Simon Price
- Published in print:
- 1998
- Published Online:
- November 2003
- ISBN:
- 9780198292371
- eISBN:
- 9780191600159
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198292376.003.0008
- Subject:
- Political Science, Reference
Extending the regression model to the analysis of non‐stationary, or trended, data. The examples demonstrate the application of unit root methodology, Engle‐Granger co‐integration procedures, and ...
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Extending the regression model to the analysis of non‐stationary, or trended, data. The examples demonstrate the application of unit root methodology, Engle‐Granger co‐integration procedures, and error correction methods. The application of appropriate statistics, such as the Augmented Dickey‐Fuller test, is also demonstrated.Less
Extending the regression model to the analysis of non‐stationary, or trended, data. The examples demonstrate the application of unit root methodology, Engle‐Granger co‐integration procedures, and error correction methods. The application of appropriate statistics, such as the Augmented Dickey‐Fuller test, is also demonstrated.
David F. Hendry
- Published in print:
- 1995
- Published Online:
- November 2003
- ISBN:
- 9780198283164
- eISBN:
- 9780191596384
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198283164.001.0001
- Subject:
- Economics and Finance, Econometrics
This systematic and integrated framework for econometric modelling is organized in terms of three levels of knowledge: probability, estimation, and modelling. All necessary concepts of econometrics ...
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This systematic and integrated framework for econometric modelling is organized in terms of three levels of knowledge: probability, estimation, and modelling. All necessary concepts of econometrics (including exogeneity and encompassing), models, processes, estimators, and inference procedures (centred on maximum likelihood) are discussed with solved examples and exercises. Practical problems in empirical modelling, such as model discovery, evaluation, and data mining are addressed, and illustrated using the software system PcGive. Background analyses cover matrix algebra, probability theory, multiple regression, stationary and non‐stationary stochastic processes, asymptotic distribution theory, Monte Carlo methods, numerical optimization, and macro‐econometric models. The reader will master the theory and practice of modelling non‐stationary (cointegrated) economic time series, based on a rigorous theory of reduction.Less
This systematic and integrated framework for econometric modelling is organized in terms of three levels of knowledge: probability, estimation, and modelling. All necessary concepts of econometrics (including exogeneity and encompassing), models, processes, estimators, and inference procedures (centred on maximum likelihood) are discussed with solved examples and exercises. Practical problems in empirical modelling, such as model discovery, evaluation, and data mining are addressed, and illustrated using the software system PcGive. Background analyses cover matrix algebra, probability theory, multiple regression, stationary and non‐stationary stochastic processes, asymptotic distribution theory, Monte Carlo methods, numerical optimization, and macro‐econometric models. The reader will master the theory and practice of modelling non‐stationary (cointegrated) economic time series, based on a rigorous theory of reduction.
Anindya Banerjee, Juan J. Dolado, John W. Galbraith, and David Hendry
- Published in print:
- 1993
- Published Online:
- November 2003
- ISBN:
- 9780198288107
- eISBN:
- 9780191595899
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198288107.001.0001
- Subject:
- Economics and Finance, Econometrics
This book considers the econometric analysis of both stationary and non‐stationary processes, which may be linked by equilibrium relationships. It provides a wide‐ranging account of the main tools, ...
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This book considers the econometric analysis of both stationary and non‐stationary processes, which may be linked by equilibrium relationships. It provides a wide‐ranging account of the main tools, techniques, models, concepts, and distributions involved in the modelling of integrated processes (i.e. those that accumulate the effects of past shocks). Since the focus is on equilibrium concepts, including co‐integration and error‐correction, the analysis begins with a discussion of the application of these concepts to stationary empirical models. Later chapters show how integrated processes can be reduced to this case by suitable transformations that take advantage of co‐integrating (equilibrium) relationships. The concepts of co‐integration and error‐correction models are shown to be fundamental in this modelling strategy. Practical modelling advice and empirical illustrations are provided.Knowledge of econometrics, statistics, and matrix algebra at the level of a final‐year undergraduate or first‐year graduate course in econometrics is sufficient for most of the book. Other mathematical tools are described as they arise.Less
This book considers the econometric analysis of both stationary and non‐stationary processes, which may be linked by equilibrium relationships. It provides a wide‐ranging account of the main tools, techniques, models, concepts, and distributions involved in the modelling of integrated processes (i.e. those that accumulate the effects of past shocks). Since the focus is on equilibrium concepts, including co‐integration and error‐correction, the analysis begins with a discussion of the application of these concepts to stationary empirical models. Later chapters show how integrated processes can be reduced to this case by suitable transformations that take advantage of co‐integrating (equilibrium) relationships. The concepts of co‐integration and error‐correction models are shown to be fundamental in this modelling strategy. Practical modelling advice and empirical illustrations are provided.
