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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 of?nancial return data7
1.2.1 Stylized features of?nancial 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-?t tests for residuals72
2.7 Model identi?cation 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 of?nancial 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 Particle?lters158
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 Market? 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(5.4 3)240
5.9.2 Proof of(5.4 8)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
6.5 Selection of factors
6.5.1 Principal component analysis
6.5.2 Factor analysis
6.6 Exercises
Chapter 7 Portfolio Allocation and Risk Assessment
7.1 Risk assessment of large portfolios
7.1.1 Stability of a portfolio
7.1.2 Stability and risk approximations
7.1.3 Errors in risk assessments
7.1.4 Representative portfolios with a given exposure
7.2 Estimation of a large volatility matrix
7.2.1 Exponential smoothing
7.2.2 Regularization by thresholding
7.2.3 Projections onto semi-positive and positive definite matrix spaces
7.2.4 Regularization by penalized likelihood
7.2.5 Factor model with observable factors
7.2.6 Approximate factor models with observable factors
7.2.7 Approximate factor models with unobservable factors
7.3 Portfolio allocation with gross-exposure constraints
7.3.1 Portfolio selection with gross-exposure constraint
7.3.2 Relation with covariance regularization
7.4 Portfolio selection and tracking
7.4.1 Relation with regression
7.4.2 Portfolio selection and tracking
7.5 Empirical applications
7.5.1 Fama-French 100 portfolios
7.5.2 Russell 3000 stocks
7.6 Complements
7.6.1 Proof of Theorem 7.2
7.6.2 Proof of Theorem 7.3
7.6.3 Proof of (7.4 8)
7.7 Exercises
Chapter 8 Consumption based CAPM
8.1 Utility optimization
8.2 Consumption-based CAPM
8.2.1 CCAPM
8.2.2 Power utility
8.3 Mean-variance frontier*.
8.4 Exercises
Chapter 9 Present-value Models
9.1 Fundamental price
9.2 Rational bubbles
9.3 Time-varying expected returns
9.4 Empirical evidence
9.5 Linear regression under dependence
9.6 Exercises
References
Author Index
Subject Index
 

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