Michio Hatanaka
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198773535
- eISBN:
- 9780191596360
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198773536.003.0004
- Subject:
- Economics and Finance, Econometrics
This chapter introduces extended asymptotic theories on the unit root developed in Fuller (1976), Dickey and Fuller (1979), Phillips (1987), and Phillips and Perron (1988) among others. The theories ...
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This chapter introduces extended asymptotic theories on the unit root developed in Fuller (1976), Dickey and Fuller (1979), Phillips (1987), and Phillips and Perron (1988) among others. The theories are explained in two steps. The first deals with the elementary but fundamental case where Δxt is i.i.d with zero mean. The second step is given in Chapter 6. It explains more advanced aspects including the case where Δxt is an ARMA.Less
This chapter introduces extended asymptotic theories on the unit root developed in Fuller (1976), Dickey and Fuller (1979), Phillips (1987), and Phillips and Perron (1988) among others. The theories are explained in two steps. The first deals with the elementary but fundamental case where Δxt is i.i.d with zero mean. The second step is given in Chapter 6. It explains more advanced aspects including the case where Δxt is an ARMA.
Andrea Rotnitzky
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566540
- eISBN:
- 9780191718038
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566540.003.0006
- Subject:
- Mathematics, Probability / Statistics
This chapter reviews some key elements of semiparametric theory and the contributions of semiparametric inference to the challenge posed by high-dimensional data, for which the specification of ...
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This chapter reviews some key elements of semiparametric theory and the contributions of semiparametric inference to the challenge posed by high-dimensional data, for which the specification of realistic parametric models for the mechanism generating the data may be difficult, if not impossible. The usefulness of semiparametric modeling is illustrated by a number of examples. A non-technical account of the formulation of the semiparametric variance bound and ways of calculating it are described. Consequences are set out for estimations that result from the curse of dimensionality. The possibilities for approaching inference are discussed when estimation of irregular parameters is inevitable; some unresolved questions are raised.Less
This chapter reviews some key elements of semiparametric theory and the contributions of semiparametric inference to the challenge posed by high-dimensional data, for which the specification of realistic parametric models for the mechanism generating the data may be difficult, if not impossible. The usefulness of semiparametric modeling is illustrated by a number of examples. A non-technical account of the formulation of the semiparametric variance bound and ways of calculating it are described. Consequences are set out for estimations that result from the curse of dimensionality. The possibilities for approaching inference are discussed when estimation of irregular parameters is inevitable; some unresolved questions are raised.
Anindya Banerjee, Juan J. Dolado, John W. Galbraith, and David F. Hendry
- Published in print:
- 1993
- Published Online:
- November 2003
- ISBN:
- 9780198288107
- eISBN:
- 9780191595899
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198288107.003.0003
- Subject:
- Economics and Finance, Econometrics
Presents the important properties of integrated variables and sets out some of the preliminary asymptotic theories essential for the consideration of such processes. It explores the concepts of unit ...
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Presents the important properties of integrated variables and sets out some of the preliminary asymptotic theories essential for the consideration of such processes. It explores the concepts of unit roots, non‐stationarity, orders of integration, and near integration, and demonstrates the use of the theory in understanding the behaviour of least‐squares estimators in spurious regressions and in models involving integrated data. The theoretical analysis is accompanied by evidence from Monte Carlo simulations. Several examples are also provided to illustrate the use of Wiener distribution theory in deriving asymptotic results for such models.Less
Presents the important properties of integrated variables and sets out some of the preliminary asymptotic theories essential for the consideration of such processes. It explores the concepts of unit roots, non‐stationarity, orders of integration, and near integration, and demonstrates the use of the theory in understanding the behaviour of least‐squares estimators in spurious regressions and in models involving integrated data. The theoretical analysis is accompanied by evidence from Monte Carlo simulations. Several examples are also provided to illustrate the use of Wiener distribution theory in deriving asymptotic results for such models.
Michio Hatanaka
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198773535
- eISBN:
- 9780191596360
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198773536.003.0013
- Subject:
- Economics and Finance, Econometrics
This chapter analyses co-integrated regressions. It considers the cases where Δxt is i.i.d without a drift, Δxt is still i.i.d. but has a deterministic drift, and Δxt is serially correlated. It ...
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This chapter analyses co-integrated regressions. It considers the cases where Δxt is i.i.d without a drift, Δxt is still i.i.d. but has a deterministic drift, and Δxt is serially correlated. It discusses testing for co-integration, and co-integrated regression models’ assumption of some basic aspect of the co-integration space called the location of non-singular submatrices in B’.Less
This chapter analyses co-integrated regressions. It considers the cases where Δxt is i.i.d without a drift, Δxt is still i.i.d. but has a deterministic drift, and Δxt is serially correlated. It discusses testing for co-integration, and co-integrated regression models’ assumption of some basic aspect of the co-integration space called the location of non-singular submatrices in B’.
