id: 06379552
dt: b
an: 2015d.00864
au: Lindgren, Georg; Rootzén, Holger; Sandsten, Maria
ti: Stationary stochastic processes for scientists and engineers.
so: Boca Raton, FL: CRC Press (ISBN 978-1-4665-8618-5/hbk). xvi, 314~p. (2014).
py: 2014
pu: Boca Raton, FL: CRC Press
la: EN
cc: K65
ut: stationary stochastic processes; time series analysis; Poisson process;
Gaussian processes; Lévy processes; linear filters; ARMA models
ci:
li:
ab: This book presents an introduction book to time series analysis. As
mentioned by the authors, it is suitable for a one-semester course. It
is a well-written and easy to read book which is illustrated by lots of
examples. The book is mainly intended for students in science and
engineering, but it is also a good source of information for
researchers who want to learn about time series analysis. The book
contains nine chapters, five appendices, 60 references and an index.
The first chapter is an introductory chapter about stochastic
processes. It starts with 11 examples of stochastic processes in
science and engineering. After this, the definition of stochastic
processes is given. The chapter ends with the definition of the
distribution of a stochastic process. In the second chapter, the
authors introduce stationary processes and consider some of their
properties. The authors focus their attention on moment functions.
Special attention is paid to the covariance function which represents a
measure of linear dependence, and to the cross-correlation function
which represents a measure of dependence between two different
stochastic processes. Some special cases of stationary processes, such
as strictly and weakly stationary processes, and ergodic processes are
briefly considered. At the end of this chapter, estimations of some
moment functions, such as the mean value and the covariance function,
are discussed, and simulation results based on the Monte-Carlo method
are provided. The third chapter deals with the Poisson process. The
authors provide two equivalent definitions of this process: the
counting definition and the arrival time definition. As the Poisson
process is a special case of processes with stationary independent
increments, more details about this general class of stochastic
processes are provided. The Monte-Carlo simulations of the homogeneous
and inhomogeneous Poisson processes are discussed at the end of this
chapter. Chapter 4 is devoted to the spectral decomposition of the
covariance function of a time series. Chapter 5 deals with a special
case of stochastic processes, the so-called Gaussian processes, whose
finite-dimensional distributions are normal, and their properties are
briefly discussed. This chapter concludes with two generalized families
of processes, the Lévy processes and the shot noise processes. Linear
systems and linear filters are introduced and discussed in Chapter 6.
Autoregressive and moving average models as basic elements in time
series analysis are described in Chapter 7. Also, in this chapter, two
important issues of time series analysis, the estimation of the unknown
parameters and the prediction in these models are discussed in more
detail. The last two chapters are about the applications of linear
filters and about frequency analysis and spectral estimation.
rv: Miroslav M. Ristić (Niš)