240 pages 16 line diagrams 18 colour plates
Hardback | ISBN: 0-521-83627-1 | available from November 2004
In this fascinating book, astronomer Joseph Silk explores the
Universe from its beginnings to its ultimate fate. He shows how
cosmologists study cosmic fossils and relics from the distant
past to construct theories of the birth, evolution and future of
the Universe. Stars, galaxies, dark matter and dark energy are
described, as successive chapters detail the evolution of the
Universe from a fraction of a microsecond after the Big Bang.
Silk describes how physicists apply theories of subatomic
particles to recreate the first moments of the Big Bang, and how
astronomers chart the vast depths of space to glimpse how the
most distant galaxies formed. He describes the search for dark
matter and the dark energy that will determine the ultimate fate
of the Universe. This highly readable account will appeal to all
those with an interest in the story of the Universe.
Contents
Prologue; 1. Building blocks of the cosmos; 2. The expansion of
the universe; 3. Cosmic microwave background; 4. The first 10-43
seconds of the Universe; 5. Genesis of baryons and helium; 6.
Testing the Big Bang; 7. Dark matter; 8. Baryonic dark matter; 9.
Intergalactic matter; 10. Origin of structure; 11. Large-scale
structure; 12. Galaxy formation; 13. What lies ahead.
400 pages 190 line diagrams 10 colour plates
Hardback | ISBN: 0-521-82356-0 | available from February 2005
The topic of ‘circle packing’ was born of the computer age
but takes its inspiration and themes from core areas of classical
mathematics. A circle packing is a configuration of circles
having a specified pattern of tangencies, as introduced by
William Thurston in 1985. This book lays out their study, from
first definitions to latest theory, computations, and
applications. The topic can be enjoyed for the visual appeal of
the packing images - over 200 in the book - and the elegance of
circle geometry, for the clean line of theory, for the deep
connections to classical topics, or for the emerging applications.
Circle packing has an experimental and visual character which is
unique in pure mathematics, and the book exploits that to carry
the reader from the very beginnings to links with complex
analysis and Riemann surfaces. There are intriguing, often very
accessible, open problems throughout the book and seven
Appendices on subtopics of independent interest. This book lays
the foundation for a topic with wide appeal and a bright future.
Contents
Part I. An Overview of Circle Packing: 1. A circle packing
menagerie; 2. Circle packings in the wild; Part II. Rigidity:
maximal Packings: 3. Preliminaries: topology, combinatorics, and
geometry; 4. Statement of the fundamental result; 5. Bookkeeping
and monodromy; 6. Proof for combinatorial closed discs; 7. Proof
for combinatorial spheres; 8. Proof for combinatorial open discs;
9. Proof for combinatorial surfaces; Part III. Flexibility:
Analytic Functions: 10. The intuitive landscape; 11. Discrete
analytic functions; 12. Construction tools; 13. Discrete analytic
functions on the disc; 14. Discrete entire functions; 15.
Discrete rational functions; 16. Discrete analytic functions on
Riemann surfaces; 17. Discrete conformal structure; 18. Random
walks on circle packings; Part IV: 19. Thurston’s Conjecture;
20. Extending the Rodin/Sullivan theorem; 21. Approximation of
analytic functions; 22. Approximation of conformal structures; 23.
Applications; Appendix A. Primer on classical complex analysis;
Appendix B. The ring lemma; Appendix C. Doyle spirals; Appendix D.
The brooks parameter; Appendix E. Schwarz and buckyballs;
Appendix F. Inversive distance packings; Appendix G. Graph
embedding; Appendix H. Square grid packings; Appendix I.
Experimenting with circle packings.
352 pages 69 line diagrams 38 tables
Paperback | ISBN: 0-521-54787-3 | available from October 2004
Hardback | ISBN: 0-521-83919-X | available from October 2004
Time series econometrics is a rapidly evolving field.
