## 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

## 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

## 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

## 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.

## 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

## 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

## 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