# Introductory Econometrics

A brief overview of the classical linear regression model What is a regression model? Regression versus correlation Simple regression Some further terminology Simple linear regression in EViews — estimation of an optimal hedge ratio The assumptions underlying the classical linear regression model Properties of the OLS estimator Precision and standard errors An introduction to statistical inference 27 27 28 28 37 2. 6 2. 7 2. 8 2. 9 v 40 43 44 46 51 vi Contents 2. 10 A special type of hypothesis test: the t-ratio 2. 11 An example of the use of a simple t-test to test a theory in ? nance: can US mutual funds beat the market? . 12 Can UK unit trust managers beat the market? 2. 13 The overreaction hypothesis and the UK stock market 2. 14 The exact signi? cance level 2. 15 Hypothesis testing in EViews — example 1: hedging revisited 2. 16 Estimation and hypothesis testing in EViews — example 2: the CAPM Appendix: Mathematical derivations of CLRM results 65 67 69 71 74 75 77 81 3 Further development and analysis of the classical linear regression model 3. 1 Generalising the simple model to multiple linear regression 3. 2 The constant term 3. 3 How are the parameters (the elements of the ? vector) calculated in the generalised case? 3. Testing multiple hypotheses: the F -test 3. 5 Sample EViews output for multiple hypothesis tests 3. 6 Multiple regression in EViews using an APT-style model 3. 7 Data mining and the true size of the test 3. 8 Goodness of ? t statistics 3. 9 Hedonic pricing models 3. 10 Tests of non-nested hypotheses Appendix 3. 1: Mathematical derivations of CLRM results Appendix 3. 2: A brief introduction to factor models and principal components analysis 120 4 Classical linear regression model assumptions and diagnostic tests 4. 1 Introduction 4. 2 Statistical distributions for diagnostic tests 4. 3 Assumption 1: E (u t ) = 0 4. Assumption 2: var(u t ) = ? 2 < ? 4. 5 Assumption 3: cov(u i , u j ) = 0 for i = j 4. 6 Assumption 4: the xt are non-stochastic 4. 7 Assumption 5: the disturbances are normally distributed 4. 8 Multicollinearity 4. 9 Adopting the wrong functional form 4. 10 Omission of an important variable 4. 11 Inclusion of an irrelevant variable 129 129 130 131 132 139 160 161 170 174 178 179 88 88 89 91 93 99 99 105 106 112 115 117 Contents vii 4. 12 Parameter stability tests 4. 13 A strategy for constructing econometric models and a discussion of model-building philosophies 4. 14 Determinants of sovereign credit ratings 191 94 5 5. 1 5. 2 5. 3 5. 4 5. 5 5. 6 5. 7 5. 8 5. 9 5. 10 5. 11 5. 12 5. 13 Univariate time series modelling and forecasting Introduction Some notation and concepts Moving average processes Autoregressive processes The partial autocorrelation function ARMA processes Building ARMA models: the Box–Jenkins approach Constructing ARMA models in EViews Examples of time series modelling in ? nance Exponential smoothing Forecasting in econometrics Forecasting using ARMA models in EViews Estimating exponential smoothing models using EViews 206 206 207 211 215 222 223 230 234 239 241 243 256 258 Multivariate models Motivations

Simultaneous equations bias So how can simultaneous equations models be validly estimated? Can the original coef? cients be retrieved from the ? s ? Simultaneous equations in ? nance A de? nition of exogeneity Triangular systems Estimation procedures for simultaneous equations systems An application of a simultaneous equations approach to modelling bid–ask spreads and trading activity Simultaneous equations modelling using EViews Vector autoregressive models Does the VAR include contemporaneous terms? Block signi? cance and causality tests VARs with exogenous variables Impulse responses and variance decompositions

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VAR model example: the interaction between property returns and the macroeconomy VAR estimation in EViews 265 265 268 269 269 272 273 275 276 6 6. 1 6. 2 6. 3 6. 4 6. 5 6. 6 6. 7 6. 8 6. 9 6. 10 6. 11 6. 12 6. 13 6. 14 6. 15 6. 16 6. 17 180 279 285 290 295 297 298 298 302 308 Contents viii 7 7. 1 7. 2 7. 3 7. 4 7. 5 7. 6 7. 7 7. 8 7. 9 7. 10 7. 11 7. 12 8 8. 1 8. 2 8. 3 8. 4 8. 5 8. 6 8. 7 8. 8 8. 9 8. 10 8. 11 8. 12 8. 13 8. 14 8. 15 8. 16 8. 17 8. 18 Modelling long-run relationships in ? nance Stationarity and unit root testing Testing for unit roots in EViews Cointegration Equilibrium correction or error correction models

