Christian Gouriéroux - Böcker

This book introduces a new generation of statistical econometrics. After linear models leading to analytical expressions for estimators, and non-linear models using numerical optimization algorithms, the availability of high- speed computing has enabled econometricians to consider econometric models without simple analytical expressions. The previous difficulties presented by the presence of integrals of large dimensions in the probability density functions or in the moments can be circumvented by a simulation-based approach.After a brief survey of classical parametric and semi-parametric non-linear estimation methods and a description of problems in which criterion functions contain integrals, the authors present a general form of the model where it is possible to simulate the observations. They then move to calibration problems and the simulated analogue of the method of moments, before considering simulated versions of maximum likelihood, pseudo-maximum likelihood, or non-linear least squares. The general principle of indirect inference is presented and is then applied to limited dependent variable models and to financial series.

1.1 The DevelopmentofARCH Models Time series models have been initially introduced either for descriptive purposes like prediction and seasonal correction or for dynamic control. In the 1970s, the researchfocusedonaspecificclassoftimeseriesmodels,theso-calledautoregres- sive moving average processes (ARMA), which were very easy to implement. In thesemodels,thecurrentvalueoftheseriesofinterestiswrittenasalinearfunction ofits own laggedvalues andcurrentandpastvaluesofsomenoiseprocess, which can be interpreted as innovations to the system. However, this approach has two major drawbacks: 1) it is essentially a linear setup, which automatically restricts the type of dynamics to be approximated; 2) it is generally applied without im- posing a priori constraintson the autoregressive and moving average parameters, which is inadequatefor structural interpretations. Among the field ofapplications where standard ARMA fit is poorare financial and monetary problems. The financial time series features various forms ofnon- lineardynamics,the crucialone being the strongdependenceofthe instantaneous variabilityoftheseriesonitsownpast.Moreover,financial theoriesbasedoncon- ceptslikeequilibriumorrationalbehavioroftheinvestorswouldnaturallysuggest including and testing some structural constraints on the parameters. In this con- text, ARCH (Autoregressive Conditionally Heteroscedastic) models, introduced by Engle (1982), arise as an appropriate framework for studying these problems. Currently, there existmorethan onehundredpapers and some dozenPh.D. theses on this topic, which reflects the importance ofthis approach for statistical theory, finance and empirical work. 2 1. Introduction From the viewpoint ofstatistical theory, the ARCH models may be considered as some specific nonlinear time series models, which allow for aquite exhaustive studyoftheunderlyingdynamics.Itisthereforepossibletoreexamineanumberof classicalquestions like the random walkhypothesis, prediction intervals building, presenceoflatentvariables [factors] etc., and to test the validity ofthe previously established results.

This textbook introduces students progressively to various aspects of qualitative models and assumes a knowledge of basic principles of statistics and econometrics. Inferring qualitative characteristics of data on socioeconomic class, education, employment status, and the like - given their discrete nature - requires an entirely different set of tools from those applied to purely quantitative data. Written in accessible language and offering cogent examples, students are given valuable means to gauge real-world economic phenomena. After the introduction, early chapters present models with endogenous qualitative variables, examining dichotomous models, model specification, estimation methods, descriptive usage, and qualitative panel data. Professor Gourieroux also looks at Tobit models, in which the exogenous variable is sometimes qualitative and sometimes quantitative, and changing-regime models, in which the dependent variable is qualitative but expressed in quantitative terms. The final two chapters describe models which explain variables assumed by discrete or continuous positive variables.

This is the first volume in a major two-volume set of advanced texts in econometrics. It is essentially a text in statistics which is adapted to deal with economic phenomena. Christian Gourieroux and Alain Monfort have written a text which synthesises a great deal of material scattered across a variety of books and journals. They present both the basic and the more sophisticated statistical models which are crucial to an understanding of econometric models, and have taken care to employ mathematical tools with which a majority of students with a basic course in econometrics will be familiar. One of the most attractive features of the books is the liberal use throughout of real-world economic examples. They are also distinctive for their emphasis on promoting an intuitive understanding of the models and results at the expense of overly technical discussions.

In this book Christian Gourieroux and Alain Monfort provide an up-to-date and comprehensive analysis of modern time series econometrics. They have succeeded in synthesising in an organised and integrated way a broad and diverse literature. While the book does not assume a deep knowledge of economics, one of its most attractive features is the close attention it pays to economic models and phenomena throughout. The coverage represents a major reference tool for graduate students, researchers and applied economists. The book is divided into four sections. Section one gives a detailed treatment of classical seasonal adjustment or smoothing methods. Section two provides a thorough coverage of various mathematical tools. Section three is the heart of the book, and is devoted to a range of important topics including causality, exogeneity shocks, multipliers, cointegration and fractionally integrated models. The final section describes the main contribution of filtering and smoothing theory to time series econometric problems.

