Dynamic Stochastic Models from Empirical Data
Erschienen am 14. Mai 2014
351 Seiten
978-0-08-095631-2 (ISBN)
Beschreibung
Dynamic Stochastic Models from Empirical Data
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Inhalt
- Front Cover
- Dynamic Stochastic Models from Empirical Data
- Copyright Page
- Contents
- Preface
- Acknowledgments
- Notation and Symbols
- CHAPTER I. INTRODUCTION TO THE CONSTRUCTION OF MODELS
- 1a. Nature and Goals of Modeling
- 1b. Description of Models
- 1c. Choice of a Model for the Given Data
- 1d. Validation
- Notes
- CHAPTER II. PRELIMINARY ANALYSIS OF STOCHASTIC DYNAMICAL SYSTEMS
- Introduction
- 2a. Assumptions and Discussion
- 2b. Stationarity
- 2c. Invertibility
- 2d. Covariance Functions and Correlograms
- 2e. Spectral Analysis
- 2f. Prediction
- 2g. Prediction in Multiplicative Systems
- 2h. Prediction in Systems with Noisy Observations
- 2i. Rescaled Range-Lag Characteristic
- 2j. Fractional Noise Models
- 2k. Conclusions
- Appendix 2.1. Characteristics of Fractional Noise Models
- Problems
- CHAPTER III. STRUCTURE OF UNIVARIATE MODELS
- Introduction
- 3a. Types of Dynamic Stochastic Models
- 3b. Types of Empirical Time Series
- 3c. Causality
- 3d. Choice of Time Scale for Modeling
- 3e. Conclusions
- Notes
- Problems
- CHAPTER IV. ESTIMABILITY IN SINGLE OUTPUT SYSTEMS
- Introduction
- 4a. Estimability of Systems in Standard Form
- 4b. Estimability in Systems with Noisy Observations
- 4c. Estimability in Systems with AR Disturbances
- 4d. The Estimation Accuracy
- 4e. Conclusions
- Appendix 4.1
- Appendix 4.2. Evaluation of the Cramér-Rao Matrix Lower Bound in Single Output Systems
- Problems
- CHAPTER V. STRUCTURE AND ESTIMABILITY IN MULTIVARIATE SYSTEMS
- Introduction
- 5a. Characterization
- 5b. The Triangular Canonical Forms
- 5c. Diagonal Canonical Forms
- 5d. Pseudocanonical Forms
- 5e. Discussion of the Three Canonical Forms
- 5f. Estimation Accuracy
- 5g. Conclusions
- Appendix 5.1. Proofs of Theorems
- Problems
- CHAPTER VI. ESTIMATION IN AUTOREGRESSIVE PROCESSES
- Introduction
- 6a. Maximum Likelihood Estimators
- 6b. Bayesian Estimators
- 6c. Quasi-Maximum Likelihood (QML) Estimators in Single Output Systems
- 6d. Computational Methods
- 6e. Combined Parameter Estimation and Prediction
- 6f. Systems with Slowly Varying Coefficients
- 6g. Robust Estimation in AR Models
- 6h. Conclusions
- Appendix 6.1. Proofs of Theorems in Section 6a
- Appendix 6.2. The Expressions for the Posterior Densities
- Appendix 6.3. The Derivation of Computational Algorithms
- Appendix 6.4. Evaluation of the Cramér-Rao Lower Bound in Multi- variate AR Systems
- Problems
- CHAPTER VII. PARAMETER ESTIMATION IN SYSTEMS WITH BOTH MOVING AVERAGE AND AUTOREGRESSIVE TERMS
- Introduction
- 7a. Maximum Likelihood Estimators
- 7b. Numerical Methods for CML Estimation
- 7c. Limited Information Estimates
- 7d. Numerical Experiments with Estimation Methods
- 7e. Conclusions
- Problems
- CHAPTER VIII. CLASS SELECTION AND VALIDATION OF UNIVARIATE MODELS
- Introduction
- 8a.The Nature of the Selection Problem
- 8b.The Different Methods of Class Selection
- 8c. Validation of Fitted Models
- 8d. Discussion of Selection and Validation
- 8e. Conclusions
- Appendix 8.1. Mean Square Prediction Error of Redundant Models
- Problems
- CHAPTER IX. CLASS SELECTION AND VALIDATION OF MULTIVARIATE MODELS
- Introduction
- 9a. Nature of the Selection Problem
- 9b. Causality and the Construction of Preliminary Models
- 9c. Direct Comparison of Multivariate Classes of Models
- 9d. Validation of Models
- 9e. Conclusions
- Appendix 9.1. Geometry of Correlation and Regression
- Notes
- Problems
- CHAPTER X. MODELING RIVER FLOWS
- 10a. The Need and Scope of Modeling
- 10b. Discussion of Data
- 10c. Models for Monthly Flows
- 10d. Modeling Daily Flow Data
- 10e. Models for Annual Flow Data
- 10f. Conclusions
- Notes
- CHAPTER XI. SOME ADDITIONAL CASE STUDIES IN MODEL BUILDING
- Introduction
- 11a. Modeling Some Biological Populations
- 11b. Analysis of the Annual Sunspot Series
- 11c. The Sales Data of Company X: An Empirical Series with Both Growth and Systematic Oscillations
- 11d. The Time Series E2 : Role of Moving Average Terms
- 11e. Causal Connection between Increases in Rainfall and Increased Urbanization
- 11f. A Multivariate Model for Groundwater Levels and Precipitation
- 11g. Conclusions
- References
- Index
