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The Elements of Financial Econometrics(计量金融精要)


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The Elements of Financial Econometrics(计量金融精要)
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目录

  • Preface to Mathematics Monograph Series
    Preface
    Chapter1 Asset Returns1
    1.1 Returns1
    1.1.1 One-period simple returns and gross returns1
    1.1.2 Multiperiod returns2
    1.1.3 Log returns and continuously compounding2
    1.1.4 Adjustment for dividends4
    1.1.5 Bond yields and prices5
    1.1.6 Excess returns6
    1.2 Behavior ofˉnancial return data7
    1.2.1 Stylized features ofˉnancial returns12
    1.3 E±cient markets hypothesis and statistical models for returns16
    1.4 Tests related to e±cient markets hypothesis20
    1.4.1 Tests for white noise20
    1.4.2 Remarks on the Ljung-Box test22
    1.4.3 Tests for random walks23
    1.4.4 Ljung-Box test and Dickey-Fuller test26
    1.5 Appendix: Q-Q plot and Jarque-Bera test26
    1.5.1 Q-Q plot26
    1.5.2 Jarque-Bera test27
    1.6 Further reading and software implementation28
    1.7 Exercises29
    Chapter2 Linear Time Series Models31
    2.1 Stationarity31
    2.2 Stationary ARMA models33
    2.2.1 Moving average processes34
    2.2.2 Autoregressive processes38
    2.2.3 Autoregressive and moving average processes45
    2.3 Nonstationary and long memory ARMA processes50
    2.3.1 Random walks50
    2.3.2 ARIMA model and exponential smoothing52
    2.3.3 FARIMA model and long memory processes53
    2.3.4 Summary of time series models54
    2.4 Model selection using ACF, PACF and EACF55
    2.5 Fitting ARMA models: MLE and LSE59
    2.5.1 Least squares estimation59
    2.5.2 Gaussian maximum likelihood estimation61
    2.5.3 Illustration with gold prices63
    2.5.4 A snapshot of maximum likelihood methods67
    2.6 Model diagnostics: residual analysis69
    2.6.1 Residual plots69
    2.6.2 Goodness-of-ˉt tests for residuals72
    2.7 Model identiˉcation based on information criteria73
    2.8 Stochastic and deterministic trends75
    2.8.1 Trend removal76
    2.8.2 Augmented Dickey-Fuller test77
    2.8.3 An illustration79
    2.8.4 Seasonality82
    2.9 Forecasting84
    2.9.1 Forecasting ARMA processes84
    2.9.2 Forecasting trends and momentum ofˉnancial markets89
    2.10 Appendix: Time series analysis in R97
    2.10.1 Start up with R97
    2.10.2 R-functions for time series analysis98
    2.10.3 TSA{ an add-on package99
    2.11 Exercises100
    Chapter3 Heteroscedastic Volatility Models104
    3.1 ARCH and GARCH models105
    3.1.1 ARCH models105
    3.1.2 GARCH models110
    3.1.3 Stationarity of GARCH models113
    3.1.4 Fourth moments115
    3.1.5 Forecasting volatility118
    3.2 Estimation for GARCH models120
    3.2.1 Conditional maximum likelihood estimation120
    3.2.2 Model diagnostics122
    3.2.3 Applications of GARCH modeling124
    3.2.4 Asymptotic properties131
    3.2.5 Least absolute deviations estimation132
    3.3 ARMA-GARCH models136
    3.4 Extended GARCH models137
    3.4.1 EGARCH models138
    3.4.2 Asymmetric power GARCH143
    3.4.3 Excess returns and GARCH-in-Mean146
    3.4.4 Integrated GARCH model147
    3.5 Stochastic volatility models148
    3.5.1 Probabilistic properties149
    3.5.2 Parameter estimation149
    3.5.3 Leverage e？ects152
    3.6 Appendix: State space models153
    3.6.1 Linear models153
    3.6.2 Kalman recursions for Gaussian models153
    3.6.3 Nonlinear models156
    3.6.4 Particleˉlters158
    3.7 Exercises160
    Chapter4 Multivariate Time Series Analysis163
    4.1 Stationarity and auto-correlation matrices163
    4.1.1 Stationary vector processes163
    4.1.2 Sample cross-covariance/correlation matrices165
    4.2 Vector autoregressive models168
    4.2.1 Stationarity169
    4.2.2 Parameter estimation170
    4.2.3 Model selection and diagnostics173