Knowledge of econometrics, statistics, and matrix algebra at the level of a final‐year undergraduate or first‐year graduate course in econometrics is sufficient for most of the book. Other mathematical tools are described as they arise.
Michio Hatanaka
- Published in print:
- 1996
- Published Online:
- November 2003
- ISBN:
- 9780198773535
- eISBN:
- 9780191596360
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198773536.003.0010
- Subject:
- Economics and Finance, Econometrics
This chapter reviews Bayesian studies of the unit root. It identifies three different categories of discrimination that have emerged in Bayesian unit-root literature, where stationarity is ...
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This chapter reviews Bayesian studies of the unit root. It identifies three different categories of discrimination that have emerged in Bayesian unit-root literature, where stationarity is discriminated from non-stationarity in the first category, and a point-null hypothesis, ρ = 1, is compared with alternative hypotheses in the second and third. It is shown that the third category, which contains only Schotman and van Dijk (1991a, b, 1993), deals with the discrimination between difference stationarity and trend stationarity.Less
This chapter reviews Bayesian studies of the unit root. It identifies three different categories of discrimination that have emerged in Bayesian unit-root literature, where stationarity is discriminated from non-stationarity in the first category, and a point-null hypothesis, ρ = 1, is compared with alternative hypotheses in the second and third. It is shown that the third category, which contains only Schotman and van Dijk (1991a, b, 1993), deals with the discrimination between difference stationarity and trend stationarity.
Angus Deaton
- Published in print:
- 1992
- Published Online:
- November 2003
- ISBN:
- 9780198288244
- eISBN:
- 9780191596131
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198288247.003.0003
- Subject:
- Economics and Finance, Macro- and Monetary Economics
Discusses the permanent income hypothesis and the mechanisms by which consumption smoothing responds to short‐run changes in income. It also reviews the role played by income and expectations in ...
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Discusses the permanent income hypothesis and the mechanisms by which consumption smoothing responds to short‐run changes in income. It also reviews the role played by income and expectations in transmitting fluctuations through the economy. The chapter considers detailed econometric evidence on the excess sensitivity of consumption to present and lagged changes in income. Explanations involving non‐stationary income, the timing of consumption, durables, and habit formation are critically evaluated.Less
Discusses the permanent income hypothesis and the mechanisms by which consumption smoothing responds to short‐run changes in income. It also reviews the role played by income and expectations in transmitting fluctuations through the economy. The chapter considers detailed econometric evidence on the excess sensitivity of consumption to present and lagged changes in income. Explanations involving non‐stationary income, the timing of consumption, durables, and habit formation are critically evaluated.
Angus Deaton
- Published in print:
- 1992
- Published Online:
- November 2003
- ISBN:
- 9780198288244
- eISBN:
- 9780191596131
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198288247.003.0004
- Subject:
- Economics and Finance, Macro- and Monetary Economics
Develops the themes of Ch. 3 by exploring how consumption responds to innovations in income. The focus is on the econometric enquiry and presents insights into how measured income differs from ...
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Develops the themes of Ch. 3 by exploring how consumption responds to innovations in income. The focus is on the econometric enquiry and presents insights into how measured income differs from permanent income and how to deal with the non‐stationarity of income. The chapter concludes by looking at how to analyse cases where the agents base their consumption plans on private information that is not available to the econometrician.Less
Develops the themes of Ch. 3 by exploring how consumption responds to innovations in income. The focus is on the econometric enquiry and presents insights into how measured income differs from permanent income and how to deal with the non‐stationarity of income. The chapter concludes by looking at how to analyse cases where the agents base their consumption plans on private information that is not available to the econometrician.
David F. Hendry
- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198293545
- eISBN:
- 9780191596391
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198293542.003.0006
- Subject:
- Economics and Finance, Econometrics
The ‘time‐series’ approach to econometrics is critically evaluated, and analytical test power response surfaces presented. Non‐stationarity, differencing and ‘error‐correction’ models (though not yet ...
