Short-Memory Linear Processes and Econometric Applications - Kairat T. Mynbaev - ebook

Short-Memory Linear Processes and Econometric Applications ebook

Kairat T. Mynbaev

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519,99 zł

Opis

This book serves as a comprehensive source of asymptotic results for econometric models with deterministic exogenous regressors. Such regressors include linear (more generally, piece-wise polynomial) trends, seasonally oscillating functions, and slowly varying functions including logarithmic trends, as well as some specifications of spatial matrices in the theory of spatial models. The book begins with central limit theorems (CLTs) for weighted sums of short memory linear processes. This part contains the analysis of certain operators in Lp spaces and their employment in the derivation of CLTs. The applications of CLTs are to the asymptotic distribution of various estimators for several econometric models. Among the models discussed are static linear models with slowly varying regressors, spatial models, time series autoregressions, and two nonlinear models (binary logit model and nonlinear model whose linearization contains slowly varying regressors). The estimation procedures include ordinary and nonlinear least squares, maximum likelihood, and method of moments. Additional topical coverage includes an introduction to operators, probabilities, and linear models; Lp-approximable sequences of vectors; convergence of linear and quadratic forms; regressions with slowly varying regressors; spatial models; convergence; nonlinear models; and tools for vector autoregressions.

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Liczba stron: 519




CONTENTS

COVER

HALF TITLE PAGE

TITLE PAGE

COPYRIGHT PAGE

DEDICATION

LIST OF TABLES

PREFACE

1 RED LIGHT

2 GREEN LIGHT

3 THE ESSENCE

4 STANDING PROBLEMS

5 REVIEW BY CHAPTERS

6 EXPOSITION

7 SUGGESTIONS FOR READING

ACKNOWLEDGMENTS

CHAPTER 1: INTRODUCTION TO OPERATORS, PROBABILITIES AND THE LINEAR MODEL

1.1 LINEAR SPACES

1.2 NORMED SPACES

1.3 LINEAR OPERATORS

1.4 HILBERT SPACES

1.5 Lp SPACES

1.6 CONDITIONING ON σ-FIELDS

1.7 MATRIX ALGEBRA

1.8 CONVERGENCE OF RANDOM VARIABLES

1.9 THE LINEAR MODEL

1.10 NORMALIZATION OF REGRESSORS

1.11 GENERAL FRAMEWORK IN THE CASE OF K REGRESSORS

1.12 INTRODUCTION TO L2-APPROXIMABILITY

CHAPTER 2: Lp-APPROXIMABLE SEQUENCES OF VECTORS

2.1 DISCRETIZATION, INTERPOLATION AND HAAR PROJECTOR IN Lp

2.2 CONVERGENCE OF BILINEAR FORMS

2.3 THE TRINITY AND ITS BOUNDEDNESS IN Ip

2.4 CONVERGENCE OF THE TRINITY ON Lp-GENERATED SEQUENCES

2.5 PROPERTIES OF Lp-APPROXIMABLE SEQUENCES

2.6 CRITERION OF Lp-APPROXIMABILITY

2.7 EXAMPLES AND COUNTEREXAMPLES

CHAPTER 3: CONVERGENCE OF LINEAR AND QUADRATIC FORMS

3.1 GENERAL INFORMATION

3.2 WEAK LAWS OF LARGE NUMBERS

3.3 CENTRAL LIMIT THEOREMS FOR MARTINGALE DIFFERENCES

3.4 CENTRAL LIMIT THEOREMS FOR WEIGHTED SUMS OF MARTINGALE DIFFERENCES

3.5 CENTRAL LIMIT THEOREMS FOR WEIGHTED SUMS OF LINEAR PROCESSES

3.6 Lp-APPROXIMABLE SEQUENCES OF MATRICES

3.7 INTEGRAL OPERATORS

