Test; 3.3.23 Seasonal Kendall Test; 3.4 Unit Root Model Trend Determination; 3.4.1 Integration and Dickey-Fuller (DF) Test; 3.4.2 The Kwiatkowski, Phillips, Schmidt, and Shin Test; 3.4.3 Critical Values of the KPSS Test; 3.4.4 Empirical Power of the KPSS; 3.4.5 Example: Comparison of the DF and KPSS Tests for Several Macro-Economic Time Series; 3.4.5.1 Test of Stationarity Around Mean; 3.4.5.2 Test of Stationarity Around a Linear Trend; 3.5 Parametric Tests; 3.5.1 Regression Analysis; 3.5.2 Regression Line Assumptions