Testing for cointegration in regression: a residuals-based approach Methods of parameter estimation in cointegrated systems Lead–lag and long-term relationships between spot and futures markets Testing for and estimating cointegrating systems using the Johansen technique based on VARs Purchasing power parity Cointegration between international bond markets Testing the expectations hypothesis of the term structure of interest rates Testing for cointegration and modelling cointegrated systems using EViews Modelling volatility and correlation Motivations: an excursion into non-linearity land Models for volatility Historical volatility

Implied volatility models Exponentially weighted moving average models Autoregressive volatility models Autoregressive conditionally heteroscedastic (ARCH) models Generalised ARCH (GARCH) models Estimation of ARCH/GARCH models Extensions to the basic GARCH model Asymmetric GARCH models The GJR model The EGARCH model GJR and EGARCH in EViews Tests for asymmetries in volatility GARCH-in-mean Uses of GARCH-type models including volatility forecasting Testing non-linear restrictions or testing hypotheses about non-linear models 8. 19 Volatility forecasting: some examples and results from the literature 8. 20 Stochastic volatility models revisited 18 318 331 335 337 339 341 343 350 355 357 362 365 379 379 383 383 384 384 385 386 392 394 404 404 405 406 406 408 409 411 417 420 427 Contents 8. 21 8. 22 8. 23 8. 24 8. 25 8. 26 8. 27 ix Forecasting covariances and correlations Covariance modelling and forecasting in ? nance: some examples Historical covariance and correlation Implied covariance models Exponentially weighted moving average model for covariances Multivariate GARCH models A multivariate GARCH model for the CAPM with time-varying covariances 8. 28 Estimating a time-varying hedge ratio for FTSE stock index returns 8. 29 Estimating multivariate GARCH models using EViews

Appendix: Parameter estimation using maximum likelihood 428 429 431 431 432 432 9 Switching models 9. 1 Motivations 9. 2 Seasonalities in ? nancial markets: introduction and literature review 9. 3 Modelling seasonality in ? nancial data 9. 4 Estimating simple piecewise linear functions 9. 5 Markov switching models 9. 6 A Markov switching model for the real exchange rate 9. 7 A Markov switching model for the gilt–equity yield ratio 9. 8 Threshold autoregressive models 9. 9 Estimation of threshold autoregressive models 9. 10 Speci? cation tests in the context of Markov switching and threshold autoregressive models: a cautionary note . 11 A SETAR model for the French franc–German mark exchange rate 9. 12 Threshold models and the dynamics of the FTSE 100 index and index futures markets 9. 13 A note on regime switching models and forecasting accuracy 451 451 10 10. 1 10. 2 10. 3 10. 4 10. 5 10. 6 10. 7 Panel data Introduction — what are panel techniques and why are they used? What panel techniques are available? The ? xed effects model Time-? xed effects models Investigating banking competition using a ? xed effects model The random effects model Panel data application to credit stability of banks in Central and Eastern Europe 10. Panel data with EViews 10. 9 Further reading 436 437 441 444 454 455 462 464 466 469 473 474 476 477 480 484 487 487 489 490 493 494 498 499 502 509 Contents x 11 11. 1 11. 2 11. 3 11. 4 11. 5 11. 6 11. 7 11. 8 11. 9 11. 10 11. 11 11. 12 11. 13 11. 14 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 ? t measures for linear dependent variable models Multinomial linear dependent variables

