vi PREFACE
including the suggestion of new and the validating of existing parametric
models.
In this book, we present an up-to-date picture of techniques for analyz-
ing time series data. Although we have tried to maintain a good balance
among methodology, theory, and numerical illustration, our primary goal
is to present a comprehensive and self-contained account for each of the
key methodologies. For practical relevant time series models, we aim for
exposure with definition, probability properties (if possible), statistical in-
ference methods, and numerical examples with real data sets. We also in-
dicate where to find our (only our!) favorite computing codes to implement
these statistical methods. When soliciting real-data examples, we attempt
to maintain a good balance among different disciplines, though our per-
sonal interests in quantitative finance, risk management, and biology can
be easily seen. It is our hope that readers can apply these techniques to
their own data sets.
We trust that the book will be of interest to those coming to the area
for the first time, and to readers more familiar with the field. Application-
oriented time series analysts will also find this book useful as it focuses on
methodology and includes several case studies with real data sets. We be-
lieve that nonparametric methods must go hand in hand with parametric
methods in applications. In particular, parametric models provide explana-
tory power and concise descriptions of the underlying dynamics, which,
when used sensibly, is an advantage over nonparametric models. For this
reason, we have also provided a compact view on the parametric methods
for both linear and selected nonlinear time series models. This will also
give new comers sufficient information on the essence of the more classical
approaches. We hope that this book will reflect the power of the integration
of nonparametric and parametric approaches in analyzing time series data.
The book has been prepared for a broad readership — the prerequisites are
merely sound basic courses in probability and statistics. Whilst advanced
mathematics has provided valuable insights into nonlinear time series, the
methodological power of both nonparametric and parametric approaches
can be understood without sophisticated technical details. Due to the in-
nate nature of the subject, it is inevitable that we occasionally appeal for
more advanced mathematics; such sections are marked with a ‘*’. Most
technical arguments are collected in ‘Complements’ section at the end of
each chapter, but key ideas are left within text.
The introduction in Chapter 1 sets the scene for the book. Chapter 2
deals with basic probabilistic properties of time series processes. The high-
lights include strict stationarity via ergodic Markov chains (§2.1) and mix-
ing properties (§2.6). We also provide a generic central limit theorm for
kernel-based nonparametric regression estimation for α-mixing processes.
A compact view of linear ARMA models is given in Chapter 3, including
Gaussian MLE (§3.3), model selection criteria (§3.4), and linear forecasting
with ARIMA models (§3.7). Chapter 4 introduces three types of paramet-
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