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Likelihood-Based Inference in Cointegrated Vector Autoregressive Models

Søren Johansen

Published in print:
1995
Published Online:
November 2003
ISBN:
9780198774501
eISBN:
9780191596476
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/0198774508.001.0001
Subject:
Economics and Finance, Econometrics

This monograph is concerned with the statistical analysis of multivariate systems of non‐stationary time series of type I(1). It applies the concepts of cointegration and common trends in the ... More


MODAL AND SUPERINTUITIONISTIC LOGICS: BASIC CONCEPTS

D.M. Gabbay and L. Maksimova

in Interpolation and Definability: Modal and Intuitionistic Logics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198511748
eISBN:
9780191705779
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198511748.003.0002
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter presents basic definitions and known results related to modal and superintuitionistic logics. Well-known Hilbert-style axiomatizations of the most known modal systems K, D, T, K4, D4, ... More


Co‐Integration

Anindya Banerjee, Juan J. Dolado, John W. Galbraith, and David F. Hendry

in Co-integration, Error Correction, and the Econometric Analysis of Non-Stationary Data

Published in print:
1993
Published Online:
November 2003
ISBN:
9780198288107
eISBN:
9780191595899
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198288107.003.0005
Subject:
Economics and Finance, Econometrics

The key concept of co‐integration of integrated time series is defined, and several examples are presented. An important theorem due to Granger on alternative representations of a system of ... More


Cointegration and Representation of Integrated Variables

Søren Johansen

in Likelihood-Based Inference in Cointegrated Vector Autoregressive Models

Published in print:
1995
Published Online:
November 2003
ISBN:
9780198774501
eISBN:
9780191596476
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774508.003.0004
Subject:
Economics and Finance, Econometrics

Contains the mathematical and algebraic results needed to understand the properties of I(1) and I(2) processes generated by autoregressive and moving average models. The basic result is Grangers ... More


The Mathematics of the Martingale Approach

Tomas Björk

in Arbitrage Theory in Continuous Time

Published in print:
2004
Published Online:
October 2005
ISBN:
9780199271269
eISBN:
9780191602849
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199271267.003.0011
Subject:
Economics and Finance, Financial Economics

This chapter presents the two main workhorses of the martingale approach to arbitrage theory: the Martingale Representation Theorem and the Girsanov Theorem. The Martingale Representation Theorem ... More


Conceptual Framework of the Co‐Integration and Its Relation to Economic Theories

Michio Hatanaka

in Time-Series-Based Econometrics: Unit Roots and Co-integrations

Published in print:
1996
Published Online:
November 2003
ISBN:
9780198773535
eISBN:
9780191596360
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198773536.003.0012
Subject:
Economics and Finance, Econometrics

This chapter discusses co-integration and the Granger representation theorem. The theoretical structure of the Granger representation theorem is illustrated with economic interpretation by a ... More


Decision Theory and the Dimensions of Rationality

José Luis Bermúdez

in Decision Theory and Rationality

Published in print:
2009
Published Online:
May 2009
ISBN:
9780199548026
eISBN:
9780191720246
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199548026.003.0002
Subject:
Philosophy, Philosophy of Mind, Philosophy of Science

This chapter begins by explaining the different explanatory projects underlying the three different dimensions of rationality (action-guiding, normative assessment, and explanatory-predictive). It ... More


Weak Convergence of Distributions

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0022
Subject:
Economics and Finance, Econometrics

This chapter introduces the fundamentals of weak convergence for real sequences. Definitions and examples are given. The Skorokhod representation theorem is proved, and the chapter then considers the ... More


BOOLEAN AND HEYTING ALGEBRAS: THE ESSENTIALS

John L. Bell

in Set Theory: Boolean-Valued Models and Independence Proofs

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198568520
eISBN:
9780191717581
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198568520.003.0001
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter provides a brief account of the theory of Boolean and Heyting algebras, including the basic representation theorems and their connections with logic.