    4.2.4 Illustration with real data175
    4.2.5 Granger causality179
    4.2.6 Impulse response functions182
    4.3 Cointegration185
    4.3.1 Unit roots and cointegration186
    4.3.2 Engle-Granger method and error correction models187
    4.3.3 Johansen's likelihood method191
    4.3.4 Illustration with real data195
    4.4 Exercises199
    Chapter5 E±cient Portfolios and Capital Asset Pricing Model201
    5.1 E±cient portfolios201
    5.1.1 Returns and risks of portfolios201
    5.1.2 Portfolio optimization202
    5.1.3 E±cient portfolios and Sharpe ratios205
    5.1.4 E±cient frontiers206
    5.1.5 Challenges of implementation207
    5.2 Optimizing expected utility function208
    5.3 Capital asset pricing model210
    5.3.1 Market portolio210
    5.3.2 Capital asset pricing model212
    5.3.3 Marketˉ and its applications214
    5.4 Validating CAPM215
    5.4.1 Econometric formulation215
    5.4.2 Maximum likelihood estimation216
    5.4.3 Testing statistics218
    5.5 Empirical studies223
    5.5.1 An overview223
    5.5.2 Fama-French portfolios224
    5.5.3 Further remarks227
    5.6 Cross-sectional regression227
    5.7 Portfolio optimization without a risk-free asset228
    5.8 CAPM with unknowing risk free rate236
    5.8.1 Validating the Black version of CAPM237
    5.8.2 Testing statistics237
    5.9 Complements240
    5.9.1 Proof of(5.43)240
    5.9.2 Proof of(5.48)240
    5.10 Exercises241
    Chapter6 Factor Pricing Models245
    6.1 Multifactor pricing models245
    6.1.1 Multifactor models245
    6.1.2 Factor pricing models249
    6.2 Applications of multifactor models250
    6.3 Model validation with tradable factors251
    6.3.1 Existence of a risk-free asset252
    6.3.2 Estimation of risk premia252
    6.3.3 Testing statistics253
    6.3.4 An empirical study using Fama-French portfolios256
    6.3.5 Absence of a risk-free asset258
    6.4 Macroeconomic variables as factors260
    6.5 Selection of factors261
    6.5.1 Principal component analysis262
    6.5.2 Factor analysis267
    6.6 Exercises269
    Chapter7 Portfolio Allocation and Risk Assessment272
    7.1 Risk assessment of large portfolios272
    7.1.1 Stability of a portfolio273
    7.1.2 Stability and risk approximations274
    7.1.3 Errors in risk assessments279
    7.1.4 Representative portfolios with a given exposure281
    7.2 Estimation of a large volatility matrix282
    7.2.1 Exponential smoothing282
    7.2.2 Regularization by thresholding284
    7.2.3 Projections onto semi-positive and positive deˉnite matrix spaces287
    7.2.4 Regularization by penalized likelihood288
    7.2.5 Factor model with observable factors291
    7.2.6 Approximate factor models with observable factors295
    7.2.7 Approximate factor models with unobservable factors298
    7.3 Portfolio allocation with gross-exposure constraints301
    7.3.1 Portfolio selection with gross-exposure constraint302
    7.3.2 Relation with covariance regularization305
    7.4 Portfolio selection and tracking306
    7.4.1 Relation with regression306
    7.4.2 Portfolio selection and tracking307
    7.5 Empirical applications308
    7.5.1 Fama-French100 portfolios309
    7.5.2 Russell3000 stocks311
    7.6 Complements312
    7.6.1 Proof of Theorem7.2312
    7.6.2 Proof of Theorem7.3313
    7.6.3 Proof of(7.48)313
    7.7 Exercises314
    Chapter8 Consumption based CAPM316
    8.1 Utility optimization316
    8.2 Consumption-based CAPM319
    8.2.1 CCAPM319
    8.2.2 Power utility321
    8.3 Mean-variance frontier325
    8.4 Exercises327
    Chapter9 Present-value Models328
    9.1 Fundamental price328
    9.2 Rational bubbles330
    9.3 Time-varying expected returns332
    9.4 Empirical evidence336
    9.5 Linear regression under dependence344
    9.6 Exercises346
    References348
    Author Index358
    Subject Index362
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