Dynamic stochastic models from empirical data / R. L. Kashyap, A. Ramachandra Rao.

Format:

Book

Author/Creator:

Kashyap, Rangasami L. (Rangasami Laksminarayana), 1938-

Contributor:

Rao, A. Ramachandra (Adiseshappa Ramachandra), 1939-

Series:

Mathematics in science and engineering ; v. 122.

Mathematics in science and engineering ; v. 122

Language:

English

Subjects (All):

Time-series analysis.

Stochastic processes.

Estimation theory.

System analysis.

Physical Description:

1 online resource (351 p.)

Place of Publication:

New York : Academic Press, 1976.

Language Note:

English

Summary:

Dynamic stochastic models from empirical data

Contents:

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 Observations2i. 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 Disturbances4d. 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 Estimators6b. 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 TERMSIntroduction; 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

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 325-330) and index.

ISBN:

1-282-28925-X

9786612289255

0-08-095631-9

OCLC:

316568482