Time Series Analysis

ISBN-13: 9781420059670 / Angielski / Twarda / 2007 / 400 str.

Henrick Madsen; Henrik Madsen

Opis

Providing an accessible yet comprehensive introduction to this important subject, Time Series Analysis emphasizes basic methods for modeling linear dynamic systems. The text presents a solid theoretical understanding of basic concepts, such as multivariate random variables, stochastic processes, and regression-based methods, while also providing a number of practical, real-world examples. It covers advanced topics that include spectral analysis, state space models, and recursive estimation. With a variety of both written and computer-based exercises, the text gives computational guidance to readers and includes an appendix on software options.

Spis treści

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

O autorze

Henrik Madsen