ECONOMETRIC FORECASTING AND HIGH-FREQUENCY DATA ANALYSIS

ECONOMETRIC FORECASTING AND HIGH-FREQUENCY DATA ANALYSIS

LECTURE NOTES SERIES Institute for Mathematical Sciences, National University of Singapore Series Editors: Louis H. Y. Chen and Ka Hin Leung Institute for Mathematical Sciences National University of Singapore ISSN: 1793-0758 Published Vol. 1 Vol. 2 Vol. 3 Vol. 4 Vol. 5 Vol. 6 Vol. 7 Vol. 8 Vol. 9 Vol. 10 Vol. 11 Coding Theory and Cryptology edited by Harald Niederreiter Representations of Real and p-adic Groups edited by Eng-Chye Tan & Chen-Bo Zhu Selected Topics in Post-Genome Knowledge Discovery edited by Limsoon Wong & Louxin Zhang An Introduction to Stein s Method edited by A. D. Barbour & Louis H. Y. Chen Stein's Method and Applications edited by A. D. Barbour & Louis H. Y. Chen Computational Methods in Large Scale Simulation edited by K.-Y. Lam & H.-P. Lee Markov Chain Monte Carlo: Innovations and Applications edited by W. S. Kendall, F. Liang & J.-S. Wang Transition and Turbulence Control edited by Mohamed Gad-el-Hak & Her Mann Tsai Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization edited by Weizhu Bao & Jian-Guo Liu Gabor and Wavelet Frames edited by Say Song Goh, Amos Ron & Zuowei Shen Mathematics and Computation in Imaging Science and Information Processing edited by Say Song Goh, Amos Ron & Zuowei Shen Vol. 12 Vol. 13 Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory In Honor of Roger E. Howe edited by Jian-Shu Li, Eng-Chye Tan, Nolan Wallach & Chen-Bo Zhu Econometric Forecasting and High-Frequency Data Analysis edited by Roberto S. Mariano & Yiu-Kuen Tse

Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore Vol. 13 ECONOMETRIC FORECASTING AND HIGH-FREQUENCY DATA ANALYSIS Editors Roberto S. Mariano Singapore Management University, Singapore & University of Pennsylvania, USA Yiu-Kuen Tse Singapore Management University, Singapore World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI

Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore Vol. 13 ECONOMETRIC FORECASTING AND HIGH-FREQUENCY DATA ANALYSIS Copyright 2008 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-981-277-895-6 ISBN-10 981-277-895-0 Printed in Singapore.

CONTENTS Foreword Preface vii ix Forecast Uncertainty, its Representation and Evaluation Kenneth F. Wallis 1 The University of Pennsylvania Models for High-Frequency Macroeconomic and Modeling Lawrence R. Klein and Suleyman Ozmucur 53 Forecasting Seasonal Time Series Philip Hans Franses 93 Car and Affine Processes Christian Gourieroux 131 Multivariate Time Series Analysis and Forecasting Manfred Deistler 159 v

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FOREWORD The Institute for Mathematical Sciences at the National University of Singapore was established on 1 July 2000. Its mission is to foster mathematical research, both fundamental and multidisciplinary, particularly research that links mathematics to other disciplines, to nurture the growth of mathematical expertise among research scientists, to train talent for research in the mathematical sciences, and to serve as a platform for research interaction between the scientific community in Singapore and the wider international community. The Institute organizes thematic programs which last from one month to six months. The theme or themes of a program will generally be of a multidisciplinary nature, chosen from areas at the forefront of current research in the mathematical sciences and their applications. Generally, for each program there will be tutorial lectures followed by workshops at research level. Notes on these lectures are usually made available to the participants for their immediate benefit during the program. The main objective of the Institute s Lecture Notes Series is to bring these lectures to a wider audience. Occasionally, the Series may also include the proceedings of workshops and expository lectures organized by the Institute. The World Scientific Publishing Company has kindly agreed to publish the Lecture Notes Series. This Volume, Econometric Forecasting and High-Frequency Data Analysis, is the thirteenth of this Series. We hope that through the regular publication of these lecture notes the Institute will achieve, in part, its objective of promoting research in the mathematical sciences and their applications. October 2007 Louis H.Y. Chen Ka Hin Leung Series Editors vii

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PREFACE This volume contains papers and tutorial notes presented in the Econometric Forecasting and High-Frequency Data Analysis Program jointly organized by the Institute for Mathematical Sciences, National University of Singapore, and the School of Economics, Singapore Management University, in April May 2004, for which, together with Tilak Abeysinghe, we were Program Co-Chairs. The chapters collected in this volume summarize some recent findings and new results in two key areas in econometrics: econometric forecasting and the analysis of high-frequency financial data. The paper by Klein and Ozmucur proposes new methods for forecasting macroeconomic variables by combining data with different frequencies. Wallis emphasizes the importance of communicating information about forecast uncertainty, and considers various statistical techniques for assessing the reliability of forecasts. Franses focuses on techniques for forecasting seasonal time series data, including some advanced techniques on modeling seasonal and periodic unit roots. Viewing daily data as aggregates of compound sums of tick-by-tick data, Gourieroux discusses the class of compound autoregressive (Car) processes. Deistler considers the important problem of modeling multivariate time series, including the issues of estimation and model selection. We are indebted to our Program Committee members for their valuable inputs into the Program, to Louis Chen, Director of IMS, for his unfailing support, and to Lai Fun Kwong of World Scientific, for her endless patience. This volume brings us some fond memory of the Program, the highlight of which was a one-and-a-half day symposium. The symposium culminated in a public forum on Econometrics Today, which was chaired by Roberto S. Mariano and attended by over 120 participants. The panel, which consists of Lawrence Klein, Robert Engle and Kenneth Wallis, freely shared its candid views about the current state of econometric methodology and its impact on economic research. October 2007 Roberto S. Mariano Singapore Management University, Singapore & University of Pennsylvania, USA Yiu-Kuen Tse Singapore Management University, Singapore ix