3.8 CLASSES σp

3.9 CONVERGENCE OF QUADRATIC FORMS OF RANDOM VARIABLES

CHAPTER 4: REGRESSIONS WITH SLOWLY VARYING REGRESSORS

4.1 SLOWLY VARYING FUNCTIONS

4.2 PHILLIPS GALLERY 1

4.3 SLOWLY VARYING FUNCTIONS WITH REMAINDER

4.4 RESULTS BASED ON Lp-APPROXIMABILITY

4.5 PHILLIPS GALLERY 2

4.6 REGRESSION WITH TWO SLOWLY VARYING REGRESSORS

CHAPTER 5: SPATIAL MODELS

5.1 A MATH INTRODUCTION TO PURELY SPATIAL MODELS

5.2 CONTINUITY OF NONLINEAR MATRIX FUNCTIONS

5.3 ASSUMPTION ON THE ERROR TERM AND IMPLICATIONS

5.4 ASSUMPTION ON THE SPATIAL MATRICES AND IMPLICATIONS

5.5 ASSUMPTION ON THE KERNEL AND IMPLICATIONS

5.6 LINEAR AND QUADRATIC FORMS INVOLVING SEGMENTS OF K

5.7 THE ROUNDABOUT ROAD

5.8 ASYMPTOTICS OF THE OLS ESTIMATOR FOR PURELY SPATIAL MODEL

5.9 METHOD OF MOMENTS AND MAXIMUM LIKELIHOOD

5.10 TWO-STEP PROCEDURE

5.11 EXAMPLES AND COMPUTER SIMULATION

5.12 MIXED SPATIAL MODEL

5.13 THE ROUNDABOUT ROAD (MIXED MODEL)

5.14 ASYMPTOTICS OF THE OLS ESTIMATOR FOR MIXED SPATIAL MODEL

CHAPTER 6: CONVERGENCE ALMOST EVERYWHERE

6.1 THEORETICAL BACKGROUND

6.2 VARIOUS BOUNDS ON MARTINGALE TRANSFORMS

6.3 MARCINKIEWICZ-ZYGMUND THEOREMS AND RELATED RESULTS

6.4 STRONG CONSISTENCY FOR MULTIPLE REGRESSION

6.5 SOME ALGEBRA RELATED TO VECTOR AUTOREGRESSION

6.6 PRELIMINARY ANALYSIS

6.7 STRONG CONSISTENCY FOR VECTOR AUTOREGRESSION AND RELATED RESULTS

CHAPTER 7: NONLINEAR MODELS

7.1 ASYMPTOTIC NORMALITY OF AN ABSTRACT ESTIMATOR

7.2 CONVERGENCE OF SOME DETERMINISTIC AND STOCHASTIC EXPRESSIONS

7.3 NONLINEAR LEAST SQUARES

7.4 BINARY LOGIT MODELS WITH UNBOUNDED EXPLANATORY VARIABLES

CHAPTER 8: TOOLS FOR VECTOR AUTOREGRESSIONS

8.1 Lp-APPROXIMABLE SEQUENCES OF MATRIX-VALUED FUNCTIONS

8.2 T-OPERATOR AND TRINITY

8.3 MATRIX OPERATIONS AND Lp-APPROXIMABILITY

8.4 RESOLVENTS

8.5 CONVERGENCE AND BOUNDS FOR DETERMINISTIC TRENDS

REFERENCES

AUTHOR INDEX

SUBJECT INDEX

SHORT-MEMORY LINEAR PROCESSES AND ECONOMETRIC APPLICATIONS

Copyright © 2011 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New JerseyPublished simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Mynbaev, K. T. (Kairat Turysbekovich)Short-memory linear processes and econometric applications / Kairat T. Mynbaev.p. cm.Includes bibliographical references and index.ISBN 978-0-470-92419-81.   Linear programming.  2.   Econometric models.  3.   Regression analysis.  4.   Probabilities. I. Title.T57.74.M98 2011519.7′2—dc22

2010040947

To my teacher Mukhtarbai Otelbaev,from whom I learnt the best I know.

ACKNOWLEDGMENTS

I am grateful to Carlos Martins Filho for his encouragement for this book and many other projects. The folks at John Wiley & Sons have been highly efficient in preparing the book for publication. The production process surely involved many people of whom I would like to especially thank Susanne Steitz-Filler, Christine Punzo, Jacqueline Palmieri, and Nick Barber (Books Manager, Techset Composition Ltd).

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Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!

Lesen Sie weiter in der vollständigen Ausgabe!