Time Series Modelling in Earth Sciences

B.K. Sahu Department of Earth Sciences, IIT Bombay, Mumbai, India

• 1. Introduction 1.1 Dynamic Earth 1.2 Time/Spatial Series 1.3 Time Domain Analysis 1.4 Frequency Domain Analysis 1.5 Spectral Analysis 1.6 Simple Time Series Models 1.7 Model Validation and Inferences 1.8 State-Space Model and Kalman Filtering 1.9 Procedures for Time Series Data Analysis 1.10 Examples 2. Stationary Univariate Time Series Models 2.1 Introduction 2.2 Stationary Processes 2.3 Identification 2.4 Forecasting 2.5 Purely Seasonal ARMA Models ARMA(P, Q)s 2.6 Model Genesis and Realization 2.7 Examples 3. Non-Stationary Univariate Time Series Models 3.1 Introduction 3.2 Transformations for Stationarity 3.3 Unit Root Problems 3.4 Forecasting ARIMA Models 3.5 SARIMA Models 4. Vector and Multidimensional Time Series Analysis 4.1 Introduction 4.2 Multivariate ARMA Processes 4.3 Transfer Function Models 4.4 Forecasting Techniques 4.5 Some Case Studies from Economic Geology 5. Advanced Time Series Models 5.1 Introduction 5.2 State-Space Models 5.3 Dynamic Linear Modelling (DLM) with Switching 5.4 Non-Linear Models