Particularly, the cointegration revolution has had a substantial
impact on applied analysis. Hence, no textbook has managed to
cover the full range of methods in current use and explain how to
proceed in applied domains. This gap in the literature motivates
the present volume. The methods are sketched out, reminding the
reader of the ideas underlying them and giving sufficient
background for empirical work. The treatment can also be used as
a textbook for a course on applied time series econometrics.
Topics include: unit root and cointegration analysis, structural
vector autoregressions, conditional heteroskedasticity and
nonlinear and nonparametric time series models. Crucial to
empirical work is the software that is available for analysis.
New methodology is typically only gradually incorporated into
existing software packages. Therefore a flexible Java interface
has been created, allowing readers to replicate the applications
and conduct their own analyses.
Contents
1. Initial tasks and overview: 1.1 Introduction; 1.2 Setting up
an econometric project; 1.3 Getting data; 1.4 Data handling; 1.5
Outline of chapters; 2. Univariate time series analysis: 2.1
Characteristics of time series; 2.2 Stationary and integrated
stochastic processes; 2.3 Some popular time series models; 2.4
Parameter estimation; 2.5 Model specification; 2.6 Model
checking; 2.7 Unit root tests; 2.8 Forecasting univariate time
series; 2.9 Examples; 2.10 Where to go from here?; 3. Vector
autoregressive and vector error correction models: 3.1
Introduction; 3.2 VARs and VECMs; 3.3 Estimation; 3.4 Model
specification; 3.5 Model checking; 3.6 Forecasting VAR processes
and VECMs; 3.7 Granger-causality analysis; 3.8 An example; 3.9
Extensions; 4. Structural vector autoregressive modelling and
impulse responses: 4.1 Introduction; 4.2 The models; 4.3 Impulse
response analysis; 4.4 Estimation of structural parameters; 4.5
Statistical inference for impulse responses; 4.6 Forecast error
variance decomposition; 4.7 Examples; 4.8 Conclusions; 5.
Conditional heteroskedasticity: 5.1 Stylized facts of empirical
price processes; 5.2 Univariate GARCH models; 5.3 Multivariate
GARCH models; 6. Smooth transition regression modelling: 6.1
Introduction; 6.2 The model; 6.3 The modelling cycle; 6.4 Two
empirical examples; 6.5 Final remarks; 7. Nonparametric time
series modelling: 7.1 Introduction; 7.2 Local linear estimation;
7.3 Bandwidth and lag selection; 7.4 Diagnostics; 7.5 Modelling
the conditional volatility; 7.6 Local linear seasonal modelling;
7.7 Example I: average weekly working hours in the U.S.; 7.8
Example II: XETRA dax index; 8. The software JMulTi: 8.1
Introduction to JMulTi 8.2 Numbers, dates and variables in JMulTi
8.3 Handling datasets; 8.4 Selecting, transforming and creating
time series; 8.5 Managing variables in JMulTi; 8.6 Notes for
econometric software developers; 8.7 Conclusion.
450 pages
Hardback | ISBN: 0-521-83440-6 | - available from March 2005
The idea of this book is to explain how Levy processes can be
used to study some problems in finance. The necessary technology
is motivated and justified in an opening chapter, and is then
followed by chapters explaining the mathematics and computational
aspects of the subject. The heart of the book describes
applications, with further mathematical ideas introduced as and
when needed. The authors cover new ideas not presented in book
form before, blending theory and practice, and this account will
be of value to all those working in mathematical finance,
financial econometrics, probability and statistics.
344 pages 19 line diagrams 12 tables
Hardback | ISBN: 0-521-83431-7 | available from November 2004
Paperback | ISBN: 0-521-54224-3 | available from November 2004
This book is intended for use in a rigorous introductory PhD
level course in econometrics, or in a field course in econometric
theory. It covers the measure-theoretical foundation of
probability theory, the multivariate normal distribution with its
application to classical linear regression analysis, various laws
of large numbers, central limit theorems and related results for
independent random variables as well as for stationary time
series, with applications to asymptotic inference of M-estimators,
and maximum likelihood theory. Some chapters have their own
appendices containing the more advanced topics and/or difficult
proofs. Moreover, there are three appendices with material that
is supposed to be known. Appendix I contains a comprehensive
review of linear algebra, including all the proofs. Appendix II
reviews a variety of mathematical topics and concepts that are
used throughout the main text, and Appendix III reviews complex
analysis. Therefore, this book is uniquely self-contained.
