Introductory Econometrics for Finance

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than deriving proofs and learning formulae ● To write an accessible textbook that required no prior knowledge of

Limited dependent variable models Introduction and motivation The linear probability model The logit model Using a logit to test the pecking order hypothesis The probit model Choosing between the logit and probit models Estimation of limited dependent variable models Goodness of fit measures for linear dependent variable models Multinomial linear dependent variables The pecking order hypothesis revisited -- the choice between financing methods Ordered response linear dependent variables models Are unsolicited credit ratings biased downwards? An ordered probit analysis Censored and truncated dependent variables Limited dependent variable models in EViews Appendix: The maximum likelihood estimator for logit and probit models Returns in financial modelling In many of the problems of interest in finance, the starting point is a time series of prices -- for example, the prices of shares in Ford, taken at 4p.m. each day for 200 days. For a number of statistical reasons, it is preferable not to work directly with the price series, so that raw price series are usually converted into series of returns. Additionally, returns have the added benefit that they are unit-free. So, for example, if an annualised return were 10%, then investors know that they would have got back £110 for a £100 investment, or £1,100 for a £1,000 investment, and so on. There are two methods used to calculate returns from a series of prices, and these involve the formation of simple returns, and continuously compounded returns, which are achieved as follows: Simple returns Rt =Is financial econometrics different from ‘economic econometrics’? As previously stated, the tools commonly used in financial applications are fundamentally the same as those used in economic applications, although the emphasis and the sets of problems that are likely to be encountered when analysing the two sets of data are somewhat different. Financial data often differ from macroeconomic data in terms of their frequency, accuracy, seasonality and other properties. In economics, a serious problem is often a lack of data at hand for testing the theory or hypothesis of interest -- this is often called a ‘small samples problem’. It might be, for example, that data are required on government budget deficits, or population figures, which are measured only on an annual basis. If the methods used to measure these quantities changed a quarter of a century ago, then only at most twenty-five of these annual observations are usefully available. Two other problems that are often encountered in conducting applied econometric work in the arena of economics are those of measurement error and data revisions. These difficulties are simply that the data may be estimated, or measured with error, and will often be subject to several vintages of subsequent revisions. For example, a researcher may estimate an economic model of the effect on national output of investment in computer technology using a set of published data, only to find that the Includes worked examples on how to conduct events studies and the Fama–MacBeth method, two of the most common empirical approaches in finance, ensuring that students are well-prepared for econometrics in practice Chris Brooks is Professor of Finance at the ICMA Centre, University of Reading, UK, where he also obtained his PhD. He has published over sixty articles in leading academic and practitioner journals including the Journal of Business, the Journal of Banking and Finance, the Journal of Empirical Finance, the Review of Economics and Statistics and the Economic Journal. He is an associate editor of a number of journals including the International Journal of Forecasting. He has also acted as consultant for various banks and professional bodies in the fields of finance, econometrics and real estate. This is one of the most readable books on financial econometrics. It will be very useful for students of finance and economics. It covers a wide variety of topics that are of interest to researchers and practitioners, in both academia and industry.' This excellent book provides practical econometric solutions for empirical finance. It is an ideal textbook for introductory courses on financial econometrics …'

data for the last two years have been revised substantially in the next, updated publication. These issues are rarely of concern in finance. Financial data come in many shapes and forms, but in general the prices and other entities that are recorded are those at which trades actually took place, or which were quoted on the screens of information providers. There exists, of course, the possibility for typos and possibility for the data measurement method to change (for example, owing to stock index re-balancing or re-basing). But in general the measurement error and revisions problems are far less serious in the financial context. Similarly, some sets of financial data are observed at much higher frequencies than macroeconomic data. Asset prices or yields are often available at daily, hourly, or minute-by-minute frequencies. Thus the number of observations available for analysis can potentially be very large -- perhaps thousands or even millions, making financial data the envy of macroeconometricians! The implication is that more powerful techniques can often be applied to financial than economic data, and that researchers may also have more confidence in the results. Furthermore, the analysis of financial data also brings with it a number of new problems. While the difficulties associated with handling and processing such a large amount of data are not usually an issue given recent and continuing advances in computer power, financial data often have a number of additional characteristics. For example, financial data are often considered very ‘noisy’, which means that it is more difficult to separate underlying trends or patterns from random and uninteresting features. Financial data are also almost always not normally distributed in spite of the fact that most techniques in econometrics assume that they are. High frequency data often contain additional ‘patterns’ which are the result of the way that the market works, or the way that prices are recorded. These features need to be considered in the model-building process, even if they are not directly of interest to the researcher.

