Mohsen Pourahmadi, Northern Illinois Univ.

Foundations of Time Series Analysis and Prediction Theory

ISBN: 0-471-39434-3
Hardcover
Pages: 448

Copyright: 2001

This book provides a mathematical foundation for prediction theory and time series analysis using the idea of regression (prediction) and the geometry of Hilbert spaces. The need for a mathematical foundation is manifested by the maturity, widespread use and truly interdisciplinary nature of time series analysis lying at the intersection of the mathematical statistical, computational, physical, engineering and system sciences, just to name a few.

Contents

Preface.
Acknowledgements.
Introduction.
Time Series Analysis: One Long Series.
Time Series Analysis: Many Short Series.
Stationary ARMA Models.
Stationary Process.
Parameterization and Prediction.
Finite Prediction and Partial Correlations.
Past and Future: Missing Values.
Stationary Sequences in Hilbert Spaces.
Stationarity and Hardy Spaces.
Appendix A: Multivariate Distributions.
Appendix B: The Bayesian Forecasting.
References.
Index.

Subject: ECONOMICS / Introductory Econometrics / Time Series Analysis

Series Title: Wiley Series in Probability and Statistics - Applied Probability and Statistics Section

Edited by Emilio Bujalance, Antonio Feliix Costa, Ernesto Martinez

Topics on Riemann Surfaces and Fuchsian Groups

London Mathematical Society Lecture Note Series series

Description

Presents a cross-section of different aspects of Riemann surfaces, introducing the reader to the
basics as well as highlighting new developments in the field. It provides a mixture of classical
material, recent results and some non-mainstream topics. The book is based on lectures from the conference Topics on Riemann Surfaces and Fuchsian Groups held in Madrid to mark the 25th anniversary of the Universidad Nacional de Educacisn a Distancia. For those wishing to pursue research in this area, this
volume offers a valuable summary of contemporary thought and a source of fresh geometric and algebraic insights. The book will be suitable for graduate courses, as well as providing a useful reference for those already working in geometry, group theory, complex analysis, algebraic geometry, topology and
theoretical physics.

Chapter Contents

Preface; Introduction A. F. Beardon; 1. The geometry of Riemann surfaces A. F. Beardon; 2. Introduction to arithmetic Fuchsian groups C. Maclachlan; 3. Riemann surfaces, Belyi functions and hypermaps D. Singerman; 4. Compact Riemann surfaces and algebraic function fields P. Turbek; 5. Symmetries of Riemann surfaces
from a combinatorial point of view G. Gromadzki; 6. Compact Klein surfaces and real algebraic
curves F. J. Cirre and J. M. Gamboa; 7. Moduli spaces of real algebraic curves M. Seppdld; 8.
Period matrices and the Schottky problem R. Silhol; 9. Hurwitz spaces S. M. Natanzon.

ISBN: 0-521-00350-4
Binding: Paperback
Pages: 192

Chris Gibson

Differentiable Curves
An Undergraduate Text

Description

This genuine introduction to the differential geometry of plane curves is designed as a first text for undergraduates in mathematics, or postgraduates and researchers in the engineering and physical sciences. The book assumes only foundational year mathematics: it is well illustrated, and contains several hundred
worked examples and exercises, making it suitable for adoption as a course text. The basic concepts are illustrated by named curves, of historical and scientific significance, leading to the central idea of curvature. The singular viewpoint is represented by a study of contact with lines and circles, illuminating the ideas of
cusp, inflexion and vertex. There are two major physical applications. Caustics are discussed via the central concepts of evolute and orthotomic. The final chapters introduce the core material of classical kinematics, developing the geometry of trajectories via the ideas of roulettes and centrodes, and culminating in the inflexion circle and cubic of stationary curvature.

Chapter Contents

1. The Euclidean plane; 2. Parametrized curves; 3. Classes of special curves; 4. Arc length; 5. Curvature; 6. Existence and uniqueness; 7. Contact with lines; 8. Contact with circles; 9. Vertices; 10. Envelopes; 11. Orthotomics; 12. Caustics by reflexion; 13. Planar kinematics; 14. Centrodes; 15. Geometry of trajectories.

ISBN: 0-521-01107-8
Binding: Paperback
Pages: 232

ISBN: 0-521-80453-1
Binding: Hardcover

Thomas Leonard, John S. J. Hsu

Bayesian Methods
An Analysis for Statisticians and Interdisciplinary Researchers

Cambridge Series in Statistical and Probabilistic Mathematics series

Description

This book describes the Bayesian approach to statistics at a level suitable for final year undergraduate and Masters students. It is unique in presenting Bayesian statistics with a practical flavor and an emphasis on mainstream statistics, showing how to infer scientific, medical, and social conclusions from numerical data. The
authors draw on many years of experience with practical and research programs and describe many new statistical methods, not available elsewhere. A first chapter on Fisherian methods, together with a strong overall emphasis on likelihood, makes the text suitable for mainstream statistics courses whose instructors
wish to follow mixed or comparative philosophies. The other chapters contain important sections
relating to many areas of statistics such as the linear model, categorical data analysis, time series, and forecasting, mixture models, survival analysis, Bayesian smoothing, and non-linear random effects models. The text includes a large number of practical examples, worked examples, and exercises. It will be essential reading for all statisticians, statistics students, and related interdisciplinary researchers.

Chapter Contents

1. Introductory statistical concepts; 2. The discrete version of Bayes・theorem; 3. Models with a single unknown parameter; 4. The expected utility hypothesis and its alternatives; 5. Models with several unknown parameters; 6. Prior structures, posterior smoothing, and Bayes-Stein estimation; Guide to worked
examples; Guide to self-study exercises.

ISBN: 0-521-00414-4
Binding: Paperback
Pages: 352

A. Skorobogatov

Torsors and Rational Points

Description

The classical descent on curves of genus one can be interpreted as providing conditions on the set
of rational points of an algebraic variety X defined over a number field, viewed as a subset of its adelic points. This is the natural set-up of the Hasse principle and various approximation properties of rational points. The most famous among such conditions is the Manin obstruction exploiting the Brauer-Grothendieck group of X. It
emerged recently that a non-abelian generalization of descent sometimes provides stronger conditions on rational points. An all-encompassing 双bstruction・is related to the X-torsors (families of principal homogenous
spaces with base X) under algebraic groups. This book represents the first detailed exposition of 1) the general theory of torsors with key examples, 2) the relation of descent to the Manin obstruction, and 3) applications of descent: to conic bundles, to bielliptic surfaces, and to homogenous spaces of algebraic groups.

Chapter Contents

1. Introduction; 2. Torsors: general theory; 3. Examples of torsors; 4. Abelian torsors; 5. Obstructions over number fields; 6. Abelian descent and Manin obstruction; 7. Conic bundle surfaces; 8. Bielliptic surfaces; 9. Homogenous surfaces.

ISBN: 0-521-80237-7
Binding: Hardback