Contents
1. Probability and measure: 1.1 The Texas lotto; 1.2 Quality
control; 1.3 Why do we need sigma-algebras of events?; 1.4
Properties of algebras and sigma-algebras; 1.5 Properties of
probability measures; 1.6 The uniform probability measures; 1.7
Lebesque measure and Lebesque integral; 1.8 Random variables and
their distributions; 1.9 Density functions; 1.10 Conditional
probability, Bayes’s rule, and independence; 1.11 Exercises; 1.A
Common structure of the proofs of Theorems 6 and 10; 1.B
Extension of an outer measure to a probability measure; 2. Borel
measurability, integration, and mathematical expectations: 2.1
Introduction; 2.2 Borel measurability; 2.3 Integral of Borel
measurable functions with respect to a probability measure; 2.4
General measurability and integrals of random variables with
respect to probability measures; 2.5 Mathematical expectation; 2.6
Some useful inequalities involving mathematical expectations; 2.7
Expectations of products of independent random variables; 2.8
Moment generating functions and characteristic functions; 2.9
Exercises; 2.A Uniqueness of characteristic functions; 3.
Conditional expectations: 3.1 Introduction; 3.2 Properties of
conditional expectations; 3.3 Conditional probability measures
and conditional independence; 3.4 Conditioning on increasing
sigma-algebras; 3.5 Conditional expectations as the best forecast
schemes; 3.6 Exercises; 3.A Proof of theorem 3.12; 4.
Distributions and transformations: 4.1 Discrete distributions; 4.2
Transformations of discrete random vectors; 4.3 Transformations
of absolutely continuous random variables; 4.4 Transformations of
absolutely continuous random vectors; 4.5 The normal
distribution; 4.6 Distributions related to the normal
distribution; 4.7 The uniform distribution and its relation to
the standard normal distribution; 4.8 The gamma distribution; 4.9
Exercises; 4.A Tedious derivations; 4.B Proof of theorem 4.4; 5.
The multivariate normal distribution and its application to
statistical inference; 5.1 Expectation and variance of random
vectors; 5.2 The multivariate normal distribution; 5.3
Conditional distributions of multivariate normal random
variables; 5.4 Independence of linear and quadratic
transformations of multivariate normal random variables; 5.5
Distribution of quadratic forms of multivariate normal random
variables; 5.6 Applications to statistical inference under
normality; 5.7 Applications to regression analysis; 5.8
Exercises; 5.A Proof of theorem 5.8; 6. Modes of convergence: 6.1
Introduction; 6.2 Convergence in probability and the weak law of
large numbers; 6.3 Almost sure convergence, and the strong law of
large numbers; 6.4 The uniform law of large numbers and its
applications; 6.5 Convergence in distribution; 6.6 Convergence of
characteristic functions; 6.7 The central limit theorem; 6.8
Stochastic boundedness, tightness, and the Op and op-notations; 6.9
Asymptotic normality of M-estimators; 6.10 Hypotheses testing; 6.11
Exercises; 6.A Proof of the uniform weak law of large numbers; 6.B
Almost sure convergence and strong laws of large numbers; 6.C
Convergence of characteristic functions and distributions; 7.
Dependent laws of large numbers and central limit theorems: 7.1
Stationary and the world decomposition; 7.2 Weak laws of large
numbers for stationary processes; 7.3 Mixing conditions; 7.4
Uniform weak laws of large numbers; 7.5 Dependent central limit
theorems; 7.6 Exercises; 7.A Hilbert spaces; 8. Maximum
likelihood theory; 8.1 Introduction; 8.2 Likelihood functions; 8.3
Examples; 8.4 Asymptotic properties if ML estimators; 8.5 Testing
parameter restrictions; 8.6 Exercises.