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where: Rt denotes the simple return at time t, rt denotes the continuously compounded return at time t, pt denotes the asset price at time t, and ln denotes the natural logarithm. If the asset under consideration is a stock or portfolio of stocks, the total return to holding it is the sum of the capital gain and any dividends paid during the holding period. However, researchers often ignore any dividend payments. This is unfortunate, and will lead to an underestimation of the total returns that accrue to investors. This is likely to be negligible for very short holding periods, but will have a severe impact on cumulative returns over investment horizons of several years. Ignoring dividends will also have a distortionary effect on the crosssection of stock returns. For example, ignoring dividends will imply that ‘growth’ stocks, with large capital gains will be inappropriately favoured over income stocks (e.g. utilities and mature industries) that pay high dividends. Cross-sectional data Cross-sectional data are data on one or more variables collected at a single point in time. For example, the data might be on: ● A poll of usage of Internet stockbroking services ● A cross-section of stock returns on the New York Stock Exchange Uncovered interest parity test results Forecast error aggregation Call bid--ask spread and trading volume regression 6.2 Put bid--ask spread and trading volume regression 6.3 Granger causality tests and implied restrictions on VAR models 6.4 Marginal significance levels associated with joint F-tests 6.5 Variance decompositions for the property sector index residuals 7.1 Critical values for DF tests (Fuller, 1976, p. 373) 7.2 DF tests on log-prices and returns for high frequency FTSE data 7.3 Estimated potentially cointegrating equation and test for cointegration for high frequency FTSE data 7.4 Estimated error correction model for high frequency FTSE data 7.5 Comparison of out-of-sample forecasting accuracy 7.6 Trading profitability of the error correction model with cost of carry 7.7 Cointegration tests of PPP with European data 7.8 DF tests for international bond indices 7.9 Cointegration tests for pairs of international bond indices 7.10 Johansen tests for cointegration between international bond yields 7.11 Variance decompositions for VAR of international bond yields

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521873062 © Chris Brooks 2008 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2008 The value of econometrics page 2 Time series data 4 Log returns 8 Points to consider when reading a published paper 11 1.5 Features of EViews 21 2.1 Names for y and xs in regression models 28 2.2 Reasons for the inclusion of the disturbance term 30 2.3 Assumptions concerning disturbance terms and their interpretation 44 2.4 Standard error estimators 48 2.5 Conducting a test of significance 56 2.6 Carrying out a hypothesis test using confidence intervals 60 2.7 The test of significance and confidence interval approaches compared 61 2.8 Type I and type II errors 64 2.9 Reasons for stock market overreactions 71 2.10 Ranking stocks and forming portfolios 72 2.11 Portfolio monitoring 72 3.1 The relationship between the regression F-statistic and R 2 111 3.2 Selecting between models 117 4.1 Conducting White’s test 134 4.2 ‘Solutions’ for heteroscedasticity 138 4.3 Conditions for DW to be a valid test 148 4.4 Conducting a Breusch--Godfrey test 149 4.5 The Cochrane--Orcutt procedure 151 Panel data Introduction -- what are panel techniques and why are they used? What panel techniques are available? The fixed effects model Time-fixed effects models Investigating banking competition using a fixed effects model The random effects model Panel data application to credit stability of banks in Central and Eastern Europe 10.8 Panel data with EViews 10.9 Further reading A normal versus a skewed distribution 4.11 A leptokurtic versus a normal distribution 4.12 Regression residuals from stock return data, showing large outlier for October 1987 4.13 Possible effect of an outlier on OLS estimation 4.14 Plot of a variable showing suggestion for break date 5.1 Autocorrelation function for sample MA(2) process 5.2 Sample autocorrelation and partial autocorrelation functions for an MA(1) model: yt = −0.5u t−1 + u t 5.3 Sample autocorrelation and partial autocorrelation functions for an MA(2) model: yt = 0.5u t−1 − 0.25u t−2 + u t 5.4 Sample autocorrelation and partial autocorrelation functions for a slowly decaying AR(1) model: yt = 0.9yt−1 + u t 5.5 Sample autocorrelation and partial autocorrelation functions for a more rapidly decaying AR(1) model: yt = 0.5yt−1 + u t 5.6 Sample autocorrelation and partial autocorrelation functions for a more rapidly decaying AR(1) model with negative coefficient: yt = −0.5yt−1 + u t 5.7 Sample autocorrelation and partial autocorrelation functions for a non-stationary model (i.e. a unit coefficient): yt = yt−1 + u t 5.8 Sample autocorrelation and partial autocorrelation functions for an ARMA(1, 1) model: yt = 0.5yt−1 + 0.5u t−1 + u t 5.9 Use of an in-sample and an out-of-sample period for analysis 6.1 Impulse responses and standard error bands for innovations in unexpected inflation equation errors 6.2 Impulse responses and standard error bands for innovations in the dividend yields 7.1 Value of R2 for 1,000 sets of regressions of a non-stationary variable on another independent non-stationary variable It is important to note that the process of building a robust empirical model is an iterative one, and it is certainly not an exact science. Often, the final preferred model could be very different from the one originally proposed, and need not be unique in the sense that another researcher with the same data and the same initial theory could arrive at a different final specification.This best-selling textbook addresses the need for an introduction to econometrics specifically written for finance students. It includes examples and case studies which finance students will recognise and relate to. This new edition builds on the successful data- and problem-driven approach of the first edition, giving students the skills to estimate and interpret models while developing an intuitive grasp of underlying theoretical concepts. Key features: ● Thoroughly revised and updated, including two new chapters on ● Steps involved in formulating an econometric model Although there are of course many different ways to go about the process of model building, a logical and valid approach would be to follow the steps described in figure 1.1. The steps involved in the model construction process are now listed and described. Further details on each stage are given in subsequent chapters of this book. ● Step 1a and 1b: general statement of the problem