The pecking order hypothesis revisited — the choice between ? nancing 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 12 12. 1 12. 2 12. 3 12. 4 12. 5 12. 6 511 511 512 514 515 517 518 518 519 521 525 527 528 533 537 544 Simulation methods Motivations Monte Carlo simulations Variance reduction techniques Bootstrapping Random number generation Disadvantages of the simulation approach to econometric or nancial problem solving 12. 7 An example of Monte Carlo simulation in econometrics: deriving a set of critical values for a Dickey–Fuller test 12. 8 An example of how to simulate the price of a ? nancial option 12. 9 An example of bootstrapping to calculate capital risk requirements 546 546 547 549 553 557 559 565 571 13 Conducting empirical research or doing a project or dissertation in ? nance 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 85 585 586 590 590 591 591 558 Contents xi 13. 7 Choice of computer software 13. 8 How might the ? nished project look? 13. 9 Presentational issues 593 593 597 14 Recent and future developments in the modelling of ? nancial time series 14. 1 Summary of the book 14. 2 What was not covered in the book 14. 3 Financial econometrics: the future? 14. 4 The ? nal word 598 598 598 602 606 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 607 607 607 08 609 611 614 Appendix 2 Tables of statistical distributions 616 Appendix 3 Sources of data used in this book 628 References Index 629 641 Figures 1. 1 2. 1 2. 2 2. 3 2. 4 2. 5 2. 6 2. 7 2. 8 2. 9 2. 10 2. 11 2. 12 2. 13 2. 14 2. 15 2. 16 Steps involved in forming an econometric model page 9 Scatter plot of two variables, y and x 29 Scatter plot of two variables with a line of best ? t chosen by eye 31 Method of OLS ? tting a line to the data by minimising the sum of squared residuals 32 Plot of a single observation, together with the line of best ? t, the residual and the ? tted value 32 Scatter plot of excess returns on fund

XXX versus excess returns on the market portfolio 35 No observations close to the y-axis 36 Effect on the standard errors of the ? coef? cient estimates when (xt ? x ) are narrowly dispersed 48 Effect on the standard errors of the ? coef? cient estimates when (xt ? x ) are widely dispersed 49 Effect on the standard errors of xt2 large 49 Effect on the standard errors of xt2 small 50 The normal distribution 54 The t-distribution versus the normal 55 Rejection regions for a two-sided 5% hypothesis test 57 Rejection regions for a one-sided hypothesis test of the form H0 : ? = ? ? , H1 : ? < ? ? 57 Rejection regions for a one-sided ypothesis test of the form H0 : ? = ? ? , H1 : ? > ? ? 57 Critical values and rejection regions for a t20;5% 61 xii 2. 17 Frequency distribution of t-ratios of mutual fund alphas (gross of transactions costs) Source: Jensen (1968). Reprinted with the permission of Blackwell Publishers 2. 18 Frequency distribution of t-ratios of mutual fund alphas (net of transactions costs) Source: Jensen (1968). Reprinted with the permission of Blackwell Publishers 2. 19 Performance of UK unit trusts, 1979–2000 3. 1 R 2 = 0 demonstrated by a ? at estimated line, i. e. a zero slope coef? cient 3. 2 R 2 = 1 when all data points lie exactly n the estimated line 4. 1 Effect of no intercept on a regression line 4. 2 Graphical illustration of heteroscedasticity ? ? 4. 3 Plot of u t against u t ? 1 , showing positive autocorrelation ? 4. 4 Plot of u t over time, showing positive autocorrelation ? ? 4. 5 Plot of u t against u t ? 1 , showing negative autocorrelation ? 4. 6 Plot of u t over time, showing negative autocorrelation ? ? 4. 7 Plot of u t against u t ? 1 , showing no autocorrelation ? 4. 8 Plot of u t over time, showing no autocorrelation 4. 9 Rejection and non-rejection regions for DW test 68 68 70 109 109 131 132 141 142 142 143 143 144 147 List of figures . 10 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 utocorrelation functions for a slowly decaying AR(1) model: yt = 0. 9 yt ? 1 + u t 5. 5 Sample autocorrelation and partial autocorrelation functions for a more rapidly decaying AR(1) model: yt = 0. 5 yt ? 1 + u t 5. 6 Sample autocorrelation and partial autocorrelation functions for a more rapidly decaying AR(1) model with negative coef? cient: yt = ? 0. 5 yt ? 1 + u t 5. 7 Sample autocorrelation and partial autocorrelation functions for a non-stationary model (i. e. a unit coef? cient): yt = yt ? 1 + u t 5. 8 Sample autocorrelation and partial autocorrelation functions for an ARMA(1, 1) model: yt = 0. 5 yt ? + 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 in? ation 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 xiii 162 7. 2 162 165 7. 3 7. 4 166 7. 5 185 7. 6 215 8. 1 8. 2 226 8. 3 226 8. 4 227 8. 5 227 9. 1 9. 2 228 9. 3 9. 4 228 9. 5 229 9. 6 245 307 11. 1 307 11. 2 11. 3 11. 4 319 Value of t-ratio of slope coef? cient for ,000 sets of regressions of a non-stationary variable on another independent non-stationary variable Example of a white noise process Time series plot of a random walk versus a random walk with drift Time series plot of a deterministic trend process Autoregressive processes with differing values of ? (0, 0. 8, 1) Daily S&P returns for January 1990–December 1999 The problem of local optima in maximum likelihood estimation News impact curves for S&P500 returns using coef? cients implied from GARCH and GJR model estimates Three approaches to hypothesis testing under maximum likelihood Source: Brooks, Henry and Persand 2002). Time-varying hedge ratios derived from symmetric and asymmetric BEKK models for FTSE returns. Sample time series plot illustrating a regime shift Use of intercept dummy variables for quarterly data Use of slope dummy variables Piecewise linear model with threshold x? Source: Brooks and Persand (2001b). Unconditional distribution of US GEYR together with a normal distribution with the same mean and variance Source: Brooks and Persand (2001b). Value of GEYR and probability that it is in the High GEYR regime for the UK The fatal ? aw of the linear probability model The logit model Modelling charitable donations as a unction of income Fitted values from the failure probit regression 320 324 324 325 325 387 397 410 418 440 452 456 459 463 470 471 513 515 534 542 Tables 1. 1 Econometric software packages for modelling ? nancial data page 12 2. 1 Sample data on fund XXX to motivate OLS estimation 34 2. 2 Critical values from the standard normal versus t-distribution 55 2. 3 Classifying hypothesis testing errors and correct conclusions 64 2. 4 Summary statistics for the estimated regression results for (2. 52) 67 2. 5 Summary statistics for unit trust returns, January 1979–May 2000 69 2. 6 CAPM regression results for unit trust eturns, January 1979–May 2000 70 2. 7 Is there an overreaction effect in the UK stock market? 73 2. 8 Part of the EViews regression output revisited 75 3. 1 Hedonic model of rental values in Quebec City, 1990. Dependent variable: Canadian dollars per month 114 3A. 1 Principal component ordered eigenvalues for Dutch interest rates, 1962–1970 123 3A. 2 Factor loadings of the ? rst and second principal components for Dutch interest rates, 1962–1970 123 4. 1 Constructing a series of lagged values and ? rst differences 140 4. 2 Determinants and impacts of sovereign credit ratings 197 4. 3 Do ratings add to public information? 99 4. 4 What determines reactions to ratings announcements? 201 xiv 5. 1 5. 2 6. 1 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 signi? cance 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 quation 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 pro? tability 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 241 252 283 283 297 305 306 328 344 345 346 346 348 356 357 358 359 360

