Introductory Econometrics for Finance

1 Introductory Econometricsfor FinanceChris BrooksThe ISMA Centre, University of Readingpublished by the press syndicate of the university of cambridgeThe Pitt Building, Trumpington Street, Cambridge, United Kingdomcambridge university pressThe Edinburgh Building, Cambridge CB2 2RU, UK40 West 20th Street, New York, NY 10011-4211, USA477 Williamstown Road, Port Melbourne, VIC 3207, AustraliaRuiz de Alarco n 13, 28014 Madrid, SpainDock House, The Waterfront, Cape Town 8001, South Chris Brooks 2002 This book is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University published 2002 Printed in the United Kingdom at the University Press, CambridgeTypefacesSwift pt.

2 And Franklin GothicSystemLATEX2 [TB]A catalogue record for this book is available from the British LibraryLibrary of Congress Cataloguing in Publication dataBrooks, ChrisIntroductory Econometrics for Finance / Chris bibliographical references and 0 521 79018 2 (hardback) -- ISBN 0 521 79367 X (paperback)1. Finance -- Econometric models. 2. Econometrics . I..B76 2002332 .01 5195 -- dc21 2001037930 ISBN 0 521 79018 2 hardbackISBN 0 521 79367 X paperbackContentsList of figurespagexiiList of tablesxvList of boxesxviiiList of screenshotsxxPrefacexxiAcknowledgementsx xv1 What is Econometrics ?

3 Is financial Econometrics different from economiceconometrics ? Some stylised characteristicsof financial Types of Returns in financial Steps involved in formulating an econometric Some points to consider when reading articles inthe empirical financial Outline of the remainder of this book112 Econometric packages for modelling financial What packages are available? Choosing a Accomplishing simple tasks using the two Further reading39 Appendix: economic software package suppliers403 A brief overview of the classical linear regression What is a regression model?

4 Regression versus correlation43v Simple Some further The assumptions underlying the classical linearregression Properties of the OLS Precision and standard An introduction to statistical Generalising the simple model to multiplelinear The constant How are the parameters (the elements of the vector)calculated in the generalised case? A special type of hypothesis test: Data mining and the true size of the An example of the use of a simplet-test to test a theoryin Finance : can US mutual funds beat the market?

5 Can UK unit trust managers beat the market? The overreaction hypothesis and the UK stock Testing multiple hypotheses: Sample EViews and RATS instructions and outputfor simple linear regression108 Appendix: mathematical derivations of CLRM Deriving the OLS coefficient estimator in thebivariate Derivation of the OLS standard error estimators forthe intercept and slope in the bivariate Derivation of the OLS coefficient estimator in the multipleregression Derivation of the OLS standard error estimator inthe multiple regression context1284 Goodness of fit Hedonic pricing Tests of non-nested Violations of the assumptions of the classicallinear regression Assumption 1: E(ut)= Assumption 2: var(ut)= 2< Assumption 3.

6 Cov(ui,uj)=0fori = Assumption 4: thextare non-stochastic178 Contents Assumption 5: the disturbances are normally Adopting the wrong functional Omission of an important Inclusion of an irrelevant Parameter stability A strategy for constructing econometric modelsand a discussion of model-building Determinants of sovereign credit ratings211 Appendix: a brief introduction to principalcomponents An application of principal components to interest Calculating principal components in practice2255 Univariate time series modelling and Some notation and Moving average Autoregressive The partial autocorrelation ARMA Building ARMA models: the Box--Jenkins Example.

7 Constructing ARMA models in Estimating ARMA models with Examples of time series modelling in Exponential Forecasting in Forecasting using ARMA models in Forecasting using ARMA models in Estimating exponential smoothing modelsusing EViews and RATS2956 Multivariate Simultaneous equations So how can simultaneous equations modelsbe validly estimated? Can the original coefficients be retrieved from the s? Simultaneous equations in A definition of A special case: a set of equations that looks likea simultaneous equations system, but isn t313 Estimation procedures for simultaneous An application of a simultaneous equations approachin Finance : modelling bid--ask spreads and trading activityin the S&P 100 index options Simultaneous equations modelling using EViewsand A Hausman test in Vector autoregressive Does the VAR include contemporaneous terms?

8 Block significance and causality VARs with exogenous Impulse responses and variance An example of the use of VAR models: the interactionbetween property returns and the VAR estimation in RATS and EViews3517 Modelling long-run relationships in Stationarity and unit root Testing for unit roots in Testing for unit roots in Equilibrium correction or error correction Testing for cointegration in regression:a residuals-based Methods of parameter estimation in cointegrated Lead--lag and long-term relationships between spotand futures Testing for and estimating cointegrating systems usingthe Johansen technique based on Purchasing power Cointegration between international bond Testing the expectations hypothesis of the term structureof interest Testing for cointegration and modelling cointegratedsystems using EViews and RATS4208 Modelling volatility and Motivations.

9 An excursion into non-linearity Models for Historical Implied volatility models442 Contents Exponentially weighted moving average Autoregressive volatility Autoregressive conditionally heteroscedastic (ARCH) Generalised ARCH (GARCH) Estimation of ARCH/GARCH Extensions to the basic GARCH Asymmetric GARCH The GJR The EGARCH GJR and EGARCH in Estimating GJR and EGARCH models using Tests for asymmetries in Uses of GARCH-type models including volatility Testing non-linear restrictions or testing hypothesesabout non-linear Volatility forecasting: some examples and resultsfrom the Stochastic volatility models Forecasting covariances and Covariance modelling and forecasting in Finance .

10 Examples of model Historical covariance and Implied covariance Exponentially weighted moving average modelsfor Multivariate GARCH A multivariate GARCH model for the CAPM withtime-varying Estimating a time-varying hedge ratio for FTSE stockindex Estimating multivariate GARCH models using RATS andEViews516 Appendix: parameter estimation using maximumlikelihood5269 Switching Seasonalities in financial markets: introductionand literature review536 Modelling seasonality in financial Estimating simple piecewise linear Markov switching An application of Markov switching models tothe gilt--equity yield Estimation of Markov switching models in Threshold autoregressive Estimation of threshold autoregressive Specification tests in the context of Markov switchingand threshold autoregressive models.