Estimating functions

Christopher G. Small and Jinfang Wang

in Numerical Methods for Nonlinear Estimating Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.003.0002
Subject:
Mathematics, Probability / Statistics

This chapter gives a survey of the basic concepts of estimating functions, which are used in subsequent chapters. The concept of unbiasedness for estimating functions is introduced as a ... More


Weak Convergence in Metric Spaces

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0026
Subject:
Economics and Finance, Econometrics

This chapter lays the foundations for functional limit theory by considering the case of general metric spaces, from a topological standpoint. It develops tools to replace the method of ... More


 Laws and their Confirmation

Wolfgang Spohn

in The Laws of Belief: Ranking Theory and Its Philosophical Applications

Published in print:
2012
Published Online:
September 2012
ISBN:
9780199697502
eISBN:
9780191739323
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199697502.003.0012
Subject:
Philosophy, Metaphysics/Epistemology, Philosophy of Science

The remaining chapters are devoted to various philosophical applications of ranking theory. The first goal is to understand natural modalities as covertly epistemological modalities by a kind of ... More


Algebra of Relations

S. N. Afriat

in Logic of Choice and Economic Theory

Published in print:
1987
Published Online:
November 2003
ISBN:
9780198284611
eISBN:
9780191595844
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198284616.003.0030
Subject:
Economics and Finance, Microeconomics

This is the second of three chapters on general mathematics as applied to economics, and presents a treatment of the algebra of relations. Relations are defined as subsets of a Cartesian product, or ... More


Logic, Graded Belief, and Preferences

David Christensen

in Putting Logic in its Place: Formal Constraints on Rational Belief

Published in print:
2004
Published Online:
July 2005
ISBN:
9780199263257
eISBN:
9780191602603
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199263256.003.0005
Subject:
Philosophy, Logic/Philosophy of Mathematics

Defends probabilistic coherence as a logical constraint on graded belief. Standard Dutch Book and Representation Theorem arguments seek to defend coherence by positing very tight—even ... More


Algebraic Tools

Robert Alicki and Mark Fannes

in Quantum Dynamical Systems

Published in print:
2001
Published Online:
February 2010
ISBN:
9780198504009
eISBN:
9780191708503
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198504009.003.0005
Subject:
Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces an abstract algebraic language unifying the description of classical systems, finite quantum systems, and infinite ones, the last appearing in particle and statistical ... More


Stochastic Integration

Gopinath Kallianpur and P. Sundar

in Stochastic Analysis and Diffusion Processes

Published in print:
2014
Published Online:
April 2014
ISBN:
9780199657063
eISBN:
9780191781759
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199657063.003.0005
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

The Itô stochastic integral with respect to a Brownian motion is constructed, and its properties are shown in detail. The Itô formula is proved. Its applications include Lévy’s characterization of a ... More


Indeterminism and Probability

Bas C. van Fraassen

in Quantum Mechanics: An Empiricist View

Published in print:
1991
Published Online:
November 2003
ISBN:
9780198239802
eISBN:
9780191597466
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198239807.003.0003
Subject:
Philosophy, Philosophy of Science

Pure indeterminism is simply the denial of determinism; a theory may augment this with models in which the uncertain events have definite probabilities. De Finetti's representation theorem, which ... More


Grounding Stories

Jason Turner

in The Facts in Logical Space: A Tractarian Ontology

Published in print:
2016
Published Online:
April 2016
ISBN:
9780199682812
eISBN:
9780191817267
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199682812.003.0004
Subject:
Philosophy, Metaphysics/Epistemology, Logic/Philosophy of Mathematics

According to the factalist, the appearances of non-facts are grounded in the facts and their Tractarian geometry. This chapter describes two ways in which those appearances must be grounded. On both ... More


Large Deviations Principle for Diffusions

Gopinath Kallianpur and P. Sundar

in Stochastic Analysis and Diffusion Processes

Published in print:
2014
Published Online:
April 2014
ISBN:
9780199657063
eISBN:
9780191781759
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199657063.003.0012
Subject:
Mathematics, Probability / Statistics, Applied Mathematics

Large deviations theory formulated by Varadhan has made a tremendous impact in a variety of fields such as mathematical physics, control theory, and statistics, to name a few. After a brief ... More


Observables and models: exchangeability and the inductive argument

Micheal Goldstein

in Bayesian Theory and Applications

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199695607
eISBN:
9780191744167
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199695607.003.0001
Subject:
Mathematics, Probability / Statistics

This chapter first provides an elementary and self-contained account of the notion of exchangeability and the derivation of Bruno de Finetti's representation theorem, which shows how to construct ... More


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