List of tables 7. 12 Impulse responses for VAR of international bond yields 7. 13 Tests of the expectations hypothesis using the US zero coupon yield curve with monthly data 8. 1 GARCH versus implied volatility 8. 2 EGARCH versus implied volatility 8. 3 Out-of-sample predictive power for weekly volatility forecasts 8. 4 Comparisons of the relative information content of out-of-sample volatility forecasts 8. 5 Hedging effectiveness: summary statistics for portfolio returns 9. 1 Values and signi? cances of days of the week coef? cients 9. 2 Day-of-the-week effects with the inclusion of interactive dummy variables with the risk proxy . 3 Estimates of the Markov switching model for real exchange rates 9. 4 Estimated parameters for the Markov switching models 9. 5 SETAR model for FRF–DEM 9. 6 FRF–DEM forecast accuracies 9. 7 Linear AR(3) model for the basis 9. 8 A two-threshold SETAR model for the basis 10. 1 Tests of banking market equilibrium with ? xed effects panel models xv 361 364 423 423 426 426 439 458 461 468 470 478 479 482 483 496 10. 2 Tests of competition in banking with ?xed 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 xternal ? nancing 11. 2 Multinomial logit estimation of the type of external ? nancing 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 ? nance and econometrics 13. Useful internet sites for ? nancial literature 13. 3 Suggested structure for a typical dissertation or project 497 503 517 527 531 532 543 574 575 578 589 592 594 Boxes 1. 1 1. 2 1. 3 1. 4 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 x s 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 signi? cance 56 2. 6 Carrying out a hypothesis test using on? dence intervals 60 2. 7 The test of signi? cance and con? dence 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 xvi 4. 6 4. 7 5. 1 5. 2 5. 3 6. 1 6. 2 6. 3 7. 1 7. 2 8. 1 . 2 8. 3 9. 1 10. 1 11. 1 11. 2 12. 1 12. 2 12. 3 12. 4 12. 5 12. 6 Observations for the dummy variable Conducting a Chow test The stationarity condition for an AR( p ) model The invertibility condition for an MA(2) model Naive forecasting methods Determining whether an equation is identi? ed Conducting a Hausman test for exogeneity Forecasting with VARs Stationarity tests Multiple cointegrating relationships Testing for ‘ARCH effects’ Estimating an ARCH or GARCH model Using maximum likelihood estimation in practice How do dummy variables work? Fixed or random effects? Parameter interpretation for probit and logit models

