Madsen Time Series Analysis

1. Auflage 2007
ISBN: 978-1-4200-5968-7
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 400 Seiten

Reihe: Chapman & Hall/CRC Texts in Statistical Science

With a focus on analyzing and modeling linear dynamic systems using statistical methods, Time Series Analysis formulates various linear models, discusses their theoretical characteristics, and explores the connections among stochastic dynamic models. Emphasizing the time domain description, the author presents theorems to highlight the most important results, proofs to clarify some results, and problems to illustrate the use of the results for modeling real-life phenomena. The book first provides the formulas and methods needed to adapt a second-order approach for characterizing random variables as well as introduces regression methods and models, including the general linear model. It subsequently covers linear dynamic deterministic systems, stochastic processes, time domain methods where the autocorrelation function is key to identification, spectral analysis, transfer-function models, and the multivariate linear process. The text also describes state space models and recursive and adaptivemethods. The final chapter examines a host of practical problems, including the predictions of wind power production and the consumption of medicine, a scheduling system for oil delivery, and the adaptive modeling of interest rates. Concentrating on the linear aspect of this subject, Time Series Analysis provides an accessible yet thorough introduction to the methods for modeling linear stochastic systems. It will help you understand the relationship between linear dynamic systems and linear stochastic processes.

Zielgruppe

Researchers and advanced undergraduate and graduate students of statistics and mathematics; postgrad students and researchers of epidemiology, econometrics, engineering, and biology.

Autoren/Hrsg.

Madsen, Henrik

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Preface

Introduction

Examples of time series

A first crash course

Contents and scope of the book

Multivariate random variables

Joint and marginal densities

Conditional distributions

Expectations and moments

Moments of multivariate random variables

Conditional expectation

The multivariate normal distribution

Distributions derived from the normal distribution

Linear projections

Problems

Regression-based methods

The regression model

The general linear model (GLM)

Prediction

Regression and exponential smoothing

Time series with seasonal variations

Global and local trend model—an example

Problems

Linear dynamic systems

Linear systems in the time domain

Linear systems in the frequency domain

Sampling

The z transform

Frequently used operators

The Laplace transform

A comparison between transformations

Problems

Stochastic processes

Introduction

Stochastic processes and their moments

Linear processes

Stationary processes in the frequency domain

Commonly used linear processes

Non-stationary models

Optimal prediction of stochastic processes

Problems

Identification, estimation, and model checking

Introduction

Estimation of covariance and correlation functions

Identification

Estimation of parameters in standard models

Selection of the model order

Model checking

Case study: Electricity consumption

Problems

Spectral analysis

The periodogram

Consistent estimates of the spectrum

The cross-spectrum

Estimation of the cross-spectrum

Problems

Linear systems and stochastic processes

Relationship between input and output processes

Systems with measurement noise

Input-output models

Identification of transfer-function models

Multiple-input models

Estimation

Model checking

Prediction in transfer-function models

Intervention models

Problems

Multivariate time series

Stationary stochastic processes and their moments

Linear processes

The multivariate ARMA process

Non-stationary models

Prediction

Identification of multivariate models

Estimation of parameters

Model checking

Problems

State space models of dynamic systems

The linear stochastic state space model

Transfer function and state space formulations

Interpolation, reconstruction, and prediction

Some common models in state space form

Time series with missing observations

ML estimates of state space models

Problems

Recursive estimation

Recursive LS

Recursive pseudo-linear regression (RPLR)

Recursive prediction error methods (RPEM)

Model-based adaptive estimation

Models with time varying parameters

Real life inspired problems

Prediction of wind power production

Prediction of the consumption of medicine

Effect of chewing gum

Prediction of stock prices

Wastewater treatment: Using root zone plants

Scheduling system for oil delivery

Warning system for slippery roads

Statistical quality control

Modeling and control

Sales numbers

Modeling and prediction of stock prices

Adaptive modeling of interest rates

appendix A: The solution to difference equations

appendix B: Partial autocorrelations

appendix C: Some results from trigonometry

appendix D: List of Acronyms

appendix E: List of symbols

Bibliography

Index