Introductory Econometrics for Finance

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Problems that could be tackled using time series data: ● How the value of a country’s stock index has varied with that country’s macroeconomic fundamentals ● How the value of a company’s stock price has varied when it announced the value of its dividend payment ● The effect on a country’s exchange rate of an increase in its trade deficit. 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 Estimating exponential smoothing models Estimating the inflation equation Estimating the rsandp equation VAR inputs screen Constructing the VAR impulse responses Combined impulse response graphs Variance decomposition graphs Options menu for unit root tests Actual, Fitted and Residual plot to check for stationarity Johansen cointegration test VAR specification for Johansen tests Estimating a GARCH-type model GARCH model estimation options Forecasting from GARCH models Dynamic forecasts of the conditional variance Static forecasts of the conditional variance Making a system Workfile structure window ‘Equation Estimation’ window for limited dependent variables ‘Equation Estimation’ options for limited dependent variables Running an EViews program Points to consider when

Creating a workfile page 15 Importing Excel data into the workfile 16 The workfile containing loaded data 17 Summary statistics for a series 19 A line graph 20 Summary statistics for spot and futures 41 Equation estimation window 42 Estimation results 43 Plot of two series 79 Stepwise procedure equation estimation window 103 Conducting PCA in EViews 126 Regression options window 139 Non-normality test results 164 Regression residuals, actual values and fitted series 168 Chow test for parameter stability 188 Plotting recursive coefficient estimates 190 CUSUM test graph 191 Estimating the correlogram 235 Plot and summary statistics for the dynamic forecasts for the percentage changes in house prices using an AR(2) 257 Plot and summary statistics for the static forecasts for the percentage changes in house prices using an AR(2) 258 This is a good book introducing the general field of financial econometrics to students, assuming they have no prior knowledge of econometrics. Undergraduate, as well as beginning graduate, students should find the wide range of topics covered useful for not only getting a good toehold into the literature, but also to be able to apply the methods to data right away.' Prasad V. Bidarkota, Florida International University 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

Box 1.2 Time series data Series Industrial production Government budget deficit Money supply The value of a stock Professor Brooks’ book provides extraordinarily comprehensive treatment of econometric techniques with application to Finance. The unique feature of this book is the presentation of rich real-world case study examples. This is an ideal text book for MS in Finance, MBA with concentration in Finance and Seniors majoring in Finance. It is also an ideal text book for financial professional training and self-study.' Tests of competition in banking with fixed effects panel models 10.3 Results of random effects panel regression for credit stability of Central and East European banks 11.1 Logit estimation of the probability of external financing 11.2 Multinomial logit estimation of the type of external financing 11.3 Ordered probit model results for the determinants of credit ratings 11.4 Two-step ordered probit model allowing for selectivity bias in the determinants of credit ratings 11.5 Marginal effects for logit and probit models for probability of MSc failure 12.1 EGARCH estimates for currency futures returns 12.2 Autoregressive volatility estimates for currency futures returns 12.3 Minimum capital risk requirements for currency futures as a percentage of the initial value of the position 13.1 Journals in finance and econometrics 13.2 Useful internet sites for financial literature 13.3 Suggested structure for a typical dissertation or project

Continuous and discrete data As well as classifying data as being of the time series or cross-sectional type, we could also distinguish it as being either continuous or discrete, exactly as their labels would suggest. Continuous data can take on any value and are not confined to take specific numbers; their values are limited only by precision. For example, the rental yield on a property could be 6.2%, 6.24% or 6.238%, and so on. On the other hand, discrete data can only take on certain values, which are usually integers1 (whole numbers), and are often defined to be count numbers. For instance, the number of people in a particular underground carriage or the number of shares traded during a day. In these cases, having 86.3 passengers in the carriage or 58571/2 shares traded would not make sense. 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.Pre-requisites for good understanding of this material In order to make the book as accessible as possible, the only background recommended in terms of quantitative techniques is that readers have introductory knowledge of calculus, algebra (including matrices) and basic statistics. However, even these are not necessarily prerequisites since they are covered briefly in an appendix to the text. The emphasis throughout the book is on a valid application of the techniques to real data and problems in finance. In the finance and investment area, it is assumed that the reader has knowledge of the fundamentals of corporate finance, financial markets and investment. Therefore, subjects such as portfolio theory, the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT), the efficient markets hypothesis, the pricing of derivative securities and the term structure of interest rates, which are frequently referred to throughout the book, are not treated in this text. There are very many good books available in corporate finance, in investments, and in futures and options, including those by Brealey and Myers (2005), Bodie, Kane and Marcus (2008) and Hull (2005) respectively. Chris Brooks, October 2007

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 Box 1.3 Log returns (1) Log-returns have the nice property that they can be interpreted as continuously compounded returns – so that the frequency of compounding of the return does not matter and thus returns across assets can more easily be compared. (2) Continuously compounded returns are time-additive. For example, suppose that a weekly returns series is required and daily log returns have been calculated for five days, numbered 1 to 5, representing the returns on Monday through Friday. It is valid to simply add up the five daily returns to obtain the return for the whole week: Monday return Tuesday return Wednesday return Thursday return Friday return Return over the week Appendix 1 A review of some fundamental mathematical and statistical concepts A1 Introduction A2 Characteristics of probability distributions A3 Properties of logarithms A4 Differential calculus A5 Matrices A6 The eigenvalues of a matrix Types of data There are broadly three types of data that can be employed in quantitative analysis of financial problems: time series data, cross-sectional data, and panel data. This excellent book provides practical econometric solutions for empirical finance. It is an ideal textbook for introductory courses on financial econometrics …'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.'

Conducting empirical research or doing a project or dissertation in finance 13.1 What is an empirical research project and what is it for? 13.2 Selecting the topic 13.3 Sponsored or independent research? 13.4 The research proposal 13.5 Working papers and literature on the internet 13.6 Getting the data there is an ever greater need for a textbook like this that applies relevant econometric topics to the field of finance. The book explains difficult concepts in a clear and easily understandable way, with plenty of real-world practical illustrations. A particularly welcome feature, and extremely helpful to students, is the use of examples with computer printouts on how to estimate models using the Eviews software. I highly recommend it.' This is a good book introducing the general field of financial econometrics to students, assuming they have no prior knowledge of econometrics. Undergraduate, as well as beginning graduate, students should find the wide range of topics covered useful for not only getting a good toehold into the literature, but also to be able to apply the methods to data right away.' What is econometrics? The literal meaning of the word econometrics is ‘measurement in economics’. The first four letters of the word suggest correctly that the origins of econometrics are rooted in economics. However, the main techniques employed for studying economic problems are of equal importance in financial applications. As the term is used in this book, financial econometrics will be defined as the application of statistical techniques to problems in finance. Financial econometrics can be useful for testing theories in finance, determining asset prices or returns, testing hypotheses concerning the relationships between variables, examining the effect on financial markets of changes in economic conditions, forecasting future values of financial variables and for financial decision-making. A list of possible examples of where econometrics may be useful is given in box 1.1. 1 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

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