Geodetic time series analysis in Earth sciences Intro Foreword: Welcome to the Not So Spherical Cow Preface References Contents Editors and Contributors Abbreviations 1 The Art and Science of Trajectory Modelling 1.1 Introduction 1.2 Trajectory Models 1.3 A Gallery of Geodetic Trajectories 1.4 Automatic Signal Decomposition Using GrAtSiD 1.5 Conclusions References 2 Introduction to Geodetic Time Series Analysis 2.1 Gaussian Noise and the Likelihood Function 2.2 Linear Models 2.3 Models for the Covariance Matrix 2.4 Power Spectral Density 2.5 Numerical Examples 2.6 Discussion References 3 Markov Chain Monte Carlo and the Application to Geodetic Time Series Analysis 3.1 Introduction 3.2 Markov Chain Monte Carlo as a Parameter Estimation Method 3.2.1 Fundamentals 3.2.2 The Random Walk Metropolis Hasting Algorithm 3.2.3 The Markov Chain Monte Carlo Algorithm 3.3 General Considerations for Markov Chain Monte Carlo 3.3.1 The Equilibrium State 3.3.2 The Acceptance Rate 3.3.3 The Spectrum of the Markov Chain 3.4 Applications 3.4.1 Position Time Series 3.4.2 Plate Motion Models 3.4.3 Gravity Time Series 3.4.4 Mean Sea Level Time Series 3.5 Summary References 4 Introduction to Dynamic Linear Models for Time Series Analysis 4.1 Introduction to Dynamic Linear Models 4.2 State Space Description 4.2.1 Example: Spline Smoothing 4.3 DLM as Hierarchical Statistical Model 4.4 State and Parameter Estimation 4.5 Recursive Kalman Formulas 4.6 Simulation Smoother 4.7 Estimating the Static Structural Parameters 4.8 Analysing Trends 4.9 Examples of Different DLM Models 4.9.1 The Effect of Level and Trend Variance Parameters 4.9.2 Seasonal Component 4.9.3 Autoregressive Process 4.9.4 Regression Covariates and Proxy Variables 4.10 Synthetic GNSS Example.