In this book Christian Gourieroux and Alain Monfort provide an up-to-date and comprehensive analysis of modern time series econometrics. They have succeeded in synthesising in an organised and integrated way a broad and diverse literature. While the book does not assume a deep knowledge of economics, one of its most attractive features is the close attention it pays to economic models and phenomena throughout. The coverage represents a major reference tool for graduate students, researchers and applied economists. The book is divided into four sections. Section one gives a detailed treatment of classical seasonal adjustment or smoothing methods. Section two provides a thorough coverage of various mathematical tools. Section three is the heart of the book, and is devoted to a range of important topics including causality, exogeneity shocks, multipliers, cointegration and fractionally integrated models. The final section describes the main contribution of filtering and smoothing theory to time series econometric problems.

This two-volume work aims to present as completely as possible the methods of statistical inference with special reference to their economic applications. The reader will find a description not only of the classical concepts and results of mathematical statistics, but also of concepts and methods recently developed for the specific needs of econometrics. The authors have sought to avoid an overly technical presentation and go to some lengths to encourage an intuitive understanding of the results by providing numerous examples throughout. The breadth of approaches and the extensive coverage of the two volumes provide for a thorough and entirely self-contained course in modern econometrics. Volume 1 provides an introduction to general concepts and methods in statistics and econometrics, and goes on to cover estimation and prediction. Volume 2 focuses on testing, confidence regions, model selection, and asymptotic theory.

This is the first volume in a major two-volume set of advanced texts in econometrics. It is essentially a text in statistics which is adapted to deal with economic phenomena. Christian Gourieroux and Alain Monfort have written a text which synthesises a great deal of material scattered across a variety of books and journals. They present both the basic and the more sophisticated statistical models which are crucial to an understanding of econometric models, and have taken care to employ mathematical tools with which a majority of students with a basic course in econometrics will be familiar. One of the most attractive features of the books is the liberal use throughout of real-world economic examples. They are also distinctive for their emphasis on promoting an intuitive understanding of the models and results at the expense of overly technical discussions.

This two-volume work aims to present as completely as possible the methods of statistical inference with special reference to their economic applications. The reader will find a description not only of the classical concepts and results of mathematical statistics, but also of concepts and methods recently developed for the specific needs of econometrics. The authors have sought to avoid an overly technical presentation and go to some lengths to encourage an intuitive understanding of the results by providing numerous examples throughout. The breadth of approaches and the extensive coverage of the two volumes provide for a thorough and entirely self-contained course in modern econometrics. Volume 1 provides an introduction to general concepts and methods in statistics and econometrics, and goes on to cover estimation and prediction. Volume 2 focuses on testing, confidence regions, model selection, and asymptotic theory.

This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-contained.

This textbook introduces students progressively to various aspects of qualitative models and assumes a knowledge of basic principles of statistics and econometrics. Inferring qualitative characteristics of data on socioeconomic class, education, employment status, and the like - given their discrete nature - requires an entirely different set of tools from those applied to purely quantitative data. Written in accessible language and offering cogent examples, students are given valuable means to gauge real-world economic phenomena. After the introduction, early chapters present models with endogenous qualitative variables, examining dichotomous models, model specification, estimation methods, descriptive usage, and qualitative panel data. Professor Gourieroux also looks at Tobit models, in which the exogenous variable is sometimes qualitative and sometimes quantitative, and changing-regime models, in which the dependent variable is qualitative but expressed in quantitative terms. The final two chapters describe models which explain variables assumed by discrete or continuous positive variables.

This book provides an accessible collection of techniques for analyzing nonparametric and semiparametric regression models. Worked examples include estimation of Engel curves and equivalence scales, scale economies, semiparametric Cobb-Douglas, translog and CES cost functions, household gasoline consumption, hedonic housing prices, option prices and state price density estimation. The book should be of interest to a broad range of economists including those working in industrial organization, labor, development, urban, energy and financial economics. A variety of testing procedures are covered including simple goodness of fit tests and residual regression tests. These procedures can be used to test hypotheses such as parametric and semiparametric specifications, significance, monotonicity and additive separability. Other topics include endogeneity of parametric and nonparametric effects, as well as heteroskedasticity and autocorrelation in the residuals. Bootstrap procedures are provided.

Financial econometrics is a great success story in economics. Econometrics uses data and statistical inference methods, together with structural and descriptive modeling, to address rigorous economic problems. Its development within the world of finance is quite recent and has been paralleled by a fast expansion of financial markets and an increasing variety and complexity of financial products. This has fueled the demand for people with advanced econometrics skills. For professionals and advanced graduate students pursuing greater expertise in econometric modeling, this is a superb guide to the field's frontier. With the goal of providing information that is absolutely up-to-date--essential in today's rapidly evolving financial environment--Gourieroux and Jasiak focus on methods related to foregoing research and those modeling techniques that seem relevant to future advances. They present a balanced synthesis of financial theory and statistical methodology.Recognizing that any model is necessarily a simplified image of reality and that econometric methods must be adapted and applied on a case-by-case basis, the authors employ a wide variety of data sampled at frequencies ranging from intraday to monthly. These data comprise time series representing both the European and North American markets for stocks, bonds, and foreign currencies. Practitioners are encouraged to keep a critical eye and are armed with graphical diagnostics to eradicate misspecification errors. This authoritative, state-of-the-art reference text is ideal for upper-level graduate students, researchers, and professionals seeking to update their skills and gain greater facility in using econometric models. All will benefit from the emphasis on practical aspects of financial modeling and statistical inference. Doctoral candidates will appreciate the inclusion of detailed mathematical derivations of the deeper results as well as the more advanced problems concerning high-frequency data and risk control.By establishing a link between practical questions and the answers provided by financial and statistical theory, the book also addresses the needs of applied researchers employed by financial institutions.

