Selection of Models by Forecasting Intervals
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A. H. Q. M. MERKIES
SELECTION OF MODELS BY FORECASTING INTERVALS
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
MODELKEUZE VIA VOORSPELLINGSINTERVALLEN
First published in 1972 by Academic Service, Amsterdam Translatedfrom the Dutch by M. van Holten-de Woljf
Library of Congress Catalog Card Number 73-83565 ISBN 978-94-010-2595-9 ISBN 978-94-010-2593-5 (eBook) DOI 10.1007/978-94-010-2593-5
All Rights Reserved Copyright© 1973 by Springer Science+Business Media Dordrecht Originally published by D. Reide1 Publishing Company, Dordrecht, Holland in 1973 Softcover reprint ofthe hardcover 1st edition 1973 No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher
TABLE OF CONTENTS
PREFACE
VII
CHAPTER I. INTRODUCTION
1
CHAPTER II. FORECASTING AS A SELECTION PROBLEM
3
2.1. 2.2. 2.3. 2.4. 2.5.
Introduction Definitions Models The Practice of Forecasting The Framework of the Problem and Its Restrictions
3 3 4 8 14
CHAPTER III. THE CRITERION FOR SELECTION
19
3.1. Introduction 3.2. Models with Parameters Known 3.2.1. The Criterion for Selection 3.2.2. The Optimal Number of Equations of the Model 3.3. Models with Estimated Variables 3.4. Evaluated Forecasts
19 19 19 23 26 38
CHAPTER IV. THE SET OF ADMITTED MODELS AND THE WAY IN WHICH THE SELECTION IS CARRIED OUT
4.1. Introduction 4.2. The Composition of the Criterion for Selection and the Standards used in Practice 4.2.1. The Composition of the Criterion 4.2.2. The Standards Used in Practice 4.2.3. Inequality Coefficients 4.3. The Set of Models Considered and the Set of Admitted Models 4.3.1. Introduction 4.3.2. The Considered Set
48 48 48 48 52 55 56 56 56
VI
TABLE OF CONTENTS
4.3.3. The Set of Admitted Models 4.3.4. Selection in Case of More Equations 4.4. Efficiency in the Selection of the Optimal Forecasting Procedure 4.4.1. Introduction 4.4.2. One Equation 4.4.3. More Equations 4.5. Some Remarks on the Use of Lagged Process Variables
64 73
CHAPTER V. EXAMPLES
99
74 74 75 82 85
5.1. Introduction 5.2. The Forecast of the Export Surplus for Two Years 5.2.1. The General Set-up 5.2.2. Some Problems 5.3. The Forecast of the Export Surplus One Year in Advance 5.3.1. Introduction 5.3.2. Models with Lagged Endogeneous Variables 5.3.3. Models with Lagged Exogeneous Variables 5.3.4. Models that can be derived from Q[L 1 Q_ 1 c] 5.3.5. The Specification Q[Q_ 1 w_tJ and the Ranking of the Relevant Admitted Models 5.3.6. Conditional Forecasts 5.3.7. The Performance of Procedure A in the Sixties 5.4. The Forecast of the Gross National Product 5.5. The Simultaneous Forecast of Yr and Qt
99 100 100 106 108 108 110 113 113
APPENDIX A
130
BIBLIOGRAPHY
133
114 115 117 121 122
PREFACE
This book appeared as a Ph.D. thesis for the University of Amsterdam. I hope it will be of interest to others. I owe grateful thanks to many people who- consciously or not- have given me their support. This refers mainly to Prof. Dr. J. S. Cramer who not only as director of the Instituut voor
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