The differences between censored and truncated dependent variables Conducting a Monte Carlo simulation Re-sampling the data Re-sampling from the residuals Setting up a Monte Carlo simulation Simulating the price of an Asian option Generating draws from a GARCH process 165 180 216 224 247 270 274 299 331 340 390 395 398 456 500 519 535 548 555 556 560 565 566 Screenshots 1. 1 1. 2 1. 3 1. 4 1. 5 2. 1 2. 2 2. 3 2. 4 3. 1 3. 2 4. 1 4. 2 4. 3 4. 4 4. 5 4. 6 5. 1 5. 2 5. 3 Creating a work? le page 15 Importing Excel data into the work? le 16 The work? le 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 ?tted series 168 Chow test for parameter stability 188 Plotting recursive coef? cient 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 hanges in house prices using an AR(2) 258 xvii 5. 4 6. 1 6. 2 6. 3 6. 4 6. 5 6. 6 7. 1 7. 2 7. 3 7. 4 8. 1 8. 2 8. 3 8. 4 8. 5 8. 6 10. 1 11. 1 11. 2 12. 1 Estimating exponential smoothing models Estimating the in? ation 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 speci? cation 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 Work? le structure window ‘Equation Estimation’ window for limited dependent variables ‘Equation Estimation’ options for limited dependent variables Running an EViews program 259 288 289 310 313 314 315 332 366 368 374 400 401 415 415 416 441 505 539 541 561 Preface to the second edition Sales of the ? rst edition of this book surpassed expectations (at least those of the author). Almost all of those who have contacted the author seem to like the book, and while other textbooks have been published since that date in the broad area of ? ancial econometrics, none is really at the introductory level. All of the motivations for the ? rst edition, described below, seem just as important today. Given that the book seems to have gone down well with readers, I have left the style largely unaltered and made small changes to the structure, described below. The main motivations for writing the ? rst edition of the book were: ? To write a book that focused on using and applying the techniques rather than deriving proofs and learning formulae ? To write an accessible textbook that required no prior knowledge of ? ? ? ? conometrics, but which also covered more recently developed approaches usually found only in more advanced texts To use examples and terminology from ? nance rather than economics since there are many introductory texts in econometrics aimed at students of economics but none for students of ? nance To litter the book with case studies of the use of econometrics in practice taken from the academic ? nance literature To include sample instructions, screen dumps and computer output from two popular econometrics packages. This enabled readers to see how the techniques can be implemented in practice

To develop a companion web site containing answers to end-of-chapter questions, PowerPoint slides and other supporting materials. xix xx Preface Why I thought a second edition was needed The second edition includes a number of important new features. (1) It could have reasonably been argued that the ? rst edition of the book had a slight bias towards time-series methods, probably in part as a consequence of the main areas of interest of the author. This second edition redresses the balance by including two new chapters, on limited dependent variables and on panel techniques. Chapters 3 and 4 from the ? st edition, which provided the core material on linear regression, have now been expanded and reorganised into three chapters (2 to 4) in the second edition. (2) As a result of the length of time it took to write the book, to produce the ? nal product, and the time that has elapsed since then, the data and examples used in the book are already several years old. More importantly, the data used in the examples for the ? rst edition were almost all obtained from Datastream International, an organisation which expressly denied the author permission to distribute the data or to put them on a web site.

By contrast, this edition as far as possible uses fully updated datasets from freely available sources, so that readers should be able to directly replicate the examples used in the text. (3) A number of new case studies from the academic ? nance literature are employed, notably on the pecking order hypothesis of ? rm ? nancing, credit ratings, banking competition, tests of purchasing power parity, and evaluation of mutual fund manager performance. (4) The previous edition incorporated sample instructions from EViews and WinRATS.