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The ‘time‐series’ approach to econometrics is critically evaluated, and analytical test power response surfaces presented. Non‐stationarity, differencing and ‘error‐correction’ models (though not yet named) are discussed. Residual autocorrelation is reinterpreted using Sargan's common factor approach, and embryonic ideas presented on how to explain competing models’ findings to reduce the proliferation of conflicting results. Finally, the respective roles of criticism and construction are considered.Less
The ‘time‐series’ approach to econometrics is critically evaluated, and analytical test power response surfaces presented. Non‐stationarity, differencing and ‘error‐correction’ models (though not yet named) are discussed. Residual autocorrelation is reinterpreted using Sargan's common factor approach, and embryonic ideas presented on how to explain competing models’ findings to reduce the proliferation of conflicting results. Finally, the respective roles of criticism and construction are considered.
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.
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.
Masashi Sugiyama and Motoaki Kawanabe
- Published in print:
- 2012
- Published Online:
- September 2013
- ISBN:
- 9780262017091
- eISBN:
- 9780262301220
- Item type:
- book
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262017091.001.0001
- Subject:
- Computer Science, Machine Learning
As the power of computing has grown over the past few decades, the field of machine learning has advanced rapidly in both theory and practice. Machine learning methods are usually based on the ...
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As the power of computing has grown over the past few decades, the field of machine learning has advanced rapidly in both theory and practice. Machine learning methods are usually based on the assumption that the data generation mechanism does not change over time. Yet real-world applications of machine learning, including image recognition, natural language processing, speech recognition, robot control, and bioinformatics, often violate this common assumption. Dealing with non-stationarity is one of modern machine learning’s greatest challenges. This book focuses on a specific non-stationary environment known as covariate shift, in which the distributions of inputs (queries) change but the conditional distribution of outputs (answers) is unchanged, and presents machine learning theory, algorithms, and applications to overcome this variety of non-stationarity. After reviewing the state-of-the-art research in the field, the book discusses topics that include learning under covariate shift, model selection, importance estimation, and active learning. It describes such real-world applications of covariate shift adaption as brain-computer interface, speaker identification, and age prediction from facial images.Less
As the power of computing has grown over the past few decades, the field of machine learning has advanced rapidly in both theory and practice. Machine learning methods are usually based on the assumption that the data generation mechanism does not change over time. Yet real-world applications of machine learning, including image recognition, natural language processing, speech recognition, robot control, and bioinformatics, often violate this common assumption. Dealing with non-stationarity is one of modern machine learning’s greatest challenges. This book focuses on a specific non-stationary environment known as covariate shift, in which the distributions of inputs (queries) change but the conditional distribution of outputs (answers) is unchanged, and presents machine learning theory, algorithms, and applications to overcome this variety of non-stationarity. After reviewing the state-of-the-art research in the field, the book discusses topics that include learning under covariate shift, model selection, importance estimation, and active learning. It describes such real-world applications of covariate shift adaption as brain-computer interface, speaker identification, and age prediction from facial images.
Alexandra M. Schmidt and Marco A. Rodríguez
- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199694587
- eISBN:
- 9780191731921
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199694587.003.0020
- Subject:
- Mathematics, Probability / Statistics
We discuss models for multivariate counts observed at fixed spatial locations of a region of interest. Our approach is based on a continuous mixture of independent Poisson distributions. The mixing ...
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We discuss models for multivariate counts observed at fixed spatial locations of a region of interest. Our approach is based on a continuous mixture of independent Poisson distributions. The mixing component is able to capture correlation among components of the observed vector and across space through the use of a linear model of coregionalization. We introduce here the use of covariates to allow for possible non‐stationarity of the covariance structure of the mixing component. We analyse joint spatial variation of counts of four fish species abundant in Lake Saint Pierre, Quebec, Canada. Models allowing the covariance structure of the spatial random effects to depend on a covariate, geodetic lake depth, showed improved fit relative to stationary models.Less
We discuss models for multivariate counts observed at fixed spatial locations of a region of interest. Our approach is based on a continuous mixture of independent Poisson distributions. The mixing component is able to capture correlation among components of the observed vector and across space through the use of a linear model of coregionalization. We introduce here the use of covariates to allow for possible non‐stationarity of the covariance structure of the mixing component. We analyse joint spatial variation of counts of four fish species abundant in Lake Saint Pierre, Quebec, Canada. Models allowing the covariance structure of the spatial random effects to depend on a covariate, geodetic lake depth, showed improved fit relative to stationary models.
