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 RangeβLag 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 CramΓ©rβRao 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 CramΓ©rβRao 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