As a result of the additional content of the new chapters, and in order to try to keep the length of the book manageable, it was decided to include only sample instructions and outputs from the EViews package in the revised version. WinRATS will continue to be supported, but in a separate handbook published by Cambridge University Press (ISBN: 9780521896955). Motivations for the ? rst edition This book had its genesis in two sets of lectures given annually by the author at the ICMA Centre (formerly ISMA Centre), University of Reading and arose partly from several years of frustration at the lack of an appropriate textbook.

In the past, ? nance was but a small sub-discipline drawn from economics and accounting, and therefore it was generally safe to Preface xxi assume that students of ? nance were well grounded in economic principles; econometrics would be taught using economic motivations and examples. However, ? nance as a subject has taken on a life of its own in recent years. Drawn in by perceptions of exciting careers and telephone-number salaries in the ? nancial markets, the number of students of ? nance has grown phenomenally, all around the world. At the same time, the diversity of educational backgrounds of students taking ? ance courses has also expanded. It is not uncommon to ? nd undergraduate students of ? nance even without advanced high-school quali? cations in mathematics or economics. Conversely, many with PhDs in physics or engineering are also attracted to study ? nance at the Masters level. Unfortunately, authors of textbooks have failed to keep pace, thus far, with the change in the nature of students. In my opinion, the currently available textbooks fall short of the requirements of this market in three main regards, which this book seeks to address: (1) Books fall into two distinct and non-overlapping categories: the introductory and the advanced.

Introductory textbooks are at the appropriate level for students with limited backgrounds in mathematics or statistics, but their focus is too narrow. They often spend too long deriving the most basic results, and treatment of important, interesting and relevant topics (such as simulations methods, VAR modelling, etc. ) is covered in only the last few pages, if at all. The more advanced textbooks, meanwhile, usually require a quantum leap in the level of mathematical ability assumed of readers, so that such books cannot be used on courses lasting only one or two semesters, or where students have differing backgrounds.

In this book, I have tried to sweep a broad brush over a large number of different econometric techniques that are relevant to the analysis of ? nancial and other data. (2) Many of the currently available textbooks with broad coverage are too theoretical in nature and students can often, after reading such a book, still have no idea of how to tackle real-world problems themselves, even if they have mastered the techniques in theory. To this end, in this book, I have tried to present examples of the use of the techniques in ? ance, together with annotated computer instructions and sample outputs for an econometrics package (EViews). This should assist students who wish to learn how to estimate models for themselves — for example, if they are required to complete a project or dissertation. Some examples have been developed especially for this book, while many others are drawn from the academic ? nance literature. In xxii Preface my opinion, this is an essential but rare feature of a textbook that should help to show students how econometrics is really applied.

It is also hoped that this approach will encourage some students to delve deeper into the literature, and will give useful pointers and stimulate ideas for research projects. It should, however, be stated at the outset that the purpose of including examples from the academic ? nance print is not to provide a comprehensive overview of the literature or to discuss all of the relevant work in those areas, but rather to illustrate the techniques. Therefore, the literature reviews may be considered deliberately de? ient, with interested readers directed to the suggested readings and the references therein. (3) With few exceptions, almost all textbooks that are aimed at the introductory level draw their motivations and examples from economics, which may be of limited interest to students of ? nance or business. To see this, try motivating regression relationships using an example such as the effect of changes in income on consumption and watch your audience, who are primarily interested in business and ? nance applications, slip away and lose interest in the ? rst ten minutes of your course.

Who should read this book? The intended audience is undergraduates or Masters/MBA students who require a broad knowledge of modern econometric techniques commonly employed in the ? nance literature. It is hoped that the book will also be useful for researchers (both academics and practitioners), who require an introduction to the statistical tools commonly employed in the area of ? nance. The book can be used for courses covering ? nancial time-series analysis or ? nancial econometrics in undergraduate or postgraduate programmes in ? nance, ? nancial economics, securities and investments.

Although the applications and motivations for model-building given in the book are drawn from ? nance, the empirical testing of theories in many other disciplines, such as management studies, business studies, real estate, economics and so on, may usefully employ econometric analysis. For this group, the book may also prove useful. Finally, while the present text is designed mainly for students at the undergraduate or Masters level, it could also provide introductory reading in ? nancial time-series modelling for ? nance doctoral programmes where students have backgrounds which do not include courses in modern econometric techniques.