Timo Teräsvirta, Dag Tjøstheim, and W. J. Granger
- Published in print:
- 2010
- Published Online:
- May 2011
- ISBN:
- 9780199587148
- eISBN:
- 9780191595387
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199587148.003.0001
- Subject:
- Economics and Finance, Econometrics
This chapter gives a brief overview of the basic concepts and topics used in the book. There exists a large literature on linear stationary models. The purpose of the present book is to look at ...
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This chapter gives a brief overview of the basic concepts and topics used in the book. There exists a large literature on linear stationary models. The purpose of the present book is to look at nonlinear models in both a stationary and nonstationary framework. Linear techniques are contrasted with typical tools used to analyse nonlinearity, such as the conditional mean and the conditional variance, and Markov chain theory. Nonlinear parametric models are mentioned as well as nonparametric ones.Less
This chapter gives a brief overview of the basic concepts and topics used in the book. There exists a large literature on linear stationary models. The purpose of the present book is to look at nonlinear models in both a stationary and nonstationary framework. Linear techniques are contrasted with typical tools used to analyse nonlinearity, such as the conditional mean and the conditional variance, and Markov chain theory. Nonlinear parametric models are mentioned as well as nonparametric ones.
David F. Hendry
- Published in print:
- 2014
- Published Online:
- January 2015
- ISBN:
- 9780262028356
- eISBN:
- 9780262324410
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262028356.003.0023
- Subject:
- Economics and Finance, Econometrics
Forecasting is different: the past is fixed, but the future is not. Practical forecasting methods rely on extrapolating presently available information into the future. No matter how good such ...
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Forecasting is different: the past is fixed, but the future is not. Practical forecasting methods rely on extrapolating presently available information into the future. No matter how good such methods are, they require that the future resembles the present in the relevant attributes. Intermittent unanticipated shifts violate that requirement, and breaks have so far eluded being predicted. If no location shifts ever occurred, then the most parsimonious, congruent, undominated model in-sample would tend to dominate out of sample as well. However, if data processes are wide-sense non-stationary, different considerations matter for formulating, selecting, or using a forecasting model. In practice, the robustness to location shifts of a model formulation can be essential for avoiding systematic forecast failure, which may entail selecting from a different class of models that need not even be congruent in-sample: complete success at locating the LDGP need not improve forecasting. However, by transforming a selected congruent parsimoniously encompassing model to a more robust form before it is used in forecasting, causal information can be retained while avoiding systematic forecast failure. The chapter also notes other ways of selecting forecasting models, including model averaging and factor approaches, but focuses on transformations of selected models of the LDGP.Less
Forecasting is different: the past is fixed, but the future is not. Practical forecasting methods rely on extrapolating presently available information into the future. No matter how good such methods are, they require that the future resembles the present in the relevant attributes. Intermittent unanticipated shifts violate that requirement, and breaks have so far eluded being predicted. If no location shifts ever occurred, then the most parsimonious, congruent, undominated model in-sample would tend to dominate out of sample as well. However, if data processes are wide-sense non-stationary, different considerations matter for formulating, selecting, or using a forecasting model. In practice, the robustness to location shifts of a model formulation can be essential for avoiding systematic forecast failure, which may entail selecting from a different class of models that need not even be congruent in-sample: complete success at locating the LDGP need not improve forecasting. However, by transforming a selected congruent parsimoniously encompassing model to a more robust form before it is used in forecasting, causal information can be retained while avoiding systematic forecast failure. The chapter also notes other ways of selecting forecasting models, including model averaging and factor approaches, but focuses on transformations of selected models of the LDGP.
Jeffrey S. Racine
- Published in print:
- 2019
- Published Online:
- January 2019
- ISBN:
- 9780190900663
- eISBN:
- 9780190933647
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190900663.003.0001
- Subject:
- Economics and Finance, Econometrics
This chapter introduces time series data and outlines how it differs from cross sectional data. It also highlights how the object of interest when modelling time series data is the forecast, which ...
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This chapter introduces time series data and outlines how it differs from cross sectional data. It also highlights how the object of interest when modelling time series data is the forecast, which differs from the object of interest in cross-sectional modelling, which is typically some parameter of interest that has an economic interpretation.Less
This chapter introduces time series data and outlines how it differs from cross sectional data. It also highlights how the object of interest when modelling time series data is the forecast, which differs from the object of interest in cross-sectional modelling, which is typically some parameter of interest that has an economic interpretation.