The individual risks faced by banks, insurers, and marketers are less well understood than aggregate risks such as market-price changes. But the risks incurred or carried by individual people, companies, insurance policies, or credit agreements can be just as devastating as macroevents such as share-price fluctuations. A comprehensive introduction, The Econometrics of Individual Risk is the first book to provide a complete econometric methodology for quantifying and managing this underappreciated but important variety of risk. The book presents a course in the econometric theory of individual risk illustrated by empirical examples. And, unlike other texts, it is focused entirely on solving the actual individual risk problems businesses confront today. Christian Gourieroux and Joann Jasiak emphasize the microeconometric aspect of risk analysis by extensively discussing practical problems such as retail credit scoring, credit card transaction dynamics, and profit maximization in promotional mailing. They address regulatory issues in sections on computing the minimum capital reserve for coverage of potential losses, and on the credit-risk measure CreditVar.The book will interest graduate students in economics, business, finance, and actuarial studies, as well as actuaries and financial analysts.

Financial econometrics is a great success story in economics. Econometrics uses data and statistical inference methods, together with structural and descriptive modeling, to address rigorous economic problems. Its development within the world of finance is quite recent and has been paralleled by a fast expansion of financial markets and an increasing variety and complexity of financial products. This has fueled the demand for people with advanced econometrics skills.For professionals and advanced graduate students pursuing greater expertise in econometric modeling, this is a superb guide to the field's frontier. With the goal of providing information that is absolutely up-to-date—essential in today's rapidly evolving financial environment—Gourieroux and Jasiak focus on methods related to foregoing research and those modeling techniques that seem relevant to future advances. They present a balanced synthesis of financial theory and statistical methodology. Recognizing that any model is necessarily a simplified image of reality and that econometric methods must be adapted and applied on a case-by-case basis, the authors employ a wide variety of data sampled at frequencies ranging from intraday to monthly. These data comprise time series representing both the European and North American markets for stocks, bonds, and foreign currencies. Practitioners are encouraged to keep a critical eye and are armed with graphical diagnostics to eradicate misspecification errors.This authoritative, state-of-the-art reference text is ideal for upper-level graduate students, researchers, and professionals seeking to update their skills and gain greater facility in using econometric models. All will benefit from the emphasis on practical aspects of financial modeling and statistical inference. Doctoral candidates will appreciate the inclusion of detailed mathematical derivations of the deeper results as well as the more advanced problems concerning high-frequency data and risk control. By establishing a link between practical questions and the answers provided by financial and statistical theory, the book also addresses the needs of applied researchers employed by financial institutions.

1.1 The DevelopmentofARCH Models Time series models have been initially introduced either for descriptive purposes like prediction and seasonal correction or for dynamic control. In the 1970s, the researchfocusedonaspecificclassoftimeseriesmodels,theso-calledautoregres- sive moving average processes (ARMA), which were very easy to implement. In thesemodels,thecurrentvalueoftheseriesofinterestiswrittenasalinearfunction ofits own laggedvalues andcurrentandpastvaluesofsomenoiseprocess, which can be interpreted as innovations to the system. However, this approach has two major drawbacks: 1) it is essentially a linear setup, which automatically restricts the type of dynamics to be approximated; 2) it is generally applied without im- posing a priori constraintson the autoregressive and moving average parameters, which is inadequatefor structural interpretations. Among the field ofapplications where standard ARMA fit is poorare financial and monetary problems. The financial time series features various forms ofnon- lineardynamics,the crucialone being the strongdependenceofthe instantaneous variabilityoftheseriesonitsownpast.Moreover,financial theoriesbasedoncon- ceptslikeequilibriumorrationalbehavioroftheinvestorswouldnaturallysuggest including and testing some structural constraints on the parameters. In this con- text, ARCH (Autoregressive Conditionally Heteroscedastic) models, introduced by Engle (1982), arise as an appropriate framework for studying these problems. Currently, there existmorethan onehundredpapers and some dozenPh.D. theses on this topic, which reflects the importance ofthis approach for statistical theory, finance and empirical work. 2 1. Introduction From the viewpoint ofstatistical theory, the ARCH models may be considered as some specific nonlinear time series models, which allow for aquite exhaustive studyoftheunderlyingdynamics.Itisthereforepossibletoreexamineanumberof classicalquestions like the random walkhypothesis, prediction intervals building, presenceoflatentvariables [factors] etc., and to test the validity ofthe previously established results.