Michio Hatanaka
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198773535
- eISBN:
- 9780191596360
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198773536.003.0006
- Subject:
- Economics and Finance, Econometrics
This chapter brings together three unrelated topics of asymptotic theories. It presents a mathematical analysis of tests on the case where {Δxt} is i.i.d., possibly with a non-zero mean. It explains ...
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This chapter brings together three unrelated topics of asymptotic theories. It presents a mathematical analysis of tests on the case where {Δxt} is i.i.d., possibly with a non-zero mean. It explains the mathematics used for the case where {Δxt} is serially correlated. The asymptotic theory of the MA unit-root test is then discussed.Less
This chapter brings together three unrelated topics of asymptotic theories. It presents a mathematical analysis of tests on the case where {Δxt} is i.i.d., possibly with a non-zero mean. It explains the mathematics used for the case where {Δxt} is serially correlated. The asymptotic theory of the MA unit-root test is then discussed.
James Davidson
- Published in print:
- 1994
- Published Online:
- November 2003
- ISBN:
- 9780198774037
- eISBN:
- 9780191596117
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774036.001.0001
- Subject:
- Economics and Finance, Econometrics
This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first half provides a handbook and reference for the ...
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This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first half provides a handbook and reference for the underlying mathematics (Part I, Chapters 1‐6), statistical theory (Part II, Chapters 7‐11) and stochastic process theory (Part III, Chapters 12‐17). The second half provides a treatment of the main convergence theorems used in analysing the large sample behaviour of econometric estimators and tests. These are the law of large numbers (Part IV, Chapters 18‐21), the central limit theorem (Part V, Chapters 22‐25) and the functional central limit theorem (Part VI, Chapters 26‐30). The focus in this treatment is on the nonparametric approach to time series properties, covering topics such as nonstationarity, mixing, martingales, and near‐epoch dependence. While the approach is not elementary, care is taken to keep the treatment self‐contained. Proofs are provided for almost all the results.Less
This book aims to introduce modern asymptotic theory to students and practitioners of econometrics. It falls broadly into two parts. The first half provides a handbook and reference for the underlying mathematics (Part I, Chapters 1‐6), statistical theory (Part II, Chapters 7‐11) and stochastic process theory (Part III, Chapters 12‐17). The second half provides a treatment of the main convergence theorems used in analysing the large sample behaviour of econometric estimators and tests. These are the law of large numbers (Part IV, Chapters 18‐21), the central limit theorem (Part V, Chapters 22‐25) and the functional central limit theorem (Part VI, Chapters 26‐30). The focus in this treatment is on the nonparametric approach to time series properties, covering topics such as nonstationarity, mixing, martingales, and near‐epoch dependence. While the approach is not elementary, care is taken to keep the treatment self‐contained. Proofs are provided for almost all the results.
David F. Hendry
- Published in print:
- 1995
- Published Online:
- November 2003
- ISBN:
- 9780198283164
- eISBN:
- 9780191596384
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198283164.003.0003
- Subject:
- Economics and Finance, Econometrics
Least squares and recursive methods for estimating the values of unknown parameters and the logic of testing in empirical modelling, are discussed. The tools needed for investigating the properties ...
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Least squares and recursive methods for estimating the values of unknown parameters and the logic of testing in empirical modelling, are discussed. The tools needed for investigating the properties of statistics in economics, namely, large‐sample distribution theory and Monte Carlo simulation techniques, are described. Ergodicity is explained, as are tools for investigating non‐stationarity due to unit roots.Less
Least squares and recursive methods for estimating the values of unknown parameters and the logic of testing in empirical modelling, are discussed. The tools needed for investigating the properties of statistics in economics, namely, large‐sample distribution theory and Monte Carlo simulation techniques, are described. Ergodicity is explained, as are tools for investigating non‐stationarity due to unit roots.
Laurent Baulieu, John Iliopoulos, and Roland Sénéor
- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198788393
- eISBN:
- 9780191830310
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198788393.003.0012
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics
The general formulation of quantum field theory. The Wightman axioms. The PCT and spin-statistics theorems. The assumption for the existence of asymptotic states. The reduction formulae and ...
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The general formulation of quantum field theory. The Wightman axioms. The PCT and spin-statistics theorems. The assumption for the existence of asymptotic states. The reduction formulae and scattering theory. The Feynman rules for the S-matrix. Discussion for spin-12 and spin-1 particles. Applications to quantum electrodynamics. A formal expression for the S-matrix.Less
The general formulation of quantum field theory. The Wightman axioms. The PCT and spin-statistics theorems. The assumption for the existence of asymptotic states. The reduction formulae and scattering theory. The Feynman rules for the S-matrix. Discussion for spin-12 and spin-1 particles. Applications to quantum electrodynamics. A formal expression for the S-matrix.