Preface xxiii 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 brie? y 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 ? nance. In the ? nance and investment area, it is assumed that the reader has knowledge of the fundamentals of corporate ? ance, ? nancial markets and investment. Therefore, subjects such as portfolio theory, the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT), the ef? cient 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 ? nance, 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

Acknowledgements I am grateful to Gita Persand, Olan Henry, James Chong and Apostolos Katsaris, who assisted with various parts of the software applications for the ? rst edition. I am also grateful to Hilary Feltham for assistance with the mathematical review appendix and to Simone Varotto for useful discussions and advice concerning the EViews example used in chapter 11. I would also like to thank Simon Burke, James Chong and Con Keating for detailed and constructive comments on various drafts of the ? rst edition and Simon Burke for comments on parts of the second edition.

The ? rst and second editions additionally bene? ted from the comments, suggestions and questions of Peter Burridge, Kyongwook Choi, Thomas Eilertsen, Waleid Eldien, Andrea Gheno, Kimon Gomozias, Abid Hameed, Arty Khemlani, David McCaffrey, Tehri Jokipii, Emese Lazar, Zhao Liuyan, Dimitri Lvov, Bill McCabe, Junshi Ma, David Merchan, Victor Murinde, Thai Pham, Jean-Sebastien Pourchet, Guilherme Silva, Silvia Stanescu, Li Qui, Panagiotis Varlagas, and Meng-Feng Yen. A number of people sent useful e-mails pointing out typos or inaccuracies in the ? rst edition.

To this end, I am grateful to Merlyn Foo, Jan de Gooijer and his colleagues, Mikael Petitjean, Fred Sterbenz, and Birgit Strikholm. Useful comments and software support from QMS and Estima are gratefully acknowledged. Any remaining errors are mine alone. The publisher and author have used their best endeavours to ensure that the URLs for external web sites referred to in this book are correct and active at the time of going to press. However, the publisher and author have no responsibility for the web sites and can make no guarantee that a site will remain live or that the content is or will remain appropriate. xiv 1 Introduction This chapter sets the scene for the book by discussing in broad terms the questions of what is econometrics, and what are the ‘stylised facts’ describing ? nancial data that researchers in this area typically try to capture in their models. It also collects together a number of preliminary issues relating to the construction of econometric models in ? nance. Learning Outcomes In this chapter, you will learn how to ? Distinguish between different types of data ? Describe the steps involved in building an econometric model ? Calculate asset price returns Construct a work? le, import data and accomplish simple tasks in EViews 1. 1 What is econometrics? The literal meaning of the word econometrics is ‘measurement in economics’. The ? rst 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 ? nancial applications. As the term is used in this book, ? nancial econometrics will be de? ned as the application of statistical techniques to problems in finance.

Financial econometrics can be useful for testing theories in ? nance, determining asset prices or returns, testing hypotheses concerning the relationships between variables, examining the effect on ? nancial markets of changes in economic conditions, forecasting future values of ? nancial variables and for ? nancial decision-making. A list of possible examples of where econometrics may be useful is given in box 1. 1. 1 2 Introductory Econometrics for Finance Box 1. 1 The value of econometrics (1) Testing whether ? nancial markets are weak-form informationally ef? ient (2) Testing whether the Capital Asset Pricing Model (CAPM) or Arbitrage Pricing Theory (APT) represent superior models for the determination of returns on risky assets (3) Measuring and forecasting the volatility of bond returns (4) Explaining the determinants of bond credit ratings used by the ratings agencies (5) Modelling long-term relationships between prices and exchange rates (6) Determining the optimal hedge ratio for a spot position in oil (7) Testing technical trading rules to determine which makes the most money (8) Testing the hypothesis that earnings or dividend announcements ave no effect on stock prices (9) Testing whether spot or futures markets react more rapidly to news (10) Forecasting the correlation between the stock indices of two countries. The list in box 1. 1 is of course by no means exhaustive, but it hopefully gives some ? avour of the usefulness of econometric tools in terms of their ? nancial applicability. 1. 2 Is ? nancial econometrics different from ‘economic conometrics’? As previously stated, the tools commonly used in ? nancial 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 de? cits, or population ? gures, 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-? ve 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 dif? culties 